IST-2001-32686 BROADWAY

WP3-Study “The 60 GHz Channel and its Modelling”

Partner:

TU Dresden (TUD)

Author(s):

J. Schönthier

Work Package Leader:

Motorola S.A. (CRM)

Security: Nature:

Study

Version:

V1.0

Total number of pages:

160

Abstract:

This document presents the results of an extensive literature study and additional investigations performed within the framework of BROADWAY, and aims to give an overview about the 60 GHz radio channel, its fundamental properties and some ideas of how to model the 60 GHz radio channel for the BROADWAY simulations.

For all citations and copied or adapted figures used within this study always the reference is given. This does not imply that these elements can be republished without permission of the respective author and/or publishing house.

Keyword list: BROADWAY, 60 GHz, channel modelling, HIPERLAN/2

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Contents 1. Abbreviations and Acronyms ........................................................................................................................ 7 2. Introduction ................................................................................................................................................... 9 2.1 Preface ..................................................................................................................................................... 9 2.2 Locations and Scenarios ........................................................................................................................ 10 2.3 Reflection, Diffraction, and Scattering.................................................................................................. 11 3. Baseband Channel ....................................................................................................................................... 13 3.1 Signal Modulation ................................................................................................................................. 13 3.2 Equivalent Lowpass Impulse Response and Channel Transfer Function.............................................. 14 3.3 Linear Time-Invariant Channel ............................................................................................................. 15 3.4 Time-Invariant vs. Time-Varying Channels.......................................................................................... 16 3.5 General Signal Transmission................................................................................................................. 17 3.6 Discrete Time Impulse Response .......................................................................................................... 17 3.6.1. Infinite Resolution ......................................................................................................................... 17 3.6.2. Finite Resolution ........................................................................................................................... 18 3.6.3. Bin Model...................................................................................................................................... 19 3.6.4. Transfer Function .......................................................................................................................... 20 3.6.5. Directional Extension .................................................................................................................... 20 4. Statistical Channel Characterisation............................................................................................................ 21 4.1 Channel Autocorrelation Function ........................................................................................................ 21 4.2 Wide Sense Stationary Uncorrelated Scattering.................................................................................... 21 4.3 Angle-Dependent Profiles and Spectras ................................................................................................ 22 4.4 Power Delay Profile .............................................................................................................................. 23 4.5 Scattering Function................................................................................................................................ 23 4.6 DOPPLER Power Spectrum..................................................................................................................... 25 4.6.1. Definition of the DPS .................................................................................................................... 25 4.6.2. DOPPLER Shift ............................................................................................................................... 26 4.6.3. Mean DOPPLER Shift and nth Moment ........................................................................................... 27 4.6.4. DOPPLER Spread ............................................................................................................................ 27 4.6.4.1. The Term “DOPPLER Spread”................................................................................................. 27 4.6.4.2. RMS DOPPLER Spread............................................................................................................ 28 4.6.4.3. RMS DOPPLER Spread in Ad Hoc Networks ......................................................................... 28 4.6.5. Dense Scatterer Model (JAKES)..................................................................................................... 30 4.6.6. GAUSS Spectrum............................................................................................................................ 32 4.6.7. Uniform Spectrum ......................................................................................................................... 33 4.6.8. Values ............................................................................................................................................ 33 4.7 TOA Multipath Shape Factors............................................................................................................... 34 4.7.1. Introduction ................................................................................................................................... 34 4.7.2. Maximum Excess Delay................................................................................................................ 34 4.7.3. Mean Excess Delay and nth Moment ............................................................................................. 35 4.7.4. Fractional Energy-Delay Window................................................................................................. 35 4.7.5. Fixed Delay Window..................................................................................................................... 35 4.7.6. RMS Delay Spread ........................................................................................................................ 35 4.8 AOA/DOA Multipath Shape Factors .................................................................................................... 36 4.8.1. Introduction ................................................................................................................................... 36 4.8.2. Mean Angle ................................................................................................................................... 37 4.8.3. RMS Angular Spread .................................................................................................................... 37 4.8.4. Angular Spread .............................................................................................................................. 37 4.8.5. Angular Constriction ..................................................................................................................... 38 4.8.6. Maximum Fading Angle................................................................................................................ 38 4.8.7. Maximum AOA Direction............................................................................................................. 38 4.8.8. Example: RICE Channel Model ..................................................................................................... 38 4.9 Channel Coherence................................................................................................................................ 39 4.9.1. Coherence vs. Selectivity .............................................................................................................. 39 4.9.2. Coherence Time............................................................................................................................. 39 4.9.3. Coherence Bandwidth ................................................................................................................... 41 3/160

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4.10 Summary of Correlation Functions and Power Densities.................................................................... 44 5. Fading.......................................................................................................................................................... 45 5.1 Introduction ........................................................................................................................................... 45 5.2 Large-scale Fading and Path Loss ......................................................................................................... 47 5.2.1. Introduction ................................................................................................................................... 47 5.2.2. Free Space Path Loss Model ......................................................................................................... 48 5.2.3. Path Loss Exponent Model and Waveguide Effect ....................................................................... 50 5.2.4. Distance-dependent Power Exponent Model................................................................................. 52 5.2.5. Partition Based Path Loss Model................................................................................................... 52 5.2.6. Oxygen Absorption ....................................................................................................................... 53 5.2.7. Water Vapour Absorption ............................................................................................................. 54 5.2.8. Rain Attenuation............................................................................................................................ 55 5.2.9. Foliage and Vegetation Loss ......................................................................................................... 56 5.2.10. Penetration Loss Values .............................................................................................................. 56 5.2.11. Reflection and Scatter Loss ......................................................................................................... 58 5.2.12. Frequency Diversity .................................................................................................................... 58 5.3 Shadowing ............................................................................................................................................. 58 5.3.1. Introduction ................................................................................................................................... 58 5.3.2. Effects of Furnishing ..................................................................................................................... 59 5.3.3. Effects of Human Body Shadowing .............................................................................................. 59 5.3.4. Modelling of Shadowing ............................................................................................................... 61 5.4 Antenna Influence ................................................................................................................................. 61 5.4.1. Antenna Gain, Aperture and EIRP ................................................................................................ 61 5.4.2. Passive Repeater ............................................................................................................................ 62 5.4.3. Antenna Pattern Model.................................................................................................................. 62 5.4.4. Directivity and Alignment ............................................................................................................. 62 5.4.5. Polarisation .................................................................................................................................... 64 5.4.6. Cross-Polarisation.......................................................................................................................... 64 5.4.7. Coverage........................................................................................................................................ 64 5.5 Small-scale Fading ................................................................................................................................ 65 5.5.1. Introduction ................................................................................................................................... 65 5.5.2. Narrowband Fading Models .......................................................................................................... 67 5.5.3. Wideband Fading Models.............................................................................................................. 67 5.5.4. Probability Density Functions ....................................................................................................... 68 5.5.4.1. General ................................................................................................................................... 68 5.5.4.2. RAYLEIGH Distribution........................................................................................................... 69 5.5.4.3. RICE Distribution.................................................................................................................... 72 5.5.4.4. NAKAGAMI m-Distribution..................................................................................................... 76 5.5.4.5. WEIBULL Distribution ............................................................................................................ 77 5.5.4.6. Lognormal Distribution .......................................................................................................... 78 5.5.4.7. FRECHET Distribution ............................................................................................................. 79 5.5.4.8. Exponential Distribution......................................................................................................... 79 5.5.4.9. SUZUKI Distribution ............................................................................................................... 79 6. Measurement and Simulation Results ......................................................................................................... 80 6.1 Indoor .................................................................................................................................................... 80 6.1.1. TU DRESDEN Measurements and IMST Simulations.................................................................... 80 6.1.2. IMST MEDIAN Measurements .................................................................................................... 84 6.1.2.1. Environment ........................................................................................................................... 84 6.1.2.2. Measurement Results.............................................................................................................. 85 6.1.3. SMULDERS Measurements at TU/e ................................................................................................ 86 6.1.3.1. Environments.......................................................................................................................... 86 6.1.3.2. Antennas ................................................................................................................................. 87 6.1.3.3. Configurations ........................................................................................................................ 87 6.1.3.4. Exemplary Results.................................................................................................................. 88 6.1.4. Normalised Received Power vs. Distance ..................................................................................... 88 6.1.5. ANDERSON Indoor Measurements at VIRGINIA TECH ................................................................... 89 6.1.6. XU Indoor Measurements at VIRGINIA TECH ................................................................................ 95 4/160

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6.1.6.1. Environment and Antennas .................................................................................................... 95 6.1.6.2. Power Angle Profiles.............................................................................................................. 95 6.1.6.3. Results for TOA Statistics ...................................................................................................... 97 6.1.6.4. Results for AOA Statistics...................................................................................................... 98 6.1.7. Single Frequency Network Results ............................................................................................... 98 6.1.7.1. Virtual Cellular Network ........................................................................................................ 98 6.1.7.2. Overlapped-Spot Diversity ................................................................................................... 100 6.2 Outdoor................................................................................................................................................ 101 6.2.1. Results from Urban Streets in OSLO............................................................................................ 101 6.2.2. Influence of Street Width ............................................................................................................ 102 6.3 Results for Coherence Bandwidth ....................................................................................................... 103 6.4 Results for TOA parameters ................................................................................................................ 105 6.4.1. Indoor .......................................................................................................................................... 105 6.4.2. Outdoor........................................................................................................................................ 107 6.4.3. Conclusions ................................................................................................................................. 108 6.4.3.1. Indoor ................................................................................................................................... 108 6.4.3.2. Outdoor................................................................................................................................. 108 6.5 Results for Power Exponent, RICE Parameter and Location Variability ............................................. 109 7. Channel Models......................................................................................................................................... 111 7.1 Introduction and Classification............................................................................................................ 111 7.2 Tapped Delay-Line Model................................................................................................................... 115 7.2.1. Principle....................................................................................................................................... 115 7.2.2. HIPERLAN/2 Channel Parameters ............................................................................................. 116 7.2.3. TU DRESDEN BW200 Indoor Channel Parameters ..................................................................... 118 7.2.4. TU DRESDEN BW500 Indoor Channel Parameters ..................................................................... 119 7.2.5. VIRGINIA TECH Indoor Channel Parameters ............................................................................... 121 7.2.6. LOS and NLOS Oslo Urban Street Parameters........................................................................... 123 7.3 The SALEH-VALENZUELA Model ........................................................................................................ 127 7.3.1. The Original Multi- and Single-Cluster Model ........................................................................... 127 7.3.2. Extension for DOA-Modelling.................................................................................................... 130 7.3.3. SAMSUNG and CHALMERS Indoor Parameter Sets ...................................................................... 131 7.3.4. IMST Indoor Model Parameters.................................................................................................. 132 7.4 DELIGNON et al Statistical Model........................................................................................................ 133 7.5 SMULDERS Time-Domain Model ........................................................................................................ 136 7.5.1. Original Model ............................................................................................................................ 136 7.5.2. TU/e Indoor Channel Parameters ................................................................................................ 137 7.5.3. Modified Model........................................................................................................................... 137 7.5.4. Parameters for Urban Streets from CORREIA .............................................................................. 138 7.6 Frequency-Domain Modelling ............................................................................................................ 138 7.6.1. WITRISAL et al Frequency-Domain Model.................................................................................. 138 7.6.2. KATTENBACH Directional Modelling.......................................................................................... 140 7.7 ∆-K Model ........................................................................................................................................... 142 7.8 HANSEN Stochastic Model .................................................................................................................. 142 7.9 KUNISCH-PAMP Ultra-Wideband Channel Model............................................................................... 143 7.10 NLOS CM Construction from LOS CM ........................................................................................... 143 7.11 Single-Frequency Network Model .................................................................................................... 143 7.11.1. SFN Model Principle ................................................................................................................. 143 7.11.2. SFN Model Parameters.............................................................................................................. 147 8. References ................................................................................................................................................. 148

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Revision History Every time something is changed or added to this document, please note the modification in the following table. Date

Revision

30/05/2003

Rev. 1.0

Description First Version.

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Contributors Jens Schönthier (Technische Universität Dresden - TUD)

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1. Abbreviations and Acronyms It must be mentioned here that abbreviations, acronyms, and symbols often may vary from author to author. We tried to use the most common and concise denotations in this study as consistently as possible. 1-D 2-D 3-D 3G ADP AOA AP BB BER BRAN CCIR CDF CIR CM CTS CW DAB DAC DLC DM DOA DPS DQPSK DVB-T EM ETSI FD FES FM GTD GO HIPERLAN HL/2 HS i.i.d. I/Q IEEE IMST ISI ISM LAN LCR LMDS LNA LOS MAC MIP MLE MT NLOS NM NRP OBS OFDM PAP PDF PDP PM PSK QAM QPSK RF RMS

1-Dimensional 2-Dimensional 3-Dimensional 3rd Generation Angle-Delay Profile Angle of Arrival Access Point (also: Base Station) Baseband Bit Error Rate Broadband Radio Access Networks Comité Consultatif International des Radiocommunications Cumulative Distribution Function Channel Impulse Response, Channel Model Connection Type Selection Continuous Wave Digital Audio Broadcasting Digital-to-Analogue Converter Data Link Control Distance Model Direction of Arrival DOPPLER Power Spectrum Differential QPSK Terrestrial Digital Video Broadcasting Electro-Magnetic European Technology Standardisation Institute Frequency Domain Front-end Sub-System Frequency Modulation Geometrical Theory of Diffraction Geometrical Optics High Performance Radio Local Area Network BRAN HIPERLAN/2 HIPERSPOT independent identically distributed In-phase/Quadrature-phase Institute of Electrical and Electronics Engineers Institut für Mobil- und Satellitenfunktechnik Intersymbol Interference Industrial, Scientific, and Medical band Local Area Network Level Crossing Rate Local Multipoint Distribution Service Low Noise Amplifier Line of Sight Media Access Control Multipath Intensity Profile Maximum Likelihood Estimation Mobile Terminal (also: Mobile Station) Non Line of Sight Normalisation Method Normalised Received Power Obstructed Direct Path Orthogonal Frequency Division Multiplex Power Angle Profile Probability Density Function Power Delay Profile Power Model Phase Shift Keying Quadrature Amplitude Modulation Quaternary PSK Radio Frequency Root Mean Square

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Receiver Simplified Attenuation Model Single Frequency Network Single Input Single Output Signal to Noise Ratio Time-Division Duplex Two-Wave with Incoherent Power Time of Arrival Technische Universität DRESDEN Technical University of EINDHOVEN Transmitter Universal Mobile Telecommunications System Uniform Theory of Diffraction Virtual Cellular Network Vector Network Analyser Wireless LAN Working Package (within the BROADWAY project) Wide Sense Stationary Uncorrelated Scattering Cross-Polarisation Power Ratio Cross-polarisation Discrimination

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2. Introduction 2.1 Preface Any communication system is strongly influenced by the communication medium. In case of mobile radio communication systems, the medium is a multipath radio channel. The channel imposes constraints on the communication quality measures, affecting for example the system’s transmission rate, error probability and the distance over which the system can operate. Therefore, characterisation of the multipath radio channel is an important task during the design process of a mobile communication system. This document intends to give – after some theoretical contemplation – an overview of propagation conditions and channel models at 60 GHz, and to summarise the results in this area. The main sources of information were studies and papers published hitherto. HASHEMI wrote in [126]: In a typical indoor portable wireless system a fixed antenna (base) installed in an elevated position communicates with a number of portable radios inside the building. Due to reflection, refraction and scattering of radio waves by structures inside a building, the transmitted signal most often reaches the receiver by more than one path, resulting in a phenomenon known as multipath fading. The signal components arriving from indirect paths and the direct path (if it exists) combine and produce a distorted version of the transmitted signal. In narrow-band transmission, the multipath medium causes fluctuations in the received signal envelope and phase. In wide-band pulse transmission, on the other hand, the effect is to produce a series of delayed and attenuated pulses (echoes) for each transmitted pulse. Both analogue and digital transmissions also suffer from severe attenuations by the intervening structure. The received signal is further corrupted by other unwanted random effects: noise and co-channel interference. Multipath fading seriously degrades the performance of communication systems operating inside buildings. Unfortunately, one can do little to eliminate multipath disturbances. However, if the multipath medium is well characterised, transmitter and receiver can be designed to “match” the channel and to reduce the effect of these disturbances. Detailed characterisation of radio propagation is therefore a major requirement for successful design of indoor communication systems. However, what are the challenges in millimetre-wave propagation? XU [291] formulated: Due to the small wavelength at millimetre-wave frequencies, the propagation channel may be extremely time varying and unpredictable. At 60 GHz, the wavelength is only 5 mm, and the phase of an electromagnetic wave shifts 180 degrees for every 2.5 mm in propagation distance. Furthermore, most reflective surfaces appear rough with respect to this wavelength, and the incident wave will be scattered both in specular and non-specular directions, resulting in both coherent and incoherent field components. Compared to the small wavelength, vegetation leaves will be large random scatterers, causing attenuation, depolarisation and beam broadening. Finally, the wideband millimetre-wave channel is subject to change under different weather conditions. Atmospheric effects, such as rain, hail and media inhomogenity will cause excess attenuation, beam bending, depolarisation, and multipath propagation. These effects must be studied quantitatively for reliable system design. By quoting FLAMENT [91] we can further add: Many reasons, such as limited emitted power, high temperature noise, and high oxygen absorption, make the range of a millimetre-wave mobile system relatively low. Moreover, layers of concrete or wood reflect the electromagnetic waves. Hence, channels in indoor and large area environments show strong multipath behaviour. The high penetration loss for most materials in the 60 GHz band is both advantageous, since it almost perfectly isolates closed rooms and limits interference, and disadvantageous, since any obstacle blocks the LOS path or alternative paths and produces strong shadow fading. Finally, we want to cite CLAVIER et al [47]: A massive amount of spectral space of about 5 GHz bandwidth has been allocated worldwide for unlicensed, dense wireless local communications at 60 GHz. At this frequency, the signal is strongly attenuated and the propagation characteristics are different from microwaves since the molecules of oxygen in the atmosphere interact with the radio wave. The peak value of the absorption attenuation coefficient reaches about 15 dB/km at 60 GHz. This property, which appears to be a disadvantage for wide range radio transmission, is an advantage for indoor cellular systems. It provides an important interference reduction, simplifying the frequency planning and allowing an efficient use of the spectrum. It also leads to a weak electro-magnetical pollution. Furthermore, the millimetre wave band facilitates miniaturisation of components and antennas. 9/160

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However, although the multipath propagation causes problems in signal reception, it should be noted that it also has an advantage – the phenomenon makes the transmission possible even if there is no direct path between the transmitter and the receiver [25].1 Moreover, the mm-wave radio channel is a multipath channel, which can be modelled as rays following discrete paths, in all types of environments.

2.2 Locations and Scenarios Locations for wireless communication reflect the complex variety of rooms, buildings and places that exists in our modern world. The following list gives – without claiming for completeness – an idea of this variety: Indoor communication may take place • •

• • • • • • •

within a small or large traditional office, within a large “cubicled” office (American style office with soft partition walls) from a central access point to a mobile terminal in a cubicle and between terminals from cubicle to cubicle between adjacent rooms (e.g., with open door between them, but NLOS) in a corridor in a lecture hall in a concert hall/theatre in a factory hall within an underground car park (which is a highly reflective environment) within a subway station (crowded, partly fast moving environment)

Outdoor or semi outdoor communication may take place • • • • •

in a narrow or wide city street with low or high-rising buildings (often fast moving environment) on a place/square from building to building (e.g., across a street) in a hot spot in front of a warehouse (coverage antenna limited) in a sport arena

Of course, in most cases different antenna types (regarding their directivity) are possible, which additionally increases the variability and number of scenarios. Typically, BROADWAY access points will be equipped with low-gain omni-directional or medium-gain sectorised antennas, whereas the mobile terminals will be equipped with some kind of omni-directional antenna. For special (stationary) cases directive high-gain horn antennas are intended. DARDARI et al found in their ray-tracing investigations [63], that the most critical situations can be identified in the NLOS case and in the empty rooms. FLAMENT [91] states, that in a room the multipath situation is much worse than in the hallway because third order reflections contribute to the multipath and hence, the variations of the channel are faster. FLAMENT also investigated on a shopping mall scenario (consisting of a 20 m by 40 m large area surrounded by shops with glass windows), two stands were placed in the middle of the area. The shopping mall situation is said to be more delicate since the dynamics of a user is difficult to predict and simulate. The channel is much more dependent on the people and moving objects surrounding the users. Thus, there is a need to consider the density of people in the shopping mall as a coverage limitation factor. As we can see, one has to limit oneself to carefully selected but representative environments and/or models. As a first idea it was planned for the BROADWAY project to consider four important cases concerning the channel models at 60 GHz [33]: 1. Typical 60 GHz channel 2. Worst case indoor 3. Worst case outdoor 4. Single-Frequency-Network (SFN) channel The channel models for type 1-3 shall be mainly based on 60 GHz measurements. The SFN channel represents for example the case where several Tx/Rx antennas are distributed within a large meeting room creating artificial multipath. The corresponding channel model shall be determined by simulation [33]. The decision which of the many channel models presented in this study will be paramountly used for BROADWAY simulations is not in the focus of this study. For this purpose simulations focusing on bit error rate (BER), synchronisation performance and other aspects are necessary, which will be presented in other documents. One should keep in mind that the decision for a specific set of models might need a rethink if, e.g., the bandwidth of the system changes. Hence, it might be supposable to use different models for the two subsystems of BROADWAY at 60 GHz (see [29] [32] [33]). 1

In some cases, for example with an L-shaped room, “Passive Repeaters” or mirrors are used to improve coverage using multipath effects [12].

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2.3 Reflection, Diffraction, and Scattering In wireless communications, the (indoor and outdoor) radio channel can be described as a multipath propagation channel. Multipath is a propagation phenomenon that results in signals reaching the receiving antenna by two or more paths, creating constructive and destructive interference as well as signal echoes [14] [71] [86]. Next to Line of Sight (LOS) propagation from transmitter to receiver, the propagation of radio waves is generally described with three basic mechanisms; these are (specular and diffuse) reflection, diffraction and scattering of electromagnetic waves from various objects in the propagation environment [14] [25] [165] [228] [291]. It should be kept in mind that at 60 GHz, the wavelength is 5 millimetres, and thus any object larger than 2.5 mm must be considered as an obstacle [164]. One result of these effects is, that the impulse response profiles collected in portable sites at different locations are normally very different due to differences in the intervening (base to portable) structure, and differences in the local environment of the portables [126]. Reflection: Electromagnetic waves arriving from a certain direction at a surface with large dimensions compared to the wavelength are (partially) reflected by this surface [25] [28] [156]. The intensity of the reflected wave depends on the radio wave frequency, the type of material, the polarisation of the wave and the angle of incidence [28]. Reflection can be modelled using the Geometrical Optics (GO) [28] [278]. Following [165], specular reflection takes place when a wave front encounters a flat, infinite plane surface. The incoming wave splits up into reflected and transmitted (refracted) waves whose magnitudes can be computed from FRESNEL’S formulas. Reflection coefficients for parallel and perpendicular polarisations are [165]

ρ =

ε 2 ε1 cos α − ε 2 ε1 − sin 2 α ε 2 ε1 cos α + ε 2 ε1 − sin 2 α

ρ⊥ =

(2.1)

cos α − ε 2 ε1 − sin 2 α

(2.2) cos α + ε 2 ε1 − sin 2 α where ε1 and ε 2 are the permittivities of medium 1 and medium 2 respectively (incoming wave is in medium 1), α is the angle between the incoming wave propagation direction and the normal of the surface. A slightly different reflection coefficient definition is given in [155], where the same absolute dielectric constant was assumed for both reflection surface and the air. Because the phase component is small enough to be negligible as long as horizontal polarisation is considered, only the magnitude component was considered in the calculation and, thus, on a smooth surface, the reflection coefficient for the horizontal component is given by [155]

ρ s ,h = −

cos α − ε − sin 2 α

(2.3) cos α + ε − sin 2 α where α is the angle of incidence and ε is the relative dielectric constant of medium given by [155] ε = ε r − j 60κλ (2.4) where ε r is the normalised relative dielectric constant of the reflecting surface, κ is the conductivity of the reflecting surface, and λ is the wavelength of the incident ray [155]. When λ is small, ε can be considered nearly equal to ε r [155]. For more detailed reflection and transmission contemplations see e.g. [168]. Polarisations are defined by means of the plane containing the normal of the surface and the propagation direction. It should be noted that although parallel and perpendicular polarisations act independently, in general polarisation changes in reflection. Even though there are no perfectly flat infinite plane surfaces in reality, specular reflection is a good approximation if the surface is sufficiently large in wavelengths and not too rough compared to the wavelength [165]. If the surface has considerable roughness, reflected energy spreads in all directions instead of one specular direction. This is called diffuse reflection and it is complicated to calculate compared to specular reflection [165]. A critical surface roughness is given by the RAYLEIGH criterion [214] which states that a reflection is specular if [165] 4πσ si cos α 1 C= < (2.5) λ 10 Here σ si is the standard deviation of surface irregularities relative to the mean height of the surface [165]. Thus, for 60 GHz and normal incidence ( α = 0° ), σ si must be smaller than 0.04 mm for a specular 11/160

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reflection.2 On the other hand, for near-grazing incidence of α = 89° the threshold value rises up to 2.3 mm. If C > 10 , highly diffuse reflection takes place and the specularly reflected wave is small enough to be neglected [165]. The threshold values of surface roughness for normal and near-grazing incidence are 4 mm and 23 cm, respectively.

Figure 2.1: Rough surface scattering: with the increase of surface Figure 2.2: Fundamental propagation mechanisms (Figure 6 from roughness, secular reflected field decreases and diffuse scattered [291]). field increases (Fig. 36 from [291]).

Diffraction: Since all surfaces in real propagation environments are finite, also edges and corners have to be considered [165]. Diffraction occurs, when a radio wave encounters sharp irregularities (edges) of a dense obstacle (impenetrable body) with large dimensions compared to the propagated wavelength [25] [156] [165]. This causes secondary waves to arise (in any conceivable direction) from the obstructing surface. There is a possibility that the secondary waves can bend around the obstructing element into shaded areas behind the edge [28] [165] and provide an almost artificial LOS between transmitter and receiver [25] [156]. Diffraction can be modelled using the Geometrical Theory of Diffraction (GTD) [149] or the more sophisticated Uniform Theory of Diffraction (UTD) [28] [278] [157]. Like reflection, this phenomenon is dependent on: frequency, amplitude, phase, and the angle of arrival of the incident wave. Scattering: Scattering is a general interaction process between an electromagnetic wave and an arbitrarily shaped obstacle [165]. However, since large and regularly shaped obstacles can be conveniently handled using the above-mentioned approximations (reflection and diffraction), only small and irregularly shaped objects will be treated as scatterers [165]. Here small means that the scatterer has dimensions on the order of ([25], [28], [156]) or smaller than the wavelength ([165]). These objects scatter (spread out) energy into all directions [25] [156] [165], in a way that is extremely difficult to accurately compute and thus is usually not included in deterministic calculations [165], but follows the same principles like diffraction [156]. Scattering also occurs when the number of obstacles is quite large [156].

The received signal will be a summation of multiple radio waves, which have usually travelled over many different paths due to reflection, refraction and scattering and arrive at the receiver [25] [28] [126] [156] • from different directions, • with different propagation delays, • with different amplitudes, • with different phases, • with different angles of arrival. This phenomenon is called multipath propagation [25] and is illustrated in Figure 2.2 and, hence, the channel is called multipath channel. If a mobile does have a clear line of sight (LOS) path to the base-station, than diffraction and scattering will not dominate the propagation; but if a mobile is without LOS (NLOS), then diffraction and scattering will probably dominate the propagation [156].

2

MAVRAKIS [188] also refers to the RAYLEIGH criterion when stating, that for an incident angle of 45° a surface can be considered smooth if the variations in the height range are within 0.8 mm. However, this value does not follow from Eqn. (2.5), which gives about 0.06 mm.

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3. Baseband Channel 3.1 Signal Modulation One of the most fundamental operations in radio communications is the act of modulating a carrier wave by a band-limited data signal. Thus, modulation converts a baseband signal to a passband signal. To represent the act of modulation, DURGIN [76] introduces the modulation operator M {⋅ } to denote transformation of a baseband signal, x ( t ) , to a passband signal, x ( t ) , that modulates a carrier wave3. Thus, using this notation one gets [76] x ( t ) = M{ x ( t )} (3.1) It is easiest to view modulation in the frequency domain using the FOURIER transforms or spectra of x ( t ) and x ( t ) [76]: +∞

X( f )=

∫ x ( t ) exp ( − j 2π ft ) dt

(3.2)

∫ x ( t ) exp ( − j 2π ft ) dt

(3.3)

−∞ +∞

X( f )=

−∞

The FOURIER transform of the passband signal may be calculated from the baseband signal as follows [76] [224]: 1 1 X ( f ) = X ( f + fC ) + X * ( − f − fC ) (3.4) 2 2 where * denotes complex conjugate. In the frequency domain, X ( f ) is simply a copy of the spectrum X ( f ) shifted to a centre frequency of f = + f C and a mirror copy of X ( f ) shifted to a centre frequency of f = − f C . The operation of modulation can be defined directly in the time domain. Given a carrier frequency, f C , we obtain [76] M { x ( t ) } Re{ x ( t ) exp ( j 2π f C t )} (3.5) mirror image

frequency shift

The complex exponential in Eqn. (3.5) shifts the baseband signal, x ( t ) up to a carrier frequency of f C and the Re {⋅ } operator produces the conjugate mirror-image spectrum at − f C . Demodulation, the inverse operation of modulation – converting a passband signal, x ( t ) , back to a baseband signal, x ( t ) – also has a time domain definition [76]:

M −1 { x ( t ) } = [ x ( t ) exp ( − j 2π f C t ) ] ⊗ [ 2 B sinc ( π Bt ) ] frequency shift

(3.6)

low − pass filter

where ⊗ denotes convolution, B is the non-zero bandwidth, and sinc ( ⋅ ) is the sinc function, sinc ( x ) = sin ( x ) x . The complex exponential term in Eqn. (3.6) shifts the passband signal spectrum, X ( f ) , by an amount f c so that the copy of X ( f ) lies centred at f = 0 and its mirror image lies at f = −2 f C . The convolution with the sinc function – a low-pass filter – then removes the high-frequency mirror image so that only X ( f ) remains. The complete operation of modulation and demodulation is shown in Figure 3.1. If the modulated signal, x ( t ) , is to represent a physically realisable transmission, then it must be a realvalued function. No such restriction is placed on the baseband signal, as any complex-valued function that modulates a carrier according to Eqn. (3.5) will produce a real-valued function. This difference between baseband and passband representations comes from the conjugate mirror image in the passband spectrum, X ( f ) . Thus, X ( f ) has twice as much non-zero bandwidth as the baseband signal. A complex function, 3

Some authors (e.g., DURGIN [76], JERUCHIM et al [139]) use the tilde ~ to mark the baseband signal, this is just the other way around we are doing here to shorten notation.

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which is actually two real-valued functions (one for the real component and one for the imaginary component), is the easiest way to accommodate this extra information so that nothing is lost in the baseband representation of a modulated signal [76].

x(t ) exp ( j 2π fC t ) exp ( − j 2π fC t )

x(t )

Figure 3.1: Baseband-Passband transformations in the time domain (inner cycle) and the frequency domain (outer cycle) (adapted from Figure 2.2 from [76]).

3.2 Equivalent Lowpass Impulse Response and Channel Transfer Function As we have already used before, the channel considered is actually a bandpass filter centred on a carrier frequency f C . The (passband) channel can be characterised in the time domain by its real (passband) impulse response h ( τ , t ) at time t due to an impulse applied at time t − τ or by its transfer function H ( f , t ) , i.e., the FOURIER transform of h ( τ , t ) with respect to τ . The fact that h ( τ , t ) is real implies – according to [224] and [253] – that H * ( − f ,t ) = H ( f ,t ) . (3.7) If we define H ( f − f C , t ) as [224] [253]

 H ( f ,t ) H ( f − fC , t ) =  0 

f >0 f 1 B can be resolved [109]. Hence, we have:

h ( t ,τ ) =

N ( t ) −1

∑

n =0

δ (τ − τ n ( t ) )

M n ( t ) −1

∑

m=0

an ,m ( t ) ⋅ e jψ n ,m ( t )

(3.36)

The second sum acts as multiplicative time-variant weighting of the n -th path. With the definitions

hn ( t ) =

M n ( t ) −1

∑

m =0

an ,m ( t ) ⋅ e jψ n ,m ( t )

(3.37)

β n ( t ) = hn ( t ) , ϕ n ( t ) = arg ( hn ( t ) ) and thus

hn ( t ) = β n ( t ) ⋅ e jϕ n ( t ) (3.38) we obtain the equivalent lowpass time-variant impulse response h ( τ , t ) of the discrete-time time-variant channel [12] [14] [25] [64] [109] [126] [150] [195] [207] [225] [226] [228] [253] [286] [289] 18/160

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N ( t ) −1

∑

n =0 N ( t ) −1

∑

n =0

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hn ( t ) ⋅ δ ( τ − τ n ( t ) ) (3.39)

β n ( t ) ⋅ e jϕn ( t ) ⋅ δ ( τ − τ n ( t ) )

where β n ( t ) , ϕ n ( t ) , and τ n ( t ) , denote the magnitude, phase, and delay of the n -th path, respectively.

3.6.3. Bin Model Usually, the model is further simplified using a discrete time approximation. For a fixed t , the time axis is divided into a number of equal small time intervals of identical duration, called „bins“, as illustrated in Figure 3.5. The subpaths are restricted to lie in one of the time interval bins, hence, each bin is assumed to contain either none, one or more than one multipath component(s). Amplitude of Multipath Component

There are N multipath components (0..N-1) τ o= 0 τ1= ∆τ

Excess Delay Bin

τi= (i)∆τ τN-1= (N-1)∆τ

τ (excess delay) ∆τ τ0

τ2

τi

τN-1

Figure 3.5: Illustration of bin model (from [156]).

A reasonable bin size is the resolution of the specific measurement since two paths arriving within a bin cannot be resolved as distinct paths, thus, τ n = n B ( B … channel resp. signal bandwidth). If a subpath falls in the n -th bin, β n and ϕ n follow an empirically determined distribution. This completes the statistical model for the discrete time approximation for a single snapshot. A sequence of profiles will model the signal over time as the channel impulse response changes, e.g. the impulse response seen by a receiver moving at some nonzero velocity through an environment. Thus, the model must include both the first order statistics of N , β n , and ϕ n (and also of the binary information rn if there are subpaths within the bin or not) for each profile (equivalently, each τ ), but also the temporal and spatial correlations between them [109] [126]. Hence, we can also write h (τ ,t ) =

N −1

∑ β n ⋅ e jϕ

n

n =0

⋅ δ ( τ − rnτ n )

(3.40)

The statistics of the received signal for a given τ are thus given by the statistics of N , { rn }0N −1 , { β n }0N −1 , and {ϕ n }0N −1 [109]. The channel is completely characterised by these path variables [126]. As we have

already stated before, for this model to hold it is generally assumed that β n ( t ) , ϕ n ( t ) , and τ n ( t ) change slowly compared to the measurement resolution. Equation (3.39) is commonly used to describe the impulse response of the time-variant multipath fading channel [25]. Such a time-variant impulse response is illustrated in Figure 3.6. Conceptually, Eqn. (3.39) represents the arrival of a line of sight signal (with some amplitude and phase distortion), and a series of multipath signals (also with associated amplitude and phase distortion), each arriving at some time delay, τ i later [14]. In other words, it represents the channel response to a unit impulse at time t , evaluated at time delay τ from the time of occurrence of the impulse [21] [138] [215]. The exact amplitude, phase, and time delay of each of the multipath components will vary with changes in the channel (e.g. mobile scatterers); hence, Figure 3.6 only represents a snapshot of the channel for an impulse occurring at a particular t [14]. In a real-life situation, a portable receiver moving through the channel experiences a space-varying fading phenomenon. One can therefore associate an impulse response “profile” with each point in space, as illustrated in Figure 3.7. It should be noted that profiles corresponding to points close in space are expected to be grossly similar because principle reflectors and scatterers which give rise to the multipath structures remain approximately the same over short distances. 19/160

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hb(t,τ) t t3

τ(t3)

t2

τ(t2)

t1

τ(t1)

t0

τo

τ1

τ2

τ3

τ4

τ5

τ6

τN-2 τN-1

τ(t0)

Figure 3.6: Time-variant impulse response, only magnitude shown, hb ( t ,τ ) = h ( t ,τ ) , (from [156]).

Figure 3.7: Sequence of profiles adjacent in space (Fig. 3 from [126]).

3.6.4. Transfer Function As already described for the general case in section 3.2, equivalently the channel is fully described by the time-variant transfer function H ( f , t ) , which is the FOURIER transform of h ( τ , t ) [289]. This channel frequency response can be written as [207] H ( f ,t ) =

N ( t ) −1

∑

n =0

hn ( t ) e − j 2π f τ n

(3.41)

3.6.5. Directional Extension New models for the mobile radio channel are essential for the study of systems incorporating smart antennas. Channel models for these applications have to include the directional information of the signals, i.e. not only do they describe the dispersion of signal power in time, but also the dispersion of power in angle. Directional channel models are, therefore, important for future mobile radio systems like UMTS or HIPERLAN. These models have to reproduce the typical characteristics observed in measurement data from different representative environments. The first general proposal was based on the directional parametric stochastic modelling approach. Using this approach, the channel impulse response can be described by the locations of the scatterers and the position of the AP and MT (scattering geometry) or by the parameters of the impinging waves (delay-angle distribution). [28] If there are L dominant multipath components (each of which corresponding to one impinging wave), the directional impulse response can be formally represented as [28] h ( r,τ , Ω ) =

L( r ) −1

∑

l =0

hl ( r,τ , Ω )

(3.42)

Here, r denotes the location of the receiver antenna, and τ is the delay variable. The direction of arrival is characterised by Ω (this may be denoted by its azimuth and elevation angle). In [11] BELLO’S [21] terminology is extended by defining the radio channels azimuth-delay spread function at the AP according to [11] L

h ( θ ,τ ) = ∑ hl ⋅ δ ( θ − θl ,τ − τ l )

(3.43)

l =1

where the parameters hl , τ l , and θ l are the complex amplitude, delay, and incidence azimuth of the l th impinging wave at the AP. In general, h ( θ ,τ ) is considered a time-variant function, since the constellation of the impinging waves is likely to change as the MT moves along a certain route. However, this dependency was omitted in Eqn. (3.43) to simplify notation. 20/160

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4. Statistical Channel Characterisation 4.1 Channel Autocorrelation Function As to BOHDANOVICZ ([25]), the next step is the description of the useful correlation functions that are exploited in channel characterisation. Since the nature of the channel is random, the channel impulse response function can be replaced by a set of autocorrelation functions, which gives a better description of the unpredictable behaviour of the channel. The channel (lowpass) impulse response function can be seen as a complex random process. The autocorrelation function of h ( τ , t ) is then defined (with x* denoting the complex conjugation) as follows [25] [139] [253] 4 1 φh ( τ 1 ,τ 2 , t1 , t2 ) = E { h* ( τ 1 , t1 ) h ( τ 2 , t2 ) } (4.1) 2

4.2 Wide Sense Stationary Uncorrelated Scattering As we have already assumed earlier, the channel is nonstationary in time due to the motion of people and equipment in most indoor environments, i.e. the channel’s statistics change, even when the transmitter and receiver are fixed [126]. This leads to time-variant channel models, which are not very easy to deal with. According to HASHEMI [126], most digital propagation measurements have therefore assumed some form of stationarity while collecting the impulse response profiles; a review of literature shows that in a number of measurements temporal stationarity or quasi-stationarity of the channel have either been observed or assumed in advance. Other experiments have shown that the channel is “quasi-static” or “wide-sense stationary”, only if data is collected over short intervals of time ([126] referring to [36], [37]). As to [64] and [195], for the indoor propagation environment where the time varying factors of the impulse response typically are human movement, it is appropriate to treat the channel as quasi-stationary. This allows multiple measurements to be taken with the knowledge that the non-noise parts of the impulse response will be acceptably constant [64]. Again HASHEMI [126]: the assumption of stationary or quasi-static channel in a time span of a few seconds may be reasonable for residential buildings or office environments in which one does not expect a large degree of movement. The situation may be different in crowded shopping malls, supermarkets, etc., where a great number of people are always in motion. However, in many situations it is reasonable to assume that the channel h ( τ , t ) is wide sense stationary with respect to t . There are two conditions for the stochastic process h ( τ , t ) to be wide sense stationary: 1. Autocorrelation stationarity: The process’ autocorrelation function does not depend on the particular time instants t1 and t2 , but only on the time difference ∆t = t2 − t1 between them [25] [76] [109] [253]. In other words, the correlation behaviour is invariant of time. 2. Mean stationarity: The process’ mean value is time independent [25] [76] [253]. For the time-varying baseband channel mean stationarity holds if the value E { h ( τ , t ) } is not a function of time, t . According to DURGIN ([76]), most processes encountered in real life modelling fail the WSS test due to their autocorrelation statistics; but DURGIN also gives the hint to be aware that pathological processes exist having nonstationary means and stationary autocorrelations. Consequently, the autocorrelation function from the Eqn. (4.1) simplifies for wide sense stationarity to [25] [109] [139] [253] 1 φh ( τ 1 ,τ 2 , ∆t ) = E { h* ( τ 1 , t ) h ( τ 2 , t + ∆t ) } (4.2) 2 If furthermore uncorrelated scattering is assumed, which means that the signals coming via different paths experience uncorrelated attenuations, phase shifts and time delays [25], that is, the complex amplitudes of contributions with different delays τ 1 ≠ τ 2 are uncorrelated [130], since the two components are caused by different scatterers5 [109], the formula (4.2) transforms to [25] [109] [145] [238] [253] 1 (4.3) E { h* ( τ 1 , t ) h ( τ 2 , t + ∆t ) } = φh ( τ 1 , ∆t ) δ ( τ 1 − τ 2 ) φh ( τ , ∆t ) 2 4

SMULDERS [253], JERUCHIM [139], KATTENBACH [145], and DURGIN [76] omitted the normalisation factor ½ in all correlation investigations. 5 This will not be true with rough reflections surfaces, where an incoming ray reflecting off the surface results in multiple reflections spaced close together in time [109].

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If so, the channel is said to be a wide sense stationary uncorrelated scattering (WSSUS) channel [25] [225]. In this case, the theory of linear time-variant filters applies [21] [225] [289] [297]. This characterisation is appropriate for describing the small-scale behaviour of the channel, which is suitable and sufficient for the air interface design of a digital communication system [289] 6. The delay cross-power density φh ( τ , ∆t ) gives the average power output as a function of the time delay τ = τ 1 = τ 2 and the difference ∆t in observation time [109] [238]. This function assumes that τ 1 and τ 2 satisfy τ 1 − τ 2 > B −1 ( B … channel bandwidth), since otherwise the receiver can’t resolve the two components. In this case, the two components are modelled as a single multipath component with delay τ ≈ τ 1 ≈ τ 2 [109]. The time-correlation function is defined as [238] def

φh ( ∆t ) = ∫ φh ( τ , ∆t ) dτ

(4.4)

According to KATTENBACH [145], the relations for WSSUS channels described above can be extended straightforwardly for directional time-variant channels from the duality between the time-DOPPLER relation, the frequency-delay relation and the aperture-angle relation. Since WSSUS channels show uncorrelated scattering with respect to delay τ and DOPPLER frequency f D , a directional WSSUS channel has to show uncorrelated scattering with respect to delay τ , DOPPLER frequency f D , and aperture θ . Thus, for a directional WSSUS channel Eqn. (4.3) has to be extended as [145] 1 φh ( ∆t ,τ 1 ,τ 2 ,θ1 ,θ 2 ) = E { h* ( t1 ,τ 1 ,θ1 ) h ( t1 + ∆t ,τ 2 ,θ 2 ) } (4.5) 2 = φh ( ∆t ,τ ,θ ) ⋅ δ ( τ 2 − τ 1 ) ⋅ δ ( θ 2 − θ1 ) with φh ( ∆t ,τ ,θ ) consequently being denoted as delay-angle cross-power spectral density [145].

4.3 Angle-Dependent Profiles and Spectras When a directional antenna at position, r , and azimuthal orientation, θ , is connected to a wideband noncoherent channel sounder, an angle-delay profile (ADP; also “angle-delay spectrum”) is measured [76]. Figure 4.1 and Figure 4.2 show two examples measured at a carrier frequency of 1920 MHz. The ADP is defined as [76] 1 (4.6) P ( τ ,θ , r ) = h ( τ ,θ , r ) 2 resp. P ( τ ,θ , r ) = h ( τ ,θ , r ) 2 2

Figure 4.1: PDP snapshot for azimuthal sweep at 1920 MHz (part of Figure 5.19 from [14], allegedly from [76]).

Figure 4.2: A local area angle-delay spectrum from a set of rotational measurements at 1920 MHz (Figure 7.7 from [76]).

Quite similar, based on Eqn. (3.43), the local average power azimuth-delay spectrum can be defined as [11]  L  P ( θ ,τ ) = E  ∑ hl 2 δ ( θ − θl ,τ − τ l )  (4.7)  l =1  6

Remark: There are statements from researchers that doubt in the validity of the WSSUS assumption for the 60 GHz channel. They suspect that the assumption of uncorrelated scattering is only valid within the scatterer’s vicinity of some 10 wavelengths.

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The power angle profile (PAP; also: “power angle spectrum”) is the spatial equivalent of a PDP [76]. Based on Eqn. (4.6), the PAP is defined as [76] 1 (4.8) P ( θ , r ) = h ( θ , r ) 2 resp. P ( θ , r ) = h ( θ , r ) 2 2 Written without a τ -dependence, Eqn. (4.8) represents the angle-of-arrival characteristics of a narrowband channel. The power angle profile accompanying to Eqn. (4.7) can be expressed as [11]

P ( θ ) = ∫ P ( θ ,τ ) dτ

(4.9)

From this function, the radio channel local RMS angular spread σ θ can be defined as the second root central moment of P ( θ ) [11] (see section 4.8.3).

4.4 Power Delay Profile The starting point for most calculations on wideband multipath propagation is the power delay profile (PDP) as this is the format in which the impulse response emerges from typical wideband measurement equipment. If the time difference ∆t is set to zero, the resulting autocorrelation function φh ( τ ) ≡ φh ( τ ,0 ) describes the time spread of the channel. We obtain with τ ≡ τ 1 [139] [253] +∞

{

1 1 P ( τ ) = φh ( τ ) = ∫ E { h* ( τ , t ) h ( τ 2 , t ) }dτ 2 = E h ( τ , t ) 2 2 −∞ 2

}

(4.10)

This function has several names, e.g., multipath intensity profile, delay power spectrum, delay power profile, power delay profile (PDP). It represents the average power output of the channel as a function of the excess delay τ with respect to a fixed time delay reference [25] [109] [139] [228] [253]. In other words: it describes the power response of the channel in the case of a δ -pulse transmitted. The PDP can also be calculated from the scattering function (see section 4.5) [35] [139] +∞

φh ( τ ) =

∫

Sh ( τ ,ν ) dν =

+ν max

∫

Sh ( τ ,ν ) dν

(4.11)

−ν max

−∞

The function is decaying since there is a limited time during which all the multipath components arrive at the receiver. Hence, the function also provides a measure for the time dispersion of the channel. The measure is called the RMS delay spread of the channel (see section 4.7.6) [25]. A power delay profile measured at a carrier frequency of 1920 MHz is shown in Figure 4.3. The power delay profile accompanying to the power azimuth-delay spectrum Eqn. (4.6) can be expressed as [11] P ( τ ) = ∫ P ( θ ,τ ) dθ

(4.12)

Based on the discrete-time impulse response model presented in section 3.6, the (time-discrete) PDP can be expressed as [64] [195] [226] [291] P (τ ) = h (τ )

2

=

N −1

∑

i =0

βi2δ

(τ − τ i ) =

N −1

∑ Piδ ( τ − τ i )

(4.13)

i =0

where β i is the amplitude, τ i is the delay, and Pi is the power of the i -th multipath component, N is the total number of the rays used in the model/measurement.

4.5 Scattering Function WSSUS-models require only two sets of parameters to characterise fading and multipath effects: the Power Delay Profiles (PDP) and the DOPPLER Power Spectra (DPS) [35]. Both parameter sets can be described by a single function, which is called Scattering Function Sh ( τ ,ν ) (often also denoted as S ( τ ,ν ) ), where τ denotes the path delay and ν denotes the DOPPLER frequency (see section 4.6.1). Figure 4.4 shows an example of an idealised scattering function with its PDP and DPS [35]. As we have already formulated in section 3.2, if h ( τ , t ) is the time-variant equivalent lowpass impulse response of the mobile channel, which is characterised as a complex-valued random process for the observation time t , the FOURIER transform H ( f , t ) of h ( τ , t ) yields [35] [109] 23/160

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Figure 4.3: A series of PDP snapshots along a linear track, measured with an omnidirectional receiver antenna at 1920 MHz (Figure 7.6 from [76], used in [14] as part of Figure 5.19).

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Figure 4.4: Example of an idealised scattering function S ( τ , f D ) with its Power Delay Profile PDP ( τ ) and its DOPPLER Power Spectrum DPS ( f D ) (Fig. 1 from [35]).

∞

H ( f ,t ) =

∫ h ( τ , t ) ⋅ exp ( −2π f τ ) dτ

(4.14)

−∞

By assuming wide-sense-stationarity for the channel, the autocorrelation function of the transfer function H ( f , t ) in time is a function of only the time-difference ∆t = t2 − t1 . In this case, the autocorrelation function in the frequency domain (equivalently to Eqn. (4.2)) is defined by [25] [109] [253] 1 φH ( f1 , f 2 , ∆t ) = E { H * ( f1 , t ) H ( f 2 , t + ∆t ) } (4.15) 2 If we now assume the uncorrelated scattering, then the autocorrelation function of H ( f , t ) in frequency is a function of only the frequency-difference ∆f = f 2 − f1 and not on the particular frequencies. The function (4.15) transforms to the autocorrelation function of H ( f , t ) in time and frequency [25] [35] [109] [145] 1 φH ( ∆f , ∆t ) φH ( f1 , f 2 , ∆t ) = E { H * ( f , t ) ⋅ H ( f + ∆f , t + ∆t ) } (4.16) 2 and is called the spaced-frequency, spaced-time correlation function. As the channel transfer function and the channel impulse response are a FOURIER pair, it is not surprising that their autocorrelation functions φh ( τ , ∆t ) and φH ( ∆f , ∆t ) are also a FOURIER pair [25]. Directional extension: Since uncorrelated scattering with respect to τ is equivalent to wide sense stationarity with respect to f , uncorrelated scattering with respect to θ will result in wide sense stationarity with respect to x , and, thus, Eqn. (4.16) will become [145] 1 φH ( ∆ t , ∆ f , ∆ x ) = E { H ∗ ( t , f , x ) H ( t + ∆ t , f + ∆ f , x + ∆ x ) } (4.17) 2 for a directional WSSUS channel, with φH ( ∆t , ∆f , ∆x ) being the time-frequency-aperture correlation function. In the same manner as for (nondirectional) WSSUS channels, the other six correlation functions of a directional WSSUS channel as well as their relations could be derived. However, they can be as well be formulated straightforwardly from the dualities described before and, thus, the complete derivations may be omitted here [145].

For ∆t = 0 , the resulting autocorrelation function φH ( ∆f ) ≡ φH ( ∆f ,0 ) is called the spaced-frequency correlation function of the channel [253], it is the FOURIER transform of φh ( τ ) [253] and thus [279] 7 +∞

φH ( ∆f ) =

∫ φh ( τ ) e

− j 2π∆ft

dτ

(4.18)

−∞

Its shape expresses the frequency coherence of the channel, i.e., the extent to which two different sinusoids with frequency separation ∆f are affected differently by the channel [253]; for frequency coherence see section 4.9.2.

7

In [250] the spaced-frequency correlation function is in principle given as φH ( ∆f ) ≅

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The scattering function Sh ( τ ,ν ) can be obtained either by applying the FOURIER transform to the autocorrelation function φh ( τ , ∆t ) with respect to the variable ∆t , or by applying the inverse FOURIER transform to the power spectral density S H ( ∆f ,ν ) with respect to the variable ∆f . The scattering function is expressed by the formula below [25] [139] [238] ∞

Sh ( τ ,ν ) =

∫ φh ( τ , ∆t ) exp ( − j 2πν∆t ) d ∆t

−∞ ∞

=

(4.19)

∫ S H ( ∆t,ν ) exp ( j 2πν∆f ) d ∆f

−∞

It can be seen, that the DOPPLER frequency ν is the dual variable of ∆t , hence it captures the rapidity with which the channel itself changes [139]. The scattering function of the channel and the spaced-frequency, spaced-time correlation function are related by the double FOURIER transform ([35] ref. to [225]) ∞ ∞

Sh ( τ ,ν ) =

∫ ∫ φH ( ∆f , ∆t ) exp ( j 2π∆f τ ) exp ( − j 2πν∆t ) d ∆fd ∆t

(4.20)

−∞ −∞

The scattering function is limited in both variables [25]: • in τ by the length of the impulse response τ MED (maximum excess delay, see section 4.7.2), • in ν it is limited by ±ν max ( ν max is the maximum DOPPLER shift, see section 4.6.1), because the impulse response only changes finitely fast (that is, the movements of transmitter, receiver and all scatterers is finitely fast). The scattering function provides a single measure of the average power output of the channel as a function of the delay τ and the DOPPLER frequency ν [139] and, thus, it is often used to approximate maximum excess delay, coherence bandwidth, DOPPLER spread, and coherence bandwidth [109].

4.6 DOPPLER Power Spectrum 4.6.1. Definition of the DPS In order to relate DOPPLER effects to the time variations in the channel due to the movement itself we consider the FOURIER transform of the spaced-frequency, spaced-time correlation function φH ( ∆f , ∆t ) with respect to the variable ∆t to the DOPPLER frequency ν domain (sometimes denoted as f D , ω , or λ ; the latter should not be mistaken for wavelength) [25] [109] [253]: +∞

S H ( ∆f ,ν ) =

∫ φH ( ∆f , ∆t ) exp ( − j 2πν∆t ) d ∆t

(4.21)

−∞

If we set ∆f = 0 , relation (4.21) becomes [25] [109] [253] +∞

SH (ν )

S H ( 0,ν ) =

∫ φH ( ∆t ) exp ( − j 2πν∆t ) d ∆t

(4.22)

−∞

The resulting function S H ( ν ) is the DOPPLER power spectrum (DPS) of the channel and represents the power spectrum of the signal as a function of the DOPPLER frequency ν [25] [253]. The DOPPLER power spectrum can also be calculated directly from the scattering function (see section 4.5) [25] [139] [154] [238]: +∞

SH (ν ) =

∫ Sh ( τ ,ν ) dτ

(4.23)

−∞

and because the scattering function is limited in τ by 0 ≤ τ ≤ τ MED (see section 4.5), this simplifies to [35] SH (ν ) =

τ MED

∫

Sh ( τ ,ν ) dτ

(4.24)

0

The spaced-time correlation function φH ( ∆t ) is the inverse FOURIER transform of S H ( ν ) [139]: +∞

φH ( ∆t ) =

∫ SH ( ν ) exp ( j 2πν∆t ) dν

−∞

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4.6.2. DOPPLER Shift According to [14], DOPPLER spreading is characteristic of a dynamic channel, where scatterers such as the transmitter, receiver, or objects in the propagation environment are mobile (whereas in the static channel scatterers are stationary), resulting in DOPPLER frequency shifts on the line-of-sight and multipath signals [229]. The motion of scatterers in the environment leads to time varying phase shifts on the individual reflected signals. When multiple signals arrive at the receiver, all with different DOPPLER shifts, the resulting composite signal (the vector sum of the line-of-sight signal and all multipath signals) will exhibit a timevarying amplitude [176]. Additionally, the time-varying phase shift imparted on the reflected signals will produce a random phase modulation, usually called random FM (as the derivative of a time-varying phase results in frequency modulation) [214] [229]. Receiver (or transmitter) motion introduces a DOPPLER frequency shift to each propagation path and thus a spectrum broadening of the received signal [28] [142] [156]. The change in frequency is called DOPPLER shift (or “DOPPLER frequency”). DOPPLER effects are related to the phase changes in the propagation path lengths and thus are a frequency-domain manifestation of the time-domain fast fading. A direct relationship between the path DOAs and the DOPPLER frequencies of the paths is [165] v ⋅u ν n = Rx n (4.26)

λ

where v Rx is the receiver velocity vector and un = cos θ n cosϑn i + cos θ n sin ϑn j + sin θ n k (4.27) is the unit vector pointing in the path DOA of path n , θ n ∈ [ − π 2,π 2 ] is the elevation angle and

ϑn ∈ ] −π , π ] the azimuth angle which define the incidence direction of the n th path in spherical coordinates. When focussing on a single wave, the DOPPLER shift ν is defined as the difference between the transmitted and received frequency and is calculated as [142]: v ν = f C Rx cos α (4.28) c0 where f C is the frequency of the pure carrier assumed being transmitted, v Rx is the (scalar) speed of the receiver, c0 is the speed of light (more general: the propagation speed of the wave within the medium), and α is the angle between the directions of incidence and movement. Thus, as GALLAGER [100] states, the expression v Rx cos α characterises the velocity at which the path length is changing. The DOPPLER shift is positive if the mobile is moving toward the direction of arrival of the wave, it is negative if the mobile is moving away from the direction of arrival of the wave [156]. Obviously the extreme values of the DOPPLER shift occur as ν = −ν max for α = π (path is arriving directly from behind the receiver resp. receiver is moving straight away from the receiver) and as ν = +ν max for α = 0 (path is arriving from directly ahead of the receiver resp. receiver is moving straight towards the transmitter) [142] [165] 8: v v ν max = Rx resp. ν max = f C Rx (4.29) λ c0 E.g., for non-frequency selective RICE fading with an angle of incidence α = π 4 for the direct component, a DOPPLER frequency of ν = ν max 2 results for this component [142]. For non-multipath systems where the system bandwidth is much smaller than the carrier frequency, it is normally assumed that the DOPPLER shift is equal within the whole system bandwidth. According to [124], the wideband propagation channel is the superposition of a number of dispersive fading paths, suffering from various attenuations and delays, aggravated by the phenomenon of DOPPLER shift caused by the MT’s movement. The momentary DOPPLER shift ν depends on the angle of incidence α , which is assumed being uniformly distributed, i.e., ν = ν max ⋅ cos α , which has hence a random cosine distribution with a DOPPLER spectrum limited to −ν max < ν < +ν max . Due to time-frequency duality, this ‘frequency-dispersive’ phenomenon results in ‘time-selective’ behaviour and the wider the DOPPLER spread, i.e., the higher the vehicular speed the faster is the time-domain impulse response fluctuation. 8

ν max is sometimes also denoted as f Dmax , f m or λm .

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4.6.3. Mean DOPPLER Shift and nth Moment The n th moment of the DOPPLER power spectrum is defined as [76] +∞

ν = n

∫ν

n

⋅ S H ( ν ) dν

−∞ +∞

(4.30)

∫ S H ( ν ) dν

−∞

Thus, the mean DOPPLER shift ν is defined according to [154] resp. [302] as

ν =

+∞

+∞

−∞ +∞

−∞ +∞

∫ ν ⋅ SH ( ν ) dν ∫ φh ( τ ) dτ

−∞

resp. ν =

∫ ν ⋅ S H (ν ) dν

(4.31)

∫ S H (ν ) dν

−∞

4.6.4. DOPPLER Spread 4.6.4.1. The Term “DOPPLER Spread” First, we must state that the term “DOPPLER spread” is not consistently used in the literature. Some authors (e.g., in [65]) use it in the same meaning as DOPPLER shift ν . More often “DOPPLER spread” is used in the following sense: The DOPPLER power spectrum S H ( ν ) gives a measure for the spectral broadening of the channel due to the DOPPLER effect; this measure is called the DOPPLER spread of the channel BD [25] (also denoted as Bd , ∆ω ). Hence, DOPPLER spread BD describes the time varying nature of the channel, and thus the severity of fading [287]. According to FLAMENT [91], the frequency dispersion of the channel is also called the DOPPLER spread of the received signal because the effect is due to the DOPPLER shift of the rays coming from different directions when the receivers or the scatterers are moving. BD is usually defined/approximated as the range of values over which S H ( ν ) is essentially nonzero [109] [156] [287], in [105] it is described as the effective bandwidth of the fading process (in [139] “fading bandwidth” ). A crude definition for DOPPLER spread is being the maximum DOPPLER shift BD = ν max [139] [156] [287] or two times the maximum DOPPLER shift (the complete nonzero width of the DOPPLER spectrum) BD = 2ν max [168], [14] ref. to RAPPAPORT [229]. Following GOLDSMITH [109], by the FOURIER transform relationship, if we define the channel coherence time Tcoh (see section 4.9.2) to be the range of values over which φh ( ∆t ) is nonzero, then BD ≈ 1 Tcoh . If the transmitter and reflectors are all stationary and the receiver is moving with velocity v , then BD ≤ v λ = ν max [109]. According to [154] [287], a more accurate characterisation is being the RMS DOPPLER spread BD = σν (see section 4.6.4.1). GALLAGER [100] gives no formula for DOPPLER spread, he only states: At the receiver, the carrier frequency is recovered. If there is only one path with a DOPPLER shift ν , the recovered carrier will be at f C − ν . When there are multiple paths, the recovered carrier will be altered by some sort of average between the different DOPPLER shifts. Thus, what is important are not the DOPPLER shifts themselves, but rather the spread between them, which is what determines how far they are from this average formed in the carrier recovery. Thus we define the DOPPLER spread on the channel as the difference between the largest and the smallest DOPPLER shift over significant paths. However, this definition is somewhat imprecise since it tries to capture the set of different DOPPLER shifts in one order-of-magnitude expression [100]. SMULDERS [253] also remarks, that for his measurement campaign (see section 6.1.3) the spectrum broadening due to DOPPLER effects is caused by scattering from randomly moving objects in the environment whereas the transceivers itself are not moving. Therefore, he expects S H ( ν ) to be bell-shaped like the GAUSS curve. For this case, a measure can be defined for the spectrum broadening due to DOPPLER effects, the DOPPLER spread BD , as the frequency shift that corresponds to S H ( ν ) = 0.5 ⋅ S H ( 0 ) [253].

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4.6.4.2. RMS DOPPLER Spread DURGIN [76] uses the term RMS DOPPLER spread being defined similarly to RMS delay spread. An increased RMS DOPPLER spread implies a channel with wilder temporal fluctuations and a smaller coherence time (see section 4.9.2). It is calculated as the second centred moment of the DOPPLER spectrum [76] [154] [302]: +∞

σν = ν − ( ν ) = 2

2

∫−∞ ν ⋅ S H (ν ) dν − (ν )2 = +∞ (ν − ν )2 ⋅ S (ν ) dν H ∫ +∞ −∞ ν ν S d ( ) H ∫−∞ 2

(4.32)

4.6.4.3. RMS DOPPLER Spread in Ad Hoc Networks WANG & COX performed in [287] an analysis of the DOPPLER spectrum and DOPPLER spread for ad hoc networks under different environmental conditions. Since all nodes can move in ad hoc networks, a link suffers from double mobility (mobility in both transmitter and receiver), resulting in unique DOPPLER effects [287]. Each node in the ad hoc network model investigated in [287] is assumed to be moving and to have a portable set with transception capabilities (transception means a transmission or a reception) and an omnidirectional antenna. In a single hop link between 2 entities such as a cellular link, there are only 1 or 2 transceptions to consider, depending on whether one is interested in pre-reception or post-reception characteristics. Also unique to ad hoc networks, sender and receiver often communicate via multiple hops over several relay nodes to reduce interference and save energy. Each single hop link along a multihop link involves 2 transceptions. Thus, for a multihop link of n nodes, the number of transceptions is 2 ( n − 1 ) , if post-reception characteristics are of interest, and 2 ( n − 1 ) − 1 , if pre-reception characteristics are of interest [287]. Environment 1: Free Space Consider the 2-D case where nodes 1 and 2 are moving toward each other with v1 and v 2 as the sender and receiver’s speed, respectively, and at angles of α1 and α 2 , respectively, from the LOS path, and one c0 ) DOPPLER shift ν transmits a carrier with frequency f C . For this case of free space, the classical ( v i observed by the other node is [287] ∆v v cos α1 + v 2 cos α 2 ν = fC = fC 1 (4.33) c0 c0 and thus proportional to the relative speed ∆v . Obviously, there is no “spread” and the one-sided DOPPLER spectrum remains an impulse in the frequency domain but translated to f C + ν [287]. Environment 2: RICE fading One expects to see RICE fading in an environment where there is a dominant path as well as many fixed local scatterers at the endpoints of the link. An example is the vehicle-to-vehicle link in a tunnel portion of an automated highway system. The RICE DOPPLER spectrum is just a superposition of the DOPPLER power spectra for the free space and the RAYLEIGH case [287]. The latter will be presented now. Environment 3: RAYLEIGH fading Here, the assumptions are a completely shadowed link with numerous fixed local scatterers in the environment such there is just multipath and no LOS, signal energy arriving equally divided in angles uniformly distributed in the horizontal plane. Thus, direction of motion of one node relative to the other does not play a role but rather direction of motion of nodes relative to their respective isolated scattering environments. The channel variation is therefore due to RAYLEIGH fading only, and it is assumed frequencyflat [287]. It is proven in [287] that, in the classical case for a multihop multipath-fading (RAYLEIGH, RICE, NAKAGAMI, etc.) link over n nodes, maximum DOPPLER shift is proportional to the sum of the speeds (rather than relative speed) of the nodes involved in each transception for multipath channels

ν max1→2,2→

→n

=

n −1

f

∑ ( vi + vi +1 ) cC0

(4.34)

i =1

It is important to note that, in practice, this analysis is useful only for the single hop link, since coherent demodulation and, thus, elimination of DOPPLER usually takes place at each node. Therefore, for multihop communication, only the last hop, or equivalently the last two transceptions, affect the DOPPLER spread at the ultimate destination [287]. For this case we obtain 28/160

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fC f resp. ν max1→2 = ( v1 + v 2 ) C (4.35) c0 c0 The generalised single hop spaced-time autocorrelation function (ignoring scaling) is then found to be [287] η 1 φH ( ∆t ) = J 0  2πν max1→2 ∆t  J 0  2πν max1→2 ∆t  (4.36)  1+η   1+η  where the degree of double mobility, η , for a link, with v1 and v 2 as the sender and receiver’s speed, respectively, is defined to be [287] min ( v1 , v 2 ) η= (4.37) max ( v1 , v 2 ) so 0 ≤ η ≤ 1 , where η = 1 for full double mobility and η = 0 for single mobility, like the cellular link.

ν max( n −1 )→n = ( v n −1 + v n )

η=0 η = 0.5 η =1

−1

−

1 2

0

ν

+

1 2

+1

−1

ν max1→ 2

−

2 3

−

1 3

0

ν

+

1 3

+

2 3

+1

ν max1→ 2

Figure 4.6: RAYLEIGH DOPPLER spectrum: ad hoc, fixed ν max1→ 2

Figure 4.5: RAYLEIGH DOPPLER spectrum: cell vs. ad hoc, fixed v1 (adapted from Fig. 5 from [287]).

(adapted from Fig. 6 from [287]).

It is noted in [287], that the autocorrelation after two transceptions is equal to the squared autocorrelation after one transception and is equal within a scaling factor to the autocorrelation coefficient after one transception. It immediately follows that the autocorrelation after n transceptions is equal to the autocorrelation after one transception to the n -th power. This implies, for the v1 fixed case, the zeros of the function are fixed regardless of n , and 0.38λC is always an approximate shortest distance over which fading becomes decorrelated (see also section 4.6.4.3). By inspection of the correlation curves in [287], it is obvious, however, that the coherence times depend on η , if, for example, one were to choose a finite threshold value of the autocorrelation function to define Tcoh [287]. For the generalised (single-hop) RMS DOPPLER spread one obtains [287]

σν = ν max1→2

1 + η2

(4.38) 2 ( 1 + η )2 For an interpretation, simply hold v1 fixed and vary v 2 from 0 to v1 , observing the DOPPLER spread, because this is arguably a more practical scenario in comparing cellular and ad hoc. Here, clearly all ad hoc cases will have worse (higher) DOPPLER spread than the cellular ( η = 0 ) link, but it is as not as bad as expected [287]. The results in [287] show a discrepancy as large as 1.5 dB between correct and incorrect characterisations of DOPPLER spread and coherence time. Here, although increasing degree of double mobility does lead to higher spread, it is not as large as the authors of [287] previously thought, and they conclude that double mobility mitigates small-scale fading. The DOPPLER spectrum on an ad hoc link is seen to be quite different from that on a cellular link. Thus, according to [287], it can be concluded that JAKES' model [137] for cellular networks does not accurately simulate multipath fading in ad hoc networks with double mobility.

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4.6.5. Dense Scatterer Model (JAKES) Assuming non-frequency-selective RAYLEIGH fading (a very large number of scattering components is equally impinging from all directions with nearly equal run times) and taking the angle of incidence θ as equally distributed random variable (the physical scattering environment is so chaotic that at the mobile the angle of arrival of a received plane wave is a uniformly distributed random variable [238]), leads to a the dense scatterer model (JAKES model) [65] [142] [154] [165] [214]. According to [238], this classical WSSUS result was derived by CLARKE [45], and later by JAKES [137], for the case of a mobile communicating with a stationary base in a two-dimensional (2-D) propagation geometry9. These well-known results state that S H ( ν ) ∝ 1

2 ν max − ν 2 or

 σ s2 1  πν S H ( ν ) =  max 1 − ( ν ν max )2  0 

ν ≤ ν max

(4.39)

elsewhere

where σ s2 is the entire power of the received signal in the equivalent low-pass sphere, and ν max is the maximum DOPPLER frequency (see section 4.6.2). The resulting RAYLEIGH DOPPLER spectrum is better known as JAKE’S spectrum [137] [289], which is commonly modelled by shaping the spectrum of a complex GAUSS noise process. This method is known in the literature as JAKES’ fading model. The resulting coloured complex GAUSS sequence has the required spaced-time correlation function φ H ( ∆t ) , which is specified by the DOPPLER power spectrum S H ( ν ) , the FOURIER transform of φ H ( ∆t ) [289].10 A distinctive feature of the spectrum is its singularity at ν = ±ν max , that is, it theoretically goes to infinity. Following GOLDSMITH [109], this will not be true in practice, due to the approximations inherent in the above assumptions, but the PSD will be maximised at frequencies associated with the maximum DOPPLER frequency away from the carrier (or from zero when focusing on the equivalent low-pass sphere) and minimised at frequencies close to the carrier (or to zero when focusing on the equivalent low-pass sphere). The intuition for this is that the multipath components at DOPPLER frequencies close to the maximum correspond to components with an angle of arrival similar to the direct path signal. There tend to be a larger number of such components, and they tend to be stronger, than multipath components received at zero DOPPLER, which correspond to an angle of arrival of π (i.e. components arrive at an angle perpendicular to the direction of motion). Another DOPPLER power spectrum results when assuming not RAYLEIGH but RICE distributed amplitudes. If differs mainly by a peak at the DOPPLER frequency of the dominating (LOS) path. The spaced-time correlation function φH ( ∆t ) [132] [139] and the time-correlation function φh ( ∆t ) [238] for the dense scatterer model are φH ( ∆t ) = J 0 ( 2πν max ∆t ) (4.40)

φh ( ∆t ) ≈ J 0 ( 2πν max ∆t )

(4.41)

where J 0 ( ⋅ ) is the zeroth-order BESSEL function of the first kind. Following [109], a plot of J 0 ( 2πν max ∆t ) = 0 allows several interesting observations (see Figure 4.7). The first observation is, that the autocorrelation is zero for ν max ∆t ≈ 0.38 or, equivalently, for v∆t ≈ 0.38λC ( λC …carrier wavelength). Thus, the signal decorrelates over a distance of approximately one half wavelength, under the uniform angle of incidence assumption. This approximation is commonly used as a rule of thumb to determine many system parameters of interest. Another interesting characteristic of this plot is that the signal recorrelates after it becomes uncorrelated. Thus, one cannot assume that the signal remains 9

AULIN [19] derived three-dimensional (3-D) generalisations. As to GALLAGER [100], due to DOPPLER shift, the bandwidth of the output signal in such models is generally slightly larger than the bandwidth of the input signal, and thus the output samples do not fully represent the output waveform. This problem is usually ignored in practice, where baseband filters are not narrow enough to eliminate the DOPPLER shifted part of the received waveform outside the bandwidth of the input signal. Since the taps are slowly varying, they behave like an LTI filter over the periods of interest and essentially model the channel. Also, it is very convenient for the sampling rate of the input and output to be the same. Alternatively, it would be possible to sample the output at twice the rate of the input. This would recapture all the information in the received waveform but would essentially require doubling the number of taps. 10

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independent from its initial value at d = 0 for separation distances greater than 0.38λC . However, it is generally assumed that once the correlation function falls below 0.5, the signal has become decorrelated and, using this assumption, the fading over a separation distance greater than half a wavelength is decorrelated [109]. A consequence of the CLARKE/JAKES assumption is – according to [238] – that the results do not depend on the mobile’s direction of travel. In addition, the time-correlation function is strictly real-valued, and the DOPPLER power spectrum is symmetric. Conversely, a non-uniform distribution of the angle of arrival will skew the DOPPLER power spectrum, which corresponds to a nonzero imaginary component of the correlation function. For example, if the angle of arrival is biased in the direction of the base station, then the DOPPLER power spectrum will be skewed toward +ν max , when the mobile Figure 4.7: BESSEL function J 0 ( 2π d ) , is moving toward the base and skewed toward −ν max when d = ν max ∆t (Figure 3.4 from [109]). moving away the base [238]. Another consequence of the CLARKE/JAKES assumption is delay/temporal separability, that is, φh ( τ , ∆t ) ∝ φh ( τ ) φh ( ∆t ) , or equivalently, Sh ( τ ,ν ) ∝ φh ( τ ) Sh ( ν ) . Often the CLARKE/JAKES DOPPLER power spectrum is used with an ad hoc or perhaps measured multipath intensity profile φh ( τ ) [238]. Formulas for the autocorrelation and PSD when the angle of incidence is not uniformly distributed, corresponding to typical distributions in microcells, can be found – according to [109] – in [137], [225]. According to [35] it can easily be shown that each PDF ( θ ) of the angle of incidence θ , which fulfils 1 PDF ( θ ) + PDF ( −θ ) = (4.42)

π

yields a JAKES-DPS. Figure 4.8 provides some examples.

Figure 4.8: Examples of PDFs of angle of incidence, which yield a JAKES-DPS in DOPPLER frequency domain (Fig. 4 from [35]).

Figure 4.9: DOPPLER power density spectra, here f D ≡ ν max (Figure 2 from [132]).

In addition, the analysis in [238] does not rely on the CLARKE/JAKES uniform angle of arrival assumption. However, SADOWSKY and KAFEDZISKI [238] still made two important assumptions: •

•

First, they assumed a spatially uncorrelated scattering field, which in turn yields a WSSUS channel. In reality, scattering elements are buildings and other large structures such as trees, hills, etc. As pointed out by BRAUN and DERSCH ([27]), a receiver of bandwidth B has a spatial resolution of roughly c0 B . If the dimensions of physical scatterers are smaller than this spatial resolution, then the scatterers are indistinguishable from “point scatterers”, and the spatially US approximation is plausible. See LAURITZEN et al [169] for channel models that do not assume US [238]. The second assumption was to consider only single scatterer propagation paths. This assumption may be questionable in indoor propagation environments and perhaps much cluttered urban environments, but it is a reasonable assumption for suburban and rural multipath models [27].

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Consequently, the results in [238] do indicate dependency on the direction of travel angle θ 0 (relative to the base-mobile baseline), and φh ( τ , ∆t ) and Sh ( τ ,ν ) are generally not separable [238]. For the case of a mobile transmitter and a stationary receiver (“stationary base station”) and θ 0 being the mobile’s direction angle relative to the transmitter-receiver baseline, they [238] obtained the following results, which, by reciprocity, hold equally for a mobile receiver and a stationary transmitter:

φh ( τ , ∆t ) = 2π

+∞

∑

n =−∞

j nψ n ( τ , ∆t ) e jnθ0 J n ( 2πν max ∆t )

(4.43)

The series coefficient functions ψ n ( τ ) are determined by the physical model that includes the spatial scattering field distribution and the mean-square propagation losses (including shadowing) [238]. The main results in [238] are not delay/temporal separable. But because J 0 ( 0 ) = 1 and J n ( 0 ) = 0 for n ≠ 0 , from Eqn. (4.43), the multipath intensity profile is found to be [238] def

φh ( τ ) = φh ( τ ,0 ) = 2πψ 0 ( τ ,0 )

(4.44) This function depends only on the spatial statistics of the scattering field and loss model and not on the mobile velocity. Moreover, observe that the zeroth term of Eqn. (4.43) clearly corresponds to the classical result of CLARKE. This term depends on the transmitter speed vTx only though the speed v (via

ν max =

v c0

f C ) and not on the mobile’s direction θ 0 . Averaging with respect to mobile direction θ 0 reduces

the series (4.43) to the satisfying result [238] 1 2π

+π

∫ φh ( τ , ∆t ) dθ0 = 2πψ 0 ( τ , ∆t ) J 0 ( 2πν max ∆t )

−π

(4.45)

≈ φh ( τ ) J 0 ( 2πν max ∆t ) where the approximation holds for very slow fading or time-invariant scattering fields. Thus, while mobile moving in a fixed (and known) direction results in a non-separable WSSUS channel model, we do obtain separability when direction of travel is averaged out [238]. For further details, e.g., a general closed-form expression for the scattering function Sh ( τ ,ν ) and illustrated examples see [238].

4.6.6. GAUSS Spectrum HUTTER and HAMMERSCHMIDT performed in [132] signal-to-interference ratio (SIR) investigations for OFDM for DVB-T. It turned out that the GAUSS shaped DOPPLER spectrum is even worse than the JAKES spectrum as far as SIR (Signal-to-Interference Ratio) performance is concerned. Furthermore, to the knowledge of the authors of [132] there is no clear evidence that the GAUSS DOPPLER spectrum models the real world adequately. However, the isotropic scatterer case (JAKES spectrum) is the more general wave incidence scenario and might better reflect the effects observed in real channels. The considered spectrum consisted of two symmetrically placed GAUSS shapes, denoted as GAUSS spectrum (see in Figure 4.9). The GAUSS spectrum corresponds to a wave incidence scenario where the signal energy is concentrated in two distinct angular regions, where the angel spread corresponds to the variance of the GAUSS shape and the mean angle corresponds to the offset of the GAUSS shape. GAUSS spectra have already been used in the early COST specifications [80] [128] and measurements carried out in PARIS [158] reinforce the assumption of the received energy being concentrated in discrete directions. Especially in urban areas, the street directions dominate the angle of arrival, a phenomenon that is also known as canyon effect. For the GAUSS spectrum they derived [132]  ( σ g iT )2  (4.46) φh ( iT ) = cos ( 2π f g iT ) ⋅ exp  −    2   where f g and σ g  are the offset frequency and the variance of the GAUSS shape, respectively, and T is the sampling time. For the figures presented in [132] (see also Figure 4.9) HUTTER and HAMMERSCHMIDT used f g = 0.8 ⋅ ν max and σ g = 0.07 ⋅ ν max .

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According to GHOGHO et al [105], other correlation models, such as GAUSS and exponential shapes, are used in ionospheric communication and in DOPPLER-radar. The GAUSS shaped S H ( ν ) they give as

SH (ν ) =

σ a2 exp  − ( ν σν )2  ↔ φh ( τ ) = σ a2 exp ( − ( πσν τ )2 ) πσν

(4.47)

which is a function of two parameters: the variance σ a2 (power of the scattered path) and the (RMS) DOPPLER spread σν . This is sometimes used as an approximation to the CLARKE model [105].

4.6.7. Uniform Spectrum As a theoretical case, an assumption of uniform distribution of DOAs on the whole unit sphere would lead to a flat spectrum, where the DOPPLER spectrum is identified as [165] 1 SH (ν ) = (4.48) 2ν max According to [165], both of the above assumptions (JAKES, uniform) on the DOA distribution are invalid but the former is more realistic.

4.6.8. Values Figure 4.10 gives a measured example for a DOPPLER spectrum at 60 GHz that looks more like a JAKES spectrum than a GAUSS or uniform spectrum.

Figure 4.10: DOPPLER spectrum plot for a 60 GHz receiver moving at a constant velocity of 0.01 m/s (Figure 2.16 from [14]).

A walking speed 1 m/s and carrier frequency f C = 60 GHz would theoretically lead to ν max = 200 Hz . DOPPLER measurements have been reported in [113] [112]. Horn antennas were used for both transmitter and receiver. In these experiments were people were moving inside a room, the maximum observable DOPPLER frequency was found to be 200 Hz only, the effective DOPPLER spread 150 Hz. These values are confirmed by [91] with the statement, that maximum DOPPLER frequency of a signal modulated on a 60 GHz carrier is around 200 Hz at a normal walking speed of 1 m/s. E.g., for the DQPSK-OFDM system at 60 GHz (subcarrier distance 195.3 kHz) investigated in [91], this leads to a normalised DOPPLER frequency around 2⋅10-3, for which the error floor is lower than 10-9 at high SNR. Thus, the DOPPLER spread due to person’s movement has no substantial influence on the performance and can be neglected in simulations. The authors of [28] refer to [253] when stating, that if persons move at a speed of 1.5 m/s (walking speed) then the DOPPLER spread that results at 60 GHz is 1200 Hz. However, they conclude that this can be considered as a worst-case value, it practice it will be much less. SMULDERS itself [253] calculated for a typical indoor environment for a carrier frequency f C = 60 GHz the following: A ray reflecting from a moving object having a speed of 5 m/s may experience a DOPPLER shift of 2 f C ⋅ v c0 = 2 kHz . Hence, the presence of many objects moving at various speeds up to 5 m/s may result in a DOPPLER spread of about 4 kHz. In [150] a vehicular velocity of 50 km/h or 13.9 m/s is assumed, which constitutes the highest possible speed of for example an indoor fork truck in a warehouse environment. This worst-case speed was employed in order to provide performance results characterising the worst possible scenario in the context of adaptive OFDM transceivers, which are sensitive to rapid CIR or transfer function variations. This speed leads to a maximum DOPPLER frequency of about 2.8 kHz, which might not be negligible anymore. 33/160

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4.7 TOA Multipath Shape Factors 4.7.1. Introduction One family of parameters characterising the CIRs temporal behaviour are the delay or Time-of-Arrival (TOA) parameters. TOA parameters characterise the time dispersion of a multipath channel. The TOA parameters include, e.g., mean excess delay, τ , and RMS delay spread, σ τ , which are the statistical measures of the time dispersion of the channel. Note that in practice, the values for these parameters depend on the choice of noise threshold used to process the power delay profile. The noise threshold is used to differentiate between received multipath components and thermal noise. Thus, if the thermal noise is set low, then noise is processed as multipath, thus giving values that are artificially high (see Figure 4.11) [156].

PDP

X dB

τ

τ max , X Figure 4.11: Illustration of time dispersion parameters (from [156]).

Figure 4.12: Detailed illustration of Maximum Excess Delay.

For the next subsections, the following definitions shall hold: • τ i : (excess) delay; the time delay between the first detectable arriving signal and the i -th multipath component of a PDP; that is, the delays are measured relative to the first arriving resp. detectable component (thus, τ 0 = 0 ) • N : total number of multipath components. • β i = hi : amplitude of the i -th channel tap (often given relative to the amplitude of the first or maximum arriving component). • P ( τ i ) = Pi : power of the i -th multipath component (often given relative to the power of the first or maximum arriving component)

4.7.2. Maximum Excess Delay The maximum excess delay τ max , X (also “excess delay spread”, “component delay span”, “delay interval”, “multipath spread”, “multipath delay spread”, “”) defines the interval from first time the power of the impulse response exceeds a given threshold to the last time it falls below this threshold, i.e. the difference in propagation time between the longest and shortest significant path.

τ MAX , X = max τ j j

Pj ≥ X

− minτ j j

Pj ≥ X

(4.49)

This threshold X , specified in dB ( X dB; e.g. 30 or 35 dB) is hereby defined relative to the tap with maximum energy (see Figure 4.12). Notice that the tap with maximum energy is not necessarily the first arriving tap [65] [100] [139] [156] [177] [286]. A common approximation for τ max is the range of τ values over which the scattering function S ( τ ,0 ) is roughly nonzero [109].

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4.7.3. Mean Excess Delay and nth Moment The n -th moment of a spectrum is defined as [76] [139] +∞

τ = n

n ∫ τ ⋅ S H ( τ ) dτ

−∞ +∞

+∞

=

∫ S H ( τ ) dτ

∫τ

n

⋅ φh ( τ ) dτ

−∞ +∞

(4.50)

∫ φh ( τ ) dτ

−∞

−∞

The mean excess delay τ (or “centroid” [76]; also “mean delay”, “average channel delay spread”) is the first order moment of the power delay profile (in other words: the power weighted average of excess delays [177]). Thus, the mean excess delay is defined for continuous respectively discrete time as [14] [65] [76] [90] [126] [142] [156] [165] [228] [246] [291] [293] [302] +∞

τ =

∫ τ ⋅ φh ( τ ) dτ

−∞ +∞

+∞

=

∫ φh ( τ ) dτ

2 ∫ τ ⋅ h ( τ ) dτ

−∞ +∞

∫

−∞

N −1

resp. τ =

∑ τ i ⋅ βi2

i =0 N −1

∑

2

h ( τ ) dτ

i =0

−∞

N −1

=

∑ τ i ⋅ h (τ i ) 2

i =0 N −1

∑

βi2

i =0

h (τi )

(4.51)

2

and with respect to the first arriving path if τ 0 ≠ 0 [188] N −1

τ =

∑ ( τ i − τ 0 ) ⋅ βi2

i =0

N −1

∑

i =0

(4.52)

βi2

4.7.4. Fractional Energy-Delay Window The Fractional Energy-Delay Window τ FED (also “Sliding Delay Window”, “Time Delay Window”) gives the length of the shortest portion of the CIR containing a certain percentage (e.g. 90 %) of the total energy found in that CIR [177] [286].

4.7.5. Fixed Delay Window The Fixed Delay Window τ FDW is the length of the middle portion of the CIR containing a certain percentage of the total energy found in each impulse response [177].

4.7.6. RMS Delay Spread There are many measures of multipath activity in the wideband channel, but the most suitable in this instance is the RMS Delay Spread στ (often also denoted as τ rms ) which has the combined advantages of being easy to compute and also being widely used in the field thus enabling comparisons to be made with other results [64]; it is a “one-number representation” of an impulse response profile [126]. Characterising the channel RMS delay spread helps to determine whether the channel is flat fading (all frequencies within the channel bandwidth experience approximately the same degree of fading) or frequency-selective fading (frequencies within the channel bandwidth will experience various degrees of fading) [14] [198]. The RMS delay spread στ is the square root of the second (order) central (or centred) moment of the power delay profile (or: the power-weighted standard deviation of the excess delays [177]) and is defined for continuous respectively discrete time as [14] [25] [63] [65] [76] [90] [109] [126] [139] [142] [156] [165] [188] [226] [228] [246] [291] [293] [302]

σ τ = τ 2 − ( τ )2 +∞

στ =

∫

−∞

(4.53)

+∞ 2

2

h ( τ ) ⋅ ( τ − τ ) dτ =

+∞

∫

−∞

2

h ( τ ) dτ

∫ φh ( τ ) ⋅ ( τ − τ )

−∞

+∞

∫ φh ( τ ) dτ

−∞

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+∞ 2

dτ =

∫τ

2

−∞ +∞

⋅ φh ( τ ) dτ

∫ φh ( τ ) dτ

−∞

−τ 2

(4.54)

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where τ 2 is the second moment of the excess delay +∞

∫ τ ⋅ φh ( τ ) dτ

+∞

2

τ2 =

−∞ +∞

∫ φh ( τ ) dτ

−∞

=

N −1

2 2 ∫ τ ⋅ h ( τ ) dτ

−∞ +∞

∫

resp. τ 2 =

∑ τ i ⋅ βi2

i =0 N −1

∑

2

h ( τ ) dτ

i =0

−∞

βi2

N −1

=

∑ τ i ⋅ h (τi ) 2

i =0 N −1

∑

i =0

h (τi )

(4.55)

2

As one can see, strong echoes (relative to the LOS path) with long delays contribute significantly to στ . So στ is a good measure of multipath spread; it gives an indication of the potential for intersymbol interference [126] [226]. The RMS delay spread is related to the frequency selectivity of a wideband multipath channel [76]. According to [65], [139], and [198], one rule of thumb to determine presence of frequency selectivity is to calculate the normalised RMS delay spread, ϑRMS , defined as

ϑRMS =

στ

(4.56) TS where TS is the symbol period. Values of ϑRMS bigger than 0.1 indicate presence of frequency selectivity within the channel and the signal suffers ISI. In other words: A channel can be considered essentially flat fading when ϑRMS is less than 0.1.

Example (taken from [246]): Assuming a channel with exponentially decaying power delay profile according to (normalised) 1 τ φh ( τ ) = exp  −  τP  τP  it is shown in [246] that there follows for an infinite length of the channel impulse response στ = τ P and also

τ =

1

τP

∞



(4.57) (4.58)

τ 

∫ τ ⋅ exp  − τ P  dτ = τ P

(4.59)

0

It is very difficult to estimate τ P explicitly, in contrast, it is very easy to estimate the RMS channel delay spread. For limited impulse responses the RMS delay spread is given as a function of τ P and the maximum length η of the impulse response:

στ =  τ P2 − e −η τ P ( η 2 + τ P2 ) − e − 2η τ P ( η 2 − τ P2 ) − e −3η τ P ( η + τ P )2  (4.60) It can be seen that the delay spread of the channel is always smaller than τ P . For large η it is important to take into account, that στ and τ P become equal. If the delay spread is estimated, to corresponding τ P is always larger than the delay spread. 0.5

4.8 AOA/DOA Multipath Shape Factors 4.8.1. Introduction Similar to the fact that a wideband receiver separates multipath components by their TOAs, a narrowbeam antenna allows spatial separation of multipath components by their Angles of Arrival (AOA). As shown in Figure 4.13, when the antenna beamwidth increases, the received signal is the vector summation of the multipath components that arrive within the antenna beamwidth. As TOA parameters characterise the temporal properties of the received multipath signal, there can be defined AOA parameters that characterise the spatial properties of the received multipath signal. That means AOA parameters characterise the directional attribution of multipath power [291].

Figure 4.13: Spatial resolution of Rx antenna (Figure 9 from [291]).

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For typical terrestrial propagation, radio waves arrive at the receiver from azimuthal directions about the horizon [102]. Channel AOA information can be characterised by the angular distribution of the multipath power, p ( θ ) , where θ is the azimuthal angle in the range of [ 0,2π ] . LAITINEN gives in [165] a somehow different argumentation: Signal spreading in the DOA (Direction of Arrival) domain is described by the DOA power spectrum that, assuming a finite number of propagation paths, is discrete. However, as the receiver moves, the path DOAs change, some paths pass away, new paths arise, and consequently the DOA spectrum also changes ultimately resulting in a continuous average spectrum. It is reasonable to assume that the DOA spectrum is uniform in the azimuth angle since a mobile receiver may take an arbitrary orientation in the horizontal plane. The elevation spectrum, on the other hand, is not uniform and depends on the environment. High elevation angles, for example, can be found in environments characterised by high buildings or in indoor environments where reflections from the ceiling are possible. As shown in [73], angular spread, angular constriction and maximum fading angle are the three key parameters to characterise the small scale fading behaviour of the channel. They can be used for diversity technique, fading rate estimation, and other space-time techniques.

4.8.2. Mean Angle Analogously to mean delay a mean (elevation or azimuthal) angle can be defined as the first central moments of the (elevation or azimuthal) spectrum [165] [175] [291]: N

∑ P ( θi )θi i =1 N

θ =

(4.61)

∑ P ( θi ) i =1

where θi , P ( θi ) are the AOA and power of the i

th

multipath component, respectively.

4.8.3. RMS Angular Spread Following [165] and [291], similar to RMS delay spread, (elevation or azimuthal) angular dispersion is characterised by RMS angular spread, σ θ , being defined as the second central moment of the (elevation or azimuthal) spectrum as following [165] [175]:

σθ = θ 2 − ( θ

)

2

(4.62)

where N

θ2 =

∑ P ( θi )θi2 i =1 N

(4.63)

∑ P ( θi ) i =1

where θi , P ( θi ) are the AOA and power of the i

th

multipath component, respectively.

4.8.4. Angular Spread An alternative angular spread definition is proposed in [72] [73] [76]. The shape factor angular spread, Λθ , is a measure of how multipath concentrates about a single azimuthal direction [76]. Angular spread is mathematically defined as following [72] [76] [291]

Λθ = 1 −

F1

2

F0

2

(4.64)

2π

Fn =

∫ P ( θ ) exp ( jnθ ) dθ

(4.65)

0

where Fn is the n th complex FOURIER coefficient of the angle spectrum P ( θ ) . There are several advantages to defining angular spread in this manner. First, since angular spread is normalised by F0 (the total amount of local average received power), it is invariant under changes in transmitted power. Second, 37/160

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Λθ is invariant under any series of rotational or reflective transformations of P ( θ ) . Finally, this definition is directly related to spatial selectivity in a narrow-band multipath channel and thus it is intuitive: larger values of angular spread imply higher spatial selectivity. Angular spread ranges from 0 to 1, with 0 denoting the extreme case of a single multipath component from a single direction and 1 denoting no clear bias in the angular distribution of received power. [72] [76]

4.8.5. Angular Constriction According to [291], the angular constriction, γ θ , is also defined based on Eqn. (4.65), the FOURIER transform of the angular distribution of multipath power, p ( θ ) , as [73] [76]:

γθ =

F0 F2 − F12

(4.66) F0 2 − F1 2 The shape factor angular constriction, γ θ , is a measure of how multipath concentrates about two azimuthal directions, i.e. it describes how multipath power concentrates about two directions-of-arrival in space. Much like the definition of angular spread, the measure for angular constriction is invariant under changes in transmitted power or any series of rotational or reflective transformations of P ( θ ) . The possible values of angular constriction, γ θ , also range from 0 to 1, with 1 denoting the extreme case of exactly two multipath components arriving from different directions, and 0 representing no clear bias in two arrival directions. Angular constriction is also directly related to spatial selectivity in a narrowband multipath channel: larger values of angular constriction imply spatial selectivity in a local area that is anisotropic, depending on the orientation of movement in space [76].

4.8.6. Maximum Fading Angle According to [291], the maximum fading angle (or “azimuthal direction of maximum fading” [76]), θ max , is also defined based on Eqn. (4.65), the FOURIER transform of the angular distribution of multipath power, P ( θ ) , as [73] [76] 1 θ max = arg ( F0 F2 − F12 ) (4.67) 2 This parameter represents the azimuthal direction in space that a receiver must move to experience the maximum possible spatial selectivity [76].

4.8.7. Maximum AOA Direction According to [291], the maximum AOA direction (or “peak angle of arrival” [76], calculated from the estimate of angle spectrum P ( θ ) ) provides the direction of the multipath component with the maximum power, i.e. the azimuthal angle in which the largest average multipath power is received [76]. It can be used in system installation to minimise the path loss [291].

4.8.8. Example: RICE Channel Model As we have already described in section 5.5.4.3, a RICE channel model results from the addition of a single plane wave and numerous diffusely scattered waves. If the power of the scattered waves is assumed to be evenly distributed in azimuth, then the angular distribution of the channel’s power, P ( θ ) , may be modelled as [76]: PT (4.68) P (θ ) = [ 1 + 2π Kδ ( θ − θ0 ) ] 2π ( K + 1 ) where K is the ratio of specular to diffuse non-specular power (RICE K -factor, see section 5.5.4.3), θ 0 is an arbitrary offset angle, and PT is the total average power. By applying Eqns. (4.64), (4.66), and (4.67), the expressions for Λθ , γ θ , and θ max for this distribution are [76] 2K + 1 K , γθ = , θ max = θ 0 (4.69) 2K + 1 K +1 For very small K -factors, the channel appears to be omnidirectional ( Λθ = 1 and γ θ = 0 ). As the K -factor increases, the angular spread of the RICE channel decreases and the angular constriction increases. This Λθ =

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indicates that the overall fading rate in the RICE channel decreases and that the differences between the minimum and maximum fading rate variances within the same local area but different directions increases. [76] Graphics for this model and some more illustrative examples (two-wave channel model, sector channel model, double sector channel model) can be found in [76].

4.9 Channel Coherence 4.9.1. Coherence vs. Selectivity Wireless channels may be functions of time, frequency, and space. The most fundamental concept in channel modelling is classifying the three possible channel dependencies of time, frequency, and space as either coherent or selective. Fading is a general term used to describe a wireless channel affected by some type of selectivity. A channel has selectivity if it varies as a function of either time, frequency, or space. The opposite of selectivity is coherence. A channel has coherence if it does not change as a function of time, frequency, or space over a specified “window” of interest. Channel coherence is an important concept in describing the wireless channel [76]. (RMS) delay spread and coherence bandwidth describe the time dispersive nature of the channel in a local area. They don’t offer information about the time varying nature of the channel caused by relative motion of transmitter and receiver. (RMS) DOPPLER Spread and coherence time are parameters that describe the time varying nature of the channel in a small-scale region [156]. In the next sections we will only discuss temporal and frequency coherence, for spatial coherence and, e.g., the definition of coherence distance see [76].

4.9.2. Coherence Time Let us first concentrate on the effects observed in the time domain. Since multipath signals arrive at the receiver with different delays, the received symbols are spread in time, which may cause adjacent symbols to overlap [25]. The phenomenon is known as inter-symbol interference (ISI) [14] [25] [61] [65] [109] [171] [215] [240]. When the data are transmitted at a slow rate, the symbol duration is long compared to the delay spread caused by the channel, and the receiver can easily resolve the transmitted symbols. However, when the data are transmitted at a high rate, the receiver is not able to resolve the adjacent symbols, because they overlap significantly. This is how multipath propagation spreads the signal in time making high bit-rate transmission difficult to achieve [25]. The (channel) coherence time Tcoh (also denoted as ( ∆t )c or Tc ; also named “correlation time”) is the time domain dual of (RMS) DOPPLER spread and is used to characterise the time varying nature of the frequency dispersiveness of the channel in the time domain. It is proportional to the inverse of the DOPPLER frequency [65]. Coherence time represents the time duration for which the channel impulse response is essentially invariant; i.e. the time during which received signals have a strong level of amplitude correlation [14] [25] [156] [229] [253], thus, during coherence time the channel impulse response is essentially invariant [156]. Therefore, if two signals arrive with a time separation greater than the coherence time, they will be affected differently by the channel. If the symbol period of the baseband signal (reciprocal of the baseband signal bandwidth) is greater than the coherence time, then the signal will be distorted, since channel will change during the transmission of the signal [156]. Following MOLISCH & STEINBAUER [194], the true relationship between coherence time Tcoh ,k of (correlation-) level k and (RMS) DOPPLER spread σν is an uncertainty relationship: arccos ( k ) Tcoh ,k ≥ . (4.70) 2πσν The equality is valid for a DOPPLER power spectral density (DoPSD) that consists of two discrete equal energy components on the v -(speed) axis. In the context of physical DoPSDs, the classical (JAKES’) DoPSD in connection with a RAYLEIGH-fading channel is most similar to this, which gives σν = ν max 2 [194]. When aiming at a correlation level k = 0.5 this gives 1 1 1 Tcoh ,0.5 = = ≈ (4.71) 6 ⋅ σ v 3 2 ⋅ ν max 2π ⋅ σ v which is rather conservative [194]. 39/160

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ANDERSON [14] uses the definition given by STEELE [261]: If coherence time is defined as the time for which two received signals have an amplitude correlation greater than 0.5, then it is approximately: 9 Tcoh ≈ (4.72) 16π ⋅ ν max DURGIN [76] uses the quantity 1 e ≈ 0.37 (which is also favoured by ZWICK [302]) to describe envelopes that have sufficiently decorrelated and gives for coherence time of the RAYLEIGH fading channel 1 1 (4.73) Tcoh = ≈ 46 ⋅ σν 6.78 ⋅ σν However, DURGIN [76] presents also a “new” coherence time rule-of-thumb 1 Tcoh ≈ (4.74) 5 ⋅ σν which according to him agrees with rule-of-thumb estimates presented in [228]. FLAMENT [90] also refers to [228] b 9 Tcoh ≈ , b≈ …1 (4.75) 16π ν max But – according to DE SOUZA [65] – RAPPAPORT [228] also defines the coherence time as the geometric mean of the two coherence time definitions (4.72) and (4.77) 1 9 3 0.423 . (4.76) Tcoh = ⋅ = ≈ ν max 16π ⋅ ν max 4 π ⋅ ν max ν max A further expression given is [156] 1 Tcoh = (4.77)

ν max

Another approach is to define the coherence time as the average measure of the time over which the phase difference between the two received signals does not change more than λ 2 . The coherence time is then expressed by Tcoh = ( λ 2 ) v where v is the velocity of the receiver [25]. With ν max = v λ one obtains [25] 1 Tcoh = (4.78) 2 ⋅ ν max This popular rule of thumb can also result from the following consideration [139]: When observing the fading behaviour in measurements, the distance between two nulls of the fading signal is half a wavelength (which is approximately the distance where the signal remains correlated). Thus the time required to traverse a distance λ 2 when travelling at velocity v is [139] λ 2 1 Tcoh ≈ = (4.79) v 2 ⋅ ν max SMULDERS [253] let Tcoh correspond to the time separation for which φH ( ∆t ) = 0.5 ⋅ φH ( 0 ) . When assuming that S H ( ν ) has the shape of a GAUSS curve, then it occurs from Eqn. (4.22) that 4 Tcoh = (4.80) BD Thus for a DOPPLER spread of 4 kHz assumed by SMULDERS (see section 4.6.8) a coherence time of about 1 ms results Coherence time is also defined based on the DOPPLER spread, in [25], [109], and [287] as 1 Tcoh ≈ (4.81) BD (in [287] with BD = σ v ), whereas in [100] it is defined as 1 Tcoh = (4.82) 2 BD The inverse relationship Tcoh ∝ 1 BD arises – according to [139] – because S H ( ν ) and φH ( ∆t ) are related through the FOURIER transform. According to [25], more details on coherence time definitions can be can be found in [108].

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DURGIN [76] notes that many of the definitions of coherence time depend solely and inversely on the RMS DOPPLER spread, σν . The other fine details and structure of the DOPPLER spectrum, S H ( ν ) , do not greatly effect temporal channel coherence. But neither BD nor Tcoh are exact quantities; their purpose is to provide a guideline for how quickly the channel is changing, and to see that this time is inversely related to the DOPPLER spread [100]. Small-scale Fading (based on RMS DOPPLER Spread)

Fast Fading 1. high RMS DOPPLER Spread 2. Coherence Time < Symbol Period 3. Channel Variations faster than Baseband Signal Variations

Slow Fading 1. low RMS DOPPLER Spread 2. Coherence Time > Symbol Period 3. Channel Variations smaller than Baseband Signal Variations

Figure 4.14: Classification of fading (adapted from [156]).

The time-variant behaviour is categorised into fast fading and slow fading: 1. A channel is said to be fast fading if Tcoh Tsym , where Tsym is the symbol time. During fast fading, the baseband symbol shapes can be severely distorted, which often results in an irreducible BER and synchronisation problems [139]. The “ ”-symbol has a loose meaning; it might mean Tsym < 10−1 ⋅ Tcoh or Tsym < 10−2 ⋅ Tcoh [253]. 2. A channel is referred to as slow fading if Tcoh Tsym . The time duration that the channel remains correlated is long compared to the transmitted symbol. The primary degradation in a slow fading channel is the loss of SNR [139].

4.9.3. Coherence Bandwidth The time dispersive effects of a channel also result in another very important effect: a non-constant frequency response of the channel [9], which means frequency selectivity [25]. Due to multipath propagation, the channel influences the transmitted signal causing enforcement at some frequencies and suppression (deep fades) at others [25]. Again, if ∆t = 0 in Eqn. (4.16), the derived function φH ( ∆f ) ≡ φH ( ∆f ,0 ) (which is the spaced-frequency correlation function from section 4.5) is the FOURIER transform of the multipath intensity profile. It provides the information about the channel’s coherence in the frequency domain [25]. The measure for this coherence is called the coherence bandwidth of the channel Bcoh (also denoted as ( ∆f )c or Bc ), which is one of the key performance indicators. Coherence bandwidth can be measured indirectly from wideband time measurements by taking the FOURIER transform of the average PDP [60], or it can be measured directly from frequency sweeping measurements using VNA. Figure 4.15 depicts a typical transfer function (magnitude only) as typically encountered at 57 GHz with omnidirectional antennas. The figure shows some dips in the order of 20 to 30 dB. It can be seen that the –30 dB dip has a width of about 5 MHz [28]. The coherence bandwidth Bcoh (also: “coherent bandwidth”, “correlation bandwidth”) of the channel is a statistical quantity derived from the RMS delay spread and frequency correlation Figure 4.15: Frequency response at 57 GHz (Figure 4-3 from [28]). function [14] and can be loosely defined as the maximum frequency difference for which two sinusoids are still strongly correlated [253] [256]. In other words: The coherence bandwidth is a statistical measure of the range of frequencies (the statistical average bandwidth) of the radio channel over which the signal spectral components are strongly correlated, they pass 41/160

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with approximately equal gain and linear phase [14] [65] [250] [228] [291], the channel can be considered “flat” [156]. The coherence bandwidth is an important measure in the characterisation of the channel since it gives an indication whether the channel is frequency selective or frequency non-selective with respect to the bandwidth of the transmitted signal. If a wideband signal is transmitted through the channel, i.e. if BS Bcoh , where BS is the bandwidth of the transmitted signal, different frequencies of the signal spectrum are affected by the channel differently, thus the signal is severely distorted by the channel (the wideband channel is said to be frequency selective [25] [65] [109] [139], there occurs frequency-selective fading [76] [109] [139]), transmission bandwidth channel protection techniques, such as coding, diversity or equalisation need to be employed [250]. Bcoh (“narrowOn the other hand, if a narrowband signal is transmitted through the channel, i.e. if BS band condition” [124]), all of the frequency components in the transmitted signal undergo the same attenuation and phase shift so that no channel distortion occurs; then the channel is said to be frequency non-selective [25] [124] [139], it has frequency-flat fading [76] [139], we have a narrowband channel [165]. Thus fading across the entire signal bandwidth is highly correlated, i.e. the fading is roughly equal across the entire signal bandwidth [109]. Note that flat fading is not a property of the channel alone, but of the relationship between BS and Bcoh [100]. Flat fading is not always desirable; for example, to achieve frequency diversity for two fading signals, it is necessary that the carrier spacing between the two signals is larger than the coherence bandwidth, so that the two signals are uncorrelated [139]. Small-scale Fading (based on RMS Delay Spread)

Flat Fading 1. BW of Signal < BW of Channel 2. RMS Delay Spread < Symbol Period

Frequency Selective Fading 1. BW of Signal > BW of Channel 2. RMS Delay Spread > Symbol Period

Figure 4.16: Classification of fading (adapted from [156]).

In the frequency-non-selective case, the multipath components arrive within a short fraction of the symbol time, so that the channel can be well modelled by a single ray and the input/output relationship can be expressed as a multiplication, whereas for a frequency-selective channel, the input/output relationship is a convolution in the τ domain [139]: y( t ) = h(t ) x(t ) flat channel (4.83) y ( t ) = h ( τ , t ) ∗ x ( t ) frequency-selective channel If BS ≈ Bcoh then the channel behaviour is somewhere between flat and frequency-selective fading [109]. Following MOLISCH & STEINBAUER [194], the true relationship between coherence bandwidth Bcoh ,k of (correlation-) level k and RMS delay spread σ τ is an uncertainty relationship: arccos ( k ) . (4.84) Bcoh ,k ≥ 2π ⋅ σ τ The equality sign is only valid for a two-delay channel model, where both paths have equal power (in other words, for the model that gives the largest delay spread for a given maximum excess delay) [194]. In principle, a larger RMS delay spread implies increased frequency selectivity and a smaller coherence bandwidth [76]. By assuming a channel with an one-cluster delay power spectral density (e.g. a channel with an exponential delay profile) and a correlation level k = 0.5 the following (rather conservative) relation is often used for the (amplitude) coherence bandwidth (see also JAKES [137]) [194] (so in principle also in [124] [165]): 1 1 Bcoh ,0.5 = ≈ . (4.85) 6 ⋅ σ τ 2π ⋅ σ τ For the phase coherence bandwidth follows in this case [194] 1 1 Bcoh ,0.5, phase = ≈ . (4.86) 12 ⋅ σ τ 4π ⋅ σ τ 42/160

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As to [253], according to the definition given by JAKES [137] the coherence bandwidth corresponds to the frequency separation when φH ( ∆f ) = 0.5 . In case φh ( τ ) ∝ exp ( −τ σ ) , which is in many cases a good approximation [137], then it can be readily shown that [253] 3 Bcoh = (4.87) π ⋅ στ Several other different definitions for coherence bandwidth exist, with the only difference being how stringent the requirements are set for the amplitude correlation function [14]. According to ANDERSON [14] and XU [291], LEE [174] [173] has shown that, as a rule of thumb, the correlation bandwidth with correlation level of 0.9 is related to RMS delay spread by: Bcoh ,0.9 = min [ ∆f ] such that φH ( ∆f ) = 0.9 (4.88) 1 (4.89) 50 ⋅ σ τ According to ANDERSON [14], other common definitions ([61], [229], [279]) relax the degree of amplitude correlation to be greater than 0.5 or 0.7; they are listed below. Bcoh ,0.7 = min [ ∆f ] such that φH ( ∆f ) = 0.7 (4.90)

Bcoh ,0.9 ≈

Bcoh ,0.5 = min [ ∆f ] such that φH ( ∆f ) = 0.5

(4.91)

1 (4.92) 5 ⋅ στ The latter approximation is also given by DURGIN [76] as arbitrary rule-of-thumb; it is also called 50 % coherence bandwidth [156]. DURGIN [76] also uses the quantity 1 e ≈ 0.37 to describe envelopes that have sufficiently decorrelated and gives for coherence bandwidth of the RAYLEIGH fading channel 1 1 (4.93) Bcoh = ≈ ⋅ στ 6.78 46 ⋅ σ τ According to JERUCHIM et al [139] it can be shown that Bcoh and τ MED are reciprocally related, which leads as rule of thumb to 1 Bcoh ≈ (4.94)

Bcoh ,0.5 ≈

τ MED

The same approximation is given by GOLDSMITH [109], whereas GALLAGER [100] gives the relationship 1 Bcoh = (4.95) 2 ⋅ τ MED as an order of magnitude relation, essentially pointing out that frequency coherence is reciprocal to multipath spread. Further referring to JERUCHIM et al [139], a general relationship between the coherence bandwidth and RMS delay spread does not exist and must be derived from actual dispersion characteristics of particular channels. For the case of mobile radio, an array of radially uniformly spaced scatterers, all with equal-magnitude reflection coefficients, but independent, randomly occurring phase angles is widely accepted. This model is referred to as the dense scatterer model and is commonly known as the JAKES model (see also section 4.6.4.3). For this channel the coherence bandwidth is defined as the bandwidth interval over which the channel’s transfer function has a correlation of at least 0.5, and can be shown to be ([228]) 0.276 1 Bcoh = ≈ (4.96) στ 5 ⋅ στ KAMMEYER [142] presents the definition 1 Bcoh = . (4.97)

στ

FLAMENT [90] refers to RAPPAPORT [228] for the generalisation 1 , a ≈ 5…50 Bcoh ≈ a ⋅ στ So again there are quite a number of definitions that one should be conscious of.

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4.10 Summary of Correlation Functions and Power Densities The summary of all introduced functions together with relations between them for the nondirectionalnonspatial case is presented in Figure 4.17.

RMS DELAY SPREAD

COHERENCE BANDWIDTH

στ

Bcoh

SPACED-FREQUENCY CORRELATION FUNCTION

φH ( ∆f )

τ ↔ ∆f

∆t = 0 DELAY CROSS-POWER SPECTRAL DENSITY

φh ( τ , ∆t )

FT

FT

TIME-VARIANT

h (τ , t )

∆f = 0

φH ( ∆f , ∆t )

SPACED-TIME CORRELATION FUNCTION

COHERENCE TIME

φH ( ∆t )

Tcoh

(WSSUS)

TIME-VARIANT

FT

τ ↔ f

∆t ↔ ν

CHANNEL TRANSFER FUNCTION

H ( f ,t )

∆t ↔ ν

SCATTERING FUNCTION

Sh ( τ ,ν )

SPACED-FREQUENCY SPACEDTIME CORRELATION FUNCTION

ACF of f

τ ↔ ∆f

CHANNEL IMPULSE RESPONSE

characterisation of time variations (narrow-band)

∆t = 0

ACF of t

(WSSUS)

wide-band characterisation (time-invariant channel)

FT

φh ( τ )

FT

FT

MULTIPATH INTENSITY PROFILE (DELAY POWER SPECTRUM)

FT

τ ↔ f

DOPPLER CROSS-POWER SPECTRAL DENSITY

S H ( ∆f ,ν )

∆t ↔ ν ∆f = 0

DOPPLER POWER SPECTRUM

SH (ν )

RMS DOPPLER SPREAD

σν

Figure 4.17: Relations among the channel correlation functions and power spectra (after Figure 1 from [289] and Figure 1-5 from [25]).

For details on the correlation functions and power densities when introducing spatial and angular extensions see [76], [145], [238], and [302].

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5. Fading 5.1 Introduction The most notable manifestation of multipath propagation are the fluctuations in the envelope of a received radio signal caused by the superposition of all multipath signals, which can lead either to signal enforcement or to radical signal cancellation. This gives rise to the general term (multipath) fading [25] [65] [156]. However, when speaking of such fluctuations, one must consider whether a short observation interval (or small distance) has been taken, or whether a long observation interval (or large distance) has been taken. For a wireless channel, the former case will show rapid fluctuations in the signal’s envelope, while the latter will give more of a slowly varying, averaged view. For this reason the first scenario is formally called smallscale fading, while the second scenario is referred to as large-scale fading or path loss. The converse of small-scale fading, large-scale fading, refers to fluctuations in spatially averaged received power due to shadowing and scattering of objects in the propagation environment. Typically, small-scale fluctuations occur when a receiver moves a distance comparable to the size of the electromagnetic wavelength of the carrier. Large-scale fluctuations occur when the receiver moves over many wavelengths. The principle of small-scale and large-scale fading for a received signal level as a function of position is illustrated in Figure 5.1 [76].

Figure 5.1: Principle of small-scale and large-scale fading (Figure 2.8 from [76]).

Figure 5.2: SIR along the hallway path at 60 GHz (from [91]).

In Figure 5.2 a real example measured by FLAMENT [91] in a large office scenario at 60 GHz is given. The scenario was composed of a number of rooms and a hallway. The hallway was three meters wide and the rooms were six by six meters. The user walking along the hallway experiences a large variation of the SIR (signal-to-interference ratio) ranging from almost no interference (25 dB) to –20 dB (see). However, the problem is not the range of the SIR values, but rather its occasionally rapid change within a short distance (or short period of time). The SIR varies very fast between adjacent small areas. E.g., first there is a drop from 15 dB to –8 dB within 1 cm, followed by a 13 dB raise then coming back under 0 dB after 2 cm [91]. HASHEMI [126] has made a distinction between three types of parameter variations in the channel. 1) 2)

3)

Small-Scale Variations: A number of impulse response profiles collected in the same “local area” or site are grossly similar since the channel’s structure does not change appreciably over short distances. Therefore, impulse responses in the same site exhibit only variations in fine details [126]. Mid-scale Variations: This is a variation in the statistics for local areas with the same antenna separation. As an example, two sets of data collected inside a room and in a hallway, both having the same antenna separation, may exhibit great differences. For amplitude fading, this type of variation is equivalent to the shadowing effects experienced in the mobile environment. Different indoor sites correspond to intersections of streets, as compared to mid-blocks [126]. Large-Scale Variations: The channel’s structure may change drastically, when the base-portable distance increases, among other reasons due to an increase in the number of intervening obstacles. As an example, for amplitude fading, increasing the antenna separation normally results in an increase in path loss. For the amplitude as parameter, this type of variation is equivalent to the distance dependent path loss experienced in the mobile environment.

The degree of a parameter’s variations depend on the type of environment, distance between samples, and on the specific parameter under consideration. This parameter (represented by a random variable) of the channel at a fixed point in the three-dimensional space might be, e.g., the amplitude of a multipath component at a 45/160

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fixed delay in the wide-band model, amplitude of a narrow-band fading signal, the number of detectable multipath components in the impulse response, the mean excess delay or delay spread, etc. For some parameters, one or more of these variations may be negligible [126]. All three types of fading have to be taken into account in the link budget analysis as depicted in Figure 5.3. In order to estimate the link budget one has to start with calculation of the path loss at a particular distance. On top of that, the shadowing effect marks its presence as a random component. Furthermore, the small-scale fading effect is contributing to the received signal power superimposed on top of the shadowing effect [25].

Figure 5.3: Link-budget considerations for fading channels (Figure 1-9 from [25] following [108]).

In connection with channels and their fading behaviour in many references and within this study the term „local area“ is used, which often is a quite nebulous thing. Following DURGIN [76], a local area is the largest volume of free space about a specified point in which the radio channel can be modelled accurately as the sum of homogeneous plane waves. The proximity of the local area to significant scatterers usually determines the acceptable size of the local area. If LA denotes the size of the local area, the following relationship must hold [76]: LA f C < (5.1) λC B In words: the ratio of the local area size to the wavelength of radiation must be less than the ratio of the carrier frequency to the signal bandwidth. Table 5.1: Maximum size of a local area according to the bandwidth-distance threshold for example wireless applications (adapted from Table 3.1 from [76]). Wireless Application

Carrier Frequency [GHz]

Signal Bandwidth [MHz]

Local Area Size [m]

Analogue Cellular Channel

0.84

0.03

28000 λC

10 k

PCS Spread-Spectrum Channel

1.91

1.25

1528 λC

240

HIPLERLAN/2

5.2

20

260 λC

15

NII Campus Link

5.7

100

57 λC

3

LMDS Link (proposed)

28

500

56 λC

0.6

BROADWAY HS/C

60

20

3000 λC

15

BROADWAY HS/E

60

80

750 λC

3.75

BROADWAY HS/E

60

240

250 λC

1.25

Propagation models that predict the mean signal strength for an arbitrary transmitter-receiver separation distance facilitate estimation of radio coverage area and are referred to as large-scale propagation models [159]. On the other hand, propagation models that characterise the rapid fluctuations of the received signal strengths over very short distances or short time durations are called small-scale fading models [159].

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5.2 Large-scale Fading and Path Loss 5.2.1. Introduction The term large scale fading denotes the variations of the mean amplitude or mean power of a received signal when a time- or space-variant multipath channel is used as the transmission medium [28]. The mean amplitude or power remains approximately constant within a certain interval of time or space; this interval has been determined to be around a few tens of a wavelength [156] [213] for the mobile radio channel. As the mobile moves away from the transmitter over larger distances, the local average received signal will gradually decrease; this is called large-scale path loss [156]. While the impulse response approach is useful in characterisation of the channel at a microscopic level, path loss models describe the channel at a macroscopic level. Path loss information in indoor and outdoor environments are essential in determination of a first order approximation of the size of the coverage area for radio communication systems [8] [156], in selecting optimum locations for base antennas and for calculating the carrier-to-interference ratio between cells using the same frequencies. Obtaining three-dimensional propagation contour plots using a site plan or building’s blueprint and the knowledge of its construction material is a challenging job that requires detailed and reliable path loss models [126]. The term "path loss", denoted by L path (sometimes also PL ), is generally used to predict the channelinduced attenuation between a transmitter and a receiver over a propagation path (as a function of the transmitter-receiver distance [14]) due to, e.g., atmospheric attenuation and multipath scattering11. It may be defined as the difference (in dB) between (or ratio of) the effective transmitted power and the received power [159] [177] [291], and may or may not include the effect of the antenna gains [228]. For the purpose of this document, path loss L path is defined as the ratio of the effective transmitted power to the received power, calibrating out all system losses, amplifier gains, and antenna gains. Subtracting out the antenna gains provides the path loss that would be experienced if isotropic antennas were used on the transmitter and receiver, even though directional antennas might actually be employed on the system [15]. The path loss from transmitter to receiver is then given by P (5.2) L path[ dB ] = PTx[ dBm ] + GTx[ dBi ] + GRx[ dBi ] − PRx[ dBm ] or L path = Tx GTx GRx PRx where PTx is the power supplied to the transmitting antenna with a gain of GTx in the direction of the receiving antenna, PRx is the power at the receiving antenna of gain GRx (for antenna gain see also section 5.4.1). Thus, for any given transmitted power, the received signal power can be calculated as [291] PRx[ dBm ] = PTx[ dBm ] + GTx[ dBi ] + GRx[ dBi ] − L path[ dB ] (5.3) Propagation within a building is affected by reflections and attenuations caused by walls, floors, furniture, people and the other components from which the indoor environment is comprised. For an indoor propagation model to be accurate, and in this sense we mean for the model to be able to predict with a suitable accuracy the received power at any location given a certain transmit power from a chosen location, these additional factors must be taken into account. It is additionally useful if the model gives some idea of the propagation mechanisms involved and is not simply a statistical fit of a few measured curves [200]. These statements also hold in principle for outdoor environments and their modelling. According to [89], the total path loss L path consists of several parts: •

the free-space path loss ( L fs ),

•

the floor and walls factors ( L fl , Lwl ),

• loss due to atmospheric absorption ( Latm ) • and slow fading (shadowing) models ( Lsf ). It is calculated in dB as: L path[ dB ] = L fs[ dB ] + Lwl[ dB ] + L fl[ dB ] + Lsf [ dB ] + Latm[ dB ]

(5.4)

Considering the atmospheric absorption, in [159] FREEMAN [97] is referenced, who states that Latm itself is a combination of several absorption/attenuation processes: 11

It should be mentioned, that in the literature often the variable for path loss is named PL .

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• excess attenuation due to water vapour ( Lwv ), • excess attenuation due to mist or fog, • excess attenuation due to oxygen ( Lox ), • sum of absorption losses due to other gases, • excess attenuation due to rainfall ( Lrain ). There are many atmospheric gases and pollutants that have absorption lines in the millimetre bands (such as SO2, NO2, O2, H2O, and N2O), however the absorption loss is primarily due to water vapour and oxygen [276]. According to [135] and [89], the attenuation produced by, e.g., oxygen and water vapour in the atmosphere is described by the specific attenuation for each component, expressed in dB/km. The specific attenuation is found by summing the contributions of each quantum level transition for the molecule. The calculation is a complex evaluation for each value of temperature, pressure, and water vapour concentration. Approximate techniques are available with sufficient accuracy, however, for the determination of specific attenuation due to atmospheric oxygen and water vapour for most practical communication application. Here we also want to include the loss due to foliage L fol into the atmospheric loss, so finally we found:

Latm[ dB ] = Lox[ dB ] + Lwv[ dB ] + Lrain[ dB ] + L fol[ dB ]

(5.5)

In the literature, many adjusted formulas for the path loss exist. E.g., also referring to [28], [110] and [291], path loss at 60 GHz was studied by CORREIA et al in [51], [54], [56]. In [51] and [56], a path loss model on the basis of the path loss exponent model explained later was proposed for outdoor environments for distances below 200 m (the same model is expected to hold in indoor environments, except for rain absorption of course) as follows: L path[ dB ] = 32.4 + 30n + 10n log ( d[ km ] ) + 20log ( f[ GHz ] ) + γ rain[ db/km ] ⋅ d[ km ] + γ ox[ db/km ] ⋅ d[ km ] (5.6) d = L fs[ dB ] ( d 0 ) + 10n log   + ( γ rain[ db/km ] + γ ox[ db/km ] ) ⋅ d[ km ]  d0  where L fs ( d 0 ) is the free-space path loss at reference distance d 0 , n is the path loss exponent, γ rain and

γ ox are the attenuation coefficients due to rain and oxygen absorption, respectively, and d is the Tx-Rx distance. In the next subsections, the several addends of Eqn. (5.4) and (5.5) (and also Eqn. (5.6)) will be presented and discussed, starting with a path loss model division following [126], [200]: Free Space Path Loss Model, Path Loss Exponent Model, and Partition based Path Loss Model. The majority of these models attempt to fit various linear (on a log scale) piecewise approximations to curves of increasing path loss with Tx-Rx separation [200].

5.2.2. Free Space Path Loss Model The term “Free Space” in propagation implies – according to DURGIN [76] – the following three characteristics: 1. There are no current sources or charges present in the medium. 2. The propagation medium is linear, isotropic, and lossless. 3. The material parameters of permittivity and permeability are constants and are equal to that of vacuous space ( ε = ε 0 and µ = µ0 ). It is generally accepted that the atmosphere – despite the presence of gases – behaves as a free-space medium for short-range propagation [76]. The free space path loss model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight path between them (assuming free space propagation and excluding antenna gains). For a path to be LOS, it is necessary that the link is designed to maintain adequate FRESNEL zone clearance between the radio path and the terrain being crossed. This is due to the fact that even if there is clearance between the direct ray and the terrain such that one can optically see the transmitting from the receiving antenna, up to 6 dB diffraction loss can be experienced if the clearance is too small [29]. According to [209], usually LOS radio links require 60 % of the first FRESNEL zone to be free of obstructions to limit diffraction loss. FRESNEL zones represent regions where secondary waves have path lengths that are nλ 2 greater than the line of sight path length, causing constructive and destructive interference to the received signal [14] [229]. 48/160

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The radius of the n -th FRESNEL zone circle, denoted by rn , can be expressed by [14] [29] [228] nλ d1d 2 rn for d1 , d 2 (5.7) d1 + d 2 where λ represents the wavelength of the propagating wave, d1 is the distance from the transmitter to the plane, d 2 is the distance from the receiver to the plane (see Figure 5.4). The path clearance criteria is specified in terms of radius of the first FRESNEL ellipsoid F1 at the most significant path obstruction, i.e. the path obstruction that would cause loss of LOS if the antenna height would be lowered. rn =

Figure 5.4: Concentric circles that define the boundaries of successive FRESNEL zones (from [291]).

According to FRIIS [98], the received signal power PRx is given in terms of the transmitted power PTx by the fundamental relationship (Free-space or FRIIS equation) [29] [126] [156] [200] P λ2 (5.8) PRx = Tx 2 GTx GRx 4π 4π d assuming perfect match between the feeding cable and the antennas at the transmitter and receiver site and with d being the distance between them. Commonly, the first FRESNEL zone should be free of any obstacle for FRIIS formula to hold. The free-space path loss L fs at distance d is therefore given by L fs ( d ) =

PTx 4π d  2 GTxGRx =   PRx  λ 

(5.9)

or in logarithmic form as [14] [228] [291]

4π d  4π d  L fs[ dB ] ( d ) = 20log  f  (5.10) = 20log    λ   c0  where c0 is the speed of light ( c0 = 299 792.458 km/s ). As becomes obvious from Eqn. (5.10) and Figure 5.5 path loss increases tremendously with increasing frequency. This is due to the reduction of the effective area Ae (see also section 5.4.1) of the receiving antenna with increasing frequency. The FRIIS free-space path loss model expressed by Eqn. (5.10) is valid only for distances that are in the farfield, or FRAUNHOFER region of the transmitter antenna. The following relationships define the far-field region [264]: (5.11) d D λ (5.12) d d df (5.13) where d represents the transmitter-receiver (Tx-Rx) separation distance, D is the largest dimension of the antenna, λ is the wavelength. d f is the FRAUNHOFER distance (Eqn. (5.14)) [14] [156] [159] [229] [264]: df =

2D2

λ

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L fs / dB

100

60 GHz

90

38 GHz

80 27 GHz 70

5 GHz

60 50 40 30 20 10

d /m

0 0

1

2

3

4

5

6

7

8

9

10

Figure 5.5: Free-space path loss for different frequencies.

For example, the antennas used on the 60 GHz upconverters in the measurement campaign in [159] are rectangular horns with a diagonal length of 5.8 cm. The corresponding FRAUNHOFER distance is 1.34 meters. If the antennas are separated by a total of 40 meters, then the radius of the first FRESNEL zone at a point midway between transmitter and receiver ( d1 = d 2 = 20 m ) is 0.23 meters [159]. Usually, a close-in distance, d 0 , also referred to as the received power reference point or reference distance, is introduced in path loss expressions. This reference distance is chosen such that it is smaller than any practical distance used in wireless communication systems ( d 0 < d ) and also such that it lies in the far-field region defined by Eqns. (5.11), (5.12) and (5.13) [228], which guarantees that near field effects of the antennas do not influence the reference point [14]. The free-space path loss at a reference distance of d 0 is given by [291] [293] 4π d 0  L fs ,[ dB ] ( d 0 ) = 20log  (5.15)   λ  A typical d 0 value for indoor systems is 1 m [25] [63] [228]. The reference path loss can be defined as a frequency-dependant quantity [8] [14]: L fs ,[ dB ] ( d 0 ) = 20log ( f / MHz ) + 20log ( d 0 / m ) − 27.55 dB (5.16) Combining Eqns. (5.10) and (5.15) gives d  L fs ,[ dB ] ( d ) = L fs ,[ dB ] ( d 0 ) + 20log   d  0 Considering a frequency of 60 GHz and d 0 = 1 m we have: L fs ,[ dB ] = 68.0 + 20log ( d / m )

(5.17) (5.18)

5.2.3. Path Loss Exponent Model and Waveguide Effect Propagation is most often affected by reflections and attenuations caused by walls, floors, furniture, people, trees, etc. In the models used at UHF for the decay of power with separation distance, the slope usually depends on the environment and on break-point distances. These are very simple models based on the interference of a direct and a ground-reflected ray, leading to a simple dependence of the power on distance d between antennas; i.e. PRx ∝ d − n , where n is the decay slope [256] or path loss exponent. On a logarithmic scale, this corresponds to a straight-line path loss with a slope of 10n log d . Both theoretical and measurement-based propagation models indicate this is applicable whether in outdoor or indoor radio channels [89]. HANSEN [121] [122] calculated analytically (using a virtual sources approach) the power delay profile of a single room with homogeneous walls at 60 GHz. It is shown to be an exponential function that depends on the delay spread only, which itself is a function of the wall attenuation and the side length of 50/160

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the room. CORREIA et al [55] performed ray tracing simulations and measurements for a scenario of an urban street with trees at 60 GHz (see also section 6.2.2 on page 102). It came out that the average impulse responses could be approximated by the well-known negative exponential behaviour (or linear decay in dB) Thus average path loss L ( d ) over distance d (such that d > d 0 ) can be described by the path loss exponent model as following [25] [89] [156] [187] [226] [228] [291] [293]: d (5.19) L[ dB ] ( d ) = L fs ,[ dB ] ( d 0 ) + 10n log   d  0 This expression cannot be used for small distances where the antennas patterns will have a great influence (depending on the elevation radiation pattern if the AP antenna is at the ceiling, for instance) [110]. Referring to [63], it is only applicable for LOS conditions. The path loss exponent n is an empirical constant that is often measured, but can also be derived theoretically in some environments. It varies depending upon the radio propagation environment (obstructions between the transmitter and receiver, and multipath propagation change the n value) and characterises the rate at which path loss increases with the increase of Tx-Rx separation for a given propagation scenario [29] [126] [177]. For free-space propagation, n equals 2, which leads back to Eqn. (5.17). In outdoor environments, the average power decays almost as in ideal free space (see FRIIS formula), with path loss exponent close to 2 [51] [258] [285], assuming a direct path plus a reflected ray. According to [110], in [192] (biconical horn receiver antenna, vertically polarised) it is shown that, in outdoor environments, in both line-of-sight and obstructed cases, power is a function of distance but not necessarily of the delay spread. According to [89], the path loss exponent approach tends to lead to large errors in the indoor case, because of the large variability in propagation mechanisms amongst different building types and different path within a single building. In order to make use of the average path loss model, path loss exponents must be determined from measured data by measuring a number of average power losses for a given channel and applying a linear regression to fit the resulting data to Eqn. (5.20) [8] [14] [89]. L50 = A + B ⋅ log ( d ) (5.20) where A and B depend on the environment, ensuring that L50 is the level not exceeded at 50 % of locations at a given distance; in other words, A and B are the coefficients that fit the path loss in the least-square sense, ensuring that the error bounds contain at least 50 % of the predictions. Measurement and simulations results for n taken from literature can be found in Table 6.7 on page 109. Values of n > 2 for the path loss exponent are probably due to large attenuations encountered when transmitted signals have to penetrate walls, ceilings, floors, etc. [126]. Values of n < 2 , i.e. better than free space, are commonly explained by wave guiding effects in hallways, corridors and reverberation effects in rooms due to highly reflective walls (concrete or metal), causing raised power levels by multipath contributions, i.e., reflections from parallel walls can contribute constructively to the received power if their phase differences are small [29] [110] [126] [187] [258]. Referring to XU [291] [293], for the hallway measurements performed there (see also section 6.1.6 on page 95), the received power decreased rapidly when the Tx-Rx separation was increased from 2 to 20 m. After 20 m, the signal power did not decrease appreciably with the increase of the distance. For instance, the received powers at locations 1.5, 1.6, and 1.7 were almost the same, although Tx-Rx distance changed from 40 to 50 and 60 m, respectively. At small distances, the reflected wave components are rejected by the directional receiver antenna and the waveguide effect is not dominant. However, at long distances, reflected wave components are close to the LOS path and are received by the receiver antenna. The total received field is stronger that it should be from free space propagation and the transmitted wave propagates in a guided fashion. According to XU [291], the interplay of the antenna pattern, site geometry and reflected wave components can be explained using the power zone theory [294]. When directional antennas are used, the majority of the radiated energy is concentrated along the LOS path. Power zone plots are developed to characterise the power concentration. When transmitter-receiver separation is relatively small, no obstacles intersect the power zones. Therefore, the received signal power is mainly from the LOS path. As a result, with an increase in distance, the received signal power decreases with a path loss exponent close to 2. However, when transmitter and receiver separation is large, the sidewalls of the hallway and the floor are close to the main power zone, and reflected power contributes to the total received power. The received signal consists of both LOS component and reflected components along the corridor (similar to a waveguide). Therefore, the total received power does not decrease appreciably for larger distances. 51/160

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When studying the great amount of available literature on 60 GHz channel measurements one should be careful when comparing the n -values especially from outdoor campaigns. In some cases, attenuation due to, e.g. oxygen or rain (see sections 5.2.6 and 5.2.8, resp.) are included in n , in other cases not. For example, in [54] results from CW measurements along a street show that if the path loss exponent model Eqn. (5.19) is used, the range for n is from 2.3 to 2.8 for d ∈ [ 0,250 ] m , and from 7.0 to 7.5 for d ∈ [ 1,2 ] km . When model (5.6) is used to separate the effects of oxygen absorption, the n values are in the range from 2.0 to 2.5. According to [200], one common failing in many published studies is to force the 1 m path loss to be the value predicted by the FRIIS equation and then to attempt to fit, for LOS situations, a straight line with a smaller value of n through the measurement points regardless of the true intersection with the ordinate.

5.2.4. Distance-dependent Power Exponent Model In this model, proposed in [10], and referenced e.g. in [126], [200], the received power also follows a d − n law. The exponent n , however, is derived from measurements carried out in a multi-storey office building and changes with distance, 1m < d < 10 m 2  3 10 m < d < 20 m  n= (5.21)  6 20 m < d < 40 m  12 d > 40 m In the measurements reported in [10] the fixed transmitter was located in the middle of a corridor and the portable receiver was placed inside rooms or along other corridors, on the same floor and on other floors. According to [200], the large values of n are probably due to an increase in the number of walls and partitions between the transmitter and receiver when d increases; this type of model works well for a regular layout of rooms but there is a problem of choosing suitable breakpoints when a building with irregularly spaced rooms is considered. Referring to [200], existing HIPERLAN/2 indoor channel modelling has used a simplified approach of this model. At 5 GHz the channel model assumes that the signal decays with an exponent of 2 until a distance of 5 m and then with an exponent of 3.5 from 5 m to infinity with local variations about the mean, typically with a standard deviation of 6 dB [116]. A path loss calculation based on this gives a somewhat optimistic range of 50 m (allowable path loss 95 dB) when compared to the actual measurements reported [200] and in [201]. Due to the high attenuation of obstacles like walls at 60 GHz this model doesn’t seem to be very useful.

5.2.5. Partition Based Path Loss Model In propagation analysis the path loss exponent, n , is useful for predicting large-scale propagation effects. However, the path loss exponent model is inadequate at predicting site-specific propagation effects such as reflection, diffraction, or penetration losses in an environment where transmitter and receiver are separated by various obstructions. For outdoor propagation environments, the obstructions can be exterior walls, trees, or terrain. For indoor propagation environments with particular building layout and construction materials, the obstructions can be interior walls, furniture, walls, doors, etc. [14] [15] [291]. It is found that path loss is highly correlated with the total number and types of obstructions between the transmitter and the receiver [75] [196] [206] [291]. A more refined (pseudo-deterministic) model uses partition-dependant attenuation factors [75] [251]. This model estimates the total path loss as the sum of the free-space path loss and the penetration loss caused by each of the obstructions intersected by a single ray drawn from transmitter to receiver. Then, the path loss is given as follows [75] [228] [291]: M

L ( d ) = L fs ( d ) + ∑ X i

(5.22)

i =1

where X i is the attenuation value (see Table 5.4) of the i th obstruction intersected by a line drawn from the transmitter to the receiver. Note that in the case of free space propagation with no partitions between transmitter and receiver, path loss calculated from Eqn. (5.22) will be identical to path loss calculated from Eqn. (5.10). 52/160

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This model can also be seen as a generalisation of the wall attenuation model and floor attenuation model, which are given in [89] by: Lwl = W f 1 ⋅ n1 + W f 2 ⋅ n2 + + W fw ⋅ nw (5.23) L fl = F f 1 ⋅ m1 + F f 2 ⋅ m2 +

+ F ff ⋅ m f

(5.24)

where nw is the number of walls traversed, W fw is the wall factor of each wall, which depends on the material traversed, m f is the number of floors traversed and F ff is the floor factor of each floor. Referring to [28], quite similar approaches are reported in [148] and [133]. According to [291], results from [75] show that the partition based path loss model effectively reduces the standard deviation of the prediction error as compared to the path loss exponent model. The partition based channel model works well for short transmitter-receiver separations, provided there are a small number of multipath scatterers in the environment. If a significant amount of the received power comes from multipath, then the partition-based model loses its physical significance [15]. One drawback to the partition-based model is the need for site-specific information, consisting of a floor plan that identifies the composition of all walls, doors, and other obstructions; however, future generations of wireless networks may warrant such detail and accuracy [230]. In practice, when the attenuation of a wall increases, the power contribution received through this wall will decrease relative to power contributions received through other paths such as open doors (also to hallways), windows, ventilation ducts etc. [28]. This behaviour is modelled in [57] by a non-linear term Ln , Ln = Lwnw( ( nw + 2 ) ( nw +1 ) − b ) ( dB ) (5.25) where Lw is the wall loss. The parameter b also depends on Lw because with increasing losses per wall, the other (non-penetration) propagation mechanisms quickly become more dominant and therefore the slope of total excess loss due to walls will become less steep [57].

5.2.6. Oxygen Absorption As Figure 5.6 and Figure 5.7 show, oxygen absorption has a peak around 60 GHz (which was the main reason for the choice of the 60 GHz band [89]). This peak of oxygen absorption is very localised in frequency, and the coverage (cell radius) can probably be tuned by choosing adequately the carrier frequency [110].

Figure 5.6: Attenuation for atmospheric oxygen (O2) and water vapour (H2O) as function of frequency (from [135]; also [85] referring to [42]).

Figure 5.7: Attenuation by oxygen and water vapour at sea level. T=20°C. Water content = 7.5 g/m3 (Figure 1.2 from [164], Figure 3.1 from [90]).

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The CCIR [41] gives an expression for its attenuation coefficient for frequencies greater than 63 GHz, or lower than 57 GHz; for frequencies in the middle range an approximation is given, which yield a maximum error of 5 % [29] [56] [89] [110]:  15.10 − 0.104 ⋅ ( f − 60 )3.26 60 ≤ f ≤ 63 (5.26) γ ox[dB/km] ( f[GHz] ) =  2.25 1.27 63 ≤ f ≤ 66 − 5.33 ⋅ ( f − 63 )  11.35 + ( f − 63 ) According to [179], a model for the prediction of the attenuation due to the absorption of oxygen is presented in [13]. This model assumes a standard atmospheric pressure of 1013 mbar and a temperature of 15 °C. There also a correction term for temperature ϑ (in °C) is given [179] ∆γ ox[dB/km] ( ϑ [ °C ] ) = γ ox[dB/km] ( 15 °C ) ⋅ [ −0.01 ⋅ ( ϑ − 15 °C ) ] −20 °C < ϑ < 40 °C (5.27) The path loss ( Lox ) for a given distance ( d ) is given by: Lox[ dB ] = γ ox[ dB / km ] ⋅ d[ km ]

(5.28)

This attenuation can take relatively high values for frequency near the 60 GHz, but it decreases by an order of magnitude when the frequency is near 66 GHz. Table 5.2 summarises the attenuation due to oxygen absorption. Table 5.2: Selected values for oxygen attenuation ([89], for 1 km also [110]). Distance (d) [km] 0.2 0.5 1.0 60 GHz 3.0 7.6 15.1 63 GHz 2.3 5.7 11.4 66 GHz 0.3 0.8 1.7 Loss [dB]

The values presented in Table 5.2 show that oxygen absorption can not be neglected in the evaluation of the average power at the millimetre waveband, if large distances (in the order of 1 km) are to be considered; for calculations within cells, with ranges less than 200 m, the loss due to oxygen absorption may not be of great importance [89]. For some outdoor scenarios (like the BROADWAY scenario 5 “campus environment” from [29]) it might be necessary to have some margin for oxygen attenuation. For indoor propagation at 60 GHz the propagation loss due to oxygen absorption is negligible [29].

5.2.7. Water Vapour Absorption The path loss due to water vapour is calculated as [89]: Lwv[ dB ] = γ wv[ dB / km ] ⋅ d[ km ]

(5.29)

Water vapour has resonant lines at 22.3 GHz, 183.3 GHz and 323.8 GHz [89] [179] (see Figure 5.6 and Figure 5.7). An approximation based on the absorption line profiles, for water vapour at 20 °C surface temperature, is determined from the following expression [89]: 

γ wv[dB / km] = 0.067 + 

2.4

(f

− 22.3) + 6.6 2

+

7.33

(f

− 183.5 ) + 5 2

+

 2 −4  ⋅ f ⋅ ρ wv ⋅ 10 323.8 10 − + f ( )  4.4

2

(5.30)

(for f ≤ 350 GHz)

where f is the frequency in GHz, and ρ wv is the water vapour concentration in g/m3. According to [179], formulas are presented in [13] for a pressure of 1013 mbar and 15°C: 

γ wv[dB / km] = 0.5 + 0.0021 ⋅ ρ wv + 

3.6

(f

− 22.2 ) + 8.5 2

+

10.6

(f

− 183.3) + 9.0 2

+

 2 −4  ⋅ f ⋅ ρ wv ⋅ 10 (5.31) f 325.4 26.3 − + ( )  8.9

2

The correction factor for temperature ϑ (in °C) can be found using: γ wv[ dB/km ] ( ϑ[ °C ] ) = γ w|15°C ⋅ [ −0.006 ( ϑ − 15°C ) ] dB / km −20°C < ϑ < 40°C

(5.32)

Regarding to [179], this formula is accurate to within 15 % over the range of measured water vapour density ρ wv of 0…50 g/m³. For a relative humidity of 42 % at 20 °C, the vapour concentration is 7.5 g/m3. This gives with Eqn. (5.30) an absorption value due to water vapour at 60 GHz of γ wv[ dB / km ] = 0.1869 . Obviously normal atmospheric humidity causes a negligible attenuation at 60 GHz; and it can be expected that there will be only very less applications for 60 GHz WLANs in roman vapour-baths. 54/160

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5.2.8. Rain Attenuation When an electromagnetic wave propagates through a rain cell, it encounters a great amount of water droplets with different radii [29]. The cumulative effect of attenuation suffered by an electromagnetic wave penetrating a rain cell is considered here. Strong rain can additionally attenuate 60 GHz propagation [106]. A light drizzle corresponds to a rain of 0.25 mm/h, light rain corresponds to about 1 mm/h, moderate rain to 4 mm/h, and heavy rain to 16 mm/h [29]. According to [245] and [282] (which refers [283] and [136]), rain of 50 mm/h – which is the maximum rain rate to be expected in EUROPE for a significant amount of time (greater than 2 min per year) – causes an additional absorption of about 17 dB/km. Up to 17 dB/km are also given in [110] which refers [256], [282]. Table 5.3 provides further numerical values, while Figure 5.8 gives an overview about both frequency and rain rate dependence. Table 5.3: Rain attenuation for different rain rates [56]. Rain Rate / mm/h 25 50 10.1 17.9 10.4 18.2 10.6 18.5

Rain attenuation / dB/km

60 GHz 63 GHz 66 GHz

Clouds of ice crystals and snow do not cause appreciable attenuation, even if the rate of fall exceeds 125 mm/h. This is due to the much-reduced loss of ice compared to water. Attenuation by concentric spheres of different dielectric constant, for example, melting ice spheres, may approach that of rain [29].

Figure 5.8: Specific attenuation (dB/km) with rain rate and frequency (from [184]; also [85] referring to [95] and [136]).

Figure 5.9: Measured rain attenuation vs. SAM/CCIR (from [159]).

According to [159] and [291], an empirical rain model based on nominal water droplet sizes and distribution by [223] and [204] facilitates calculation of attenuation rate (dB/km) due to a specified rainfall rate. The model is referred to as the Simplified Attenuation Model (SAM/CCIR). The attenuation rate can be approximately expressed by (5.33), where R represents the rainfall rate in millimetres per hour (often R0.01 is used, which is the point rainfall rate for the region in question for 0.01 percent of an average year [179]). The parameters ‘ a ’ and ‘ b ’ are functions of frequency and rain temperature and respectively expressed using Eqns. (5.34) and (5.35); in [204] a more complete resulting set of values for a and b is presented in both tabular and graphical form for the frequency range of 1 to 1000 GHz (for coefficient values see also [134]; according to [179], coefficient values are also given in [13]). Note that in Eqns. (5.34) and (5.35), the frequency f is expressed in GHz.

γ rain[ dB / km ] = aR b a = 4.09 ⋅ 10−2 f 0.669 b = 2.63 f

−0.272

for 54 GHz ≤ f ≤ 180 GHz

for 25 GHz ≤ f ≤ 164 GHz 55/160

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The path loss due to rain is then calculated as: Lrain[ dB ] = γ rain[ dB / km ] ⋅ d[ km ]

(5.36)

An attenuation due to rain of 3.7 dB results for R = 50 mm/h and d = 200 m at 60 GHz. Measurements presented in [159] showed, that the rain attenuation values are in good accordance to the SAM/CCIR model presented here, as it can be seen in Figure 5.9. The measured statistics clearly indicated a linear increase in path loss values and rain attenuation values with increase in rain rate. The rain attenuation is as high as 3.5 dB during heavy rain events with rain rates on the order of 60 mm/h. The highest recorded rain attenuation value is 3.90 dB for a rain rate of 76.20 mm/h. As it can be seen from the values presented above, it might be necessary to have some margin for rain attenuation for selected outdoor scenarios (like the BROADWAY scenario 5 “campus environment” from [29]).

5.2.9. Foliage and Vegetation Loss A generic vegetation attenuation model for 1 to 60 GHz is presented in [249]. It models the excess attenuation from vegetation, which may arise from both signal absorption and scatter and also depends on season, vegetation species, frequency, etc. The model is based on extensive measurements at twelve locations in England including several species of trees. Some of the measurements were performed with 120 MHz bandwidth at 61.5 GHz, and, hence, are of interest for 60 GHz propagation. For more details on this model the reader is referred to [249]. Following [85], the foliage losses at millimetre wave frequencies are significant. In fact, the foliage loss may be a limiting propagation impairment in some cases. An empirical relationship has been developed [40], which can predict the loss. For the case where the foliage depth is less than 400 metres, the loss is given by L fol[ dB ] = 0.2 f 0.3d 0.6 (5.37) fol where f is the frequency in MHz and d fol is the depth of foliage transversed in metres, and applies for

d fol < 400 m . This relationship is applicable for frequencies in the range 200 MHz – 95 GHz. The foliage loss at 60 GHz for a penetration of 10 metres (which is about equivalent to a large tree or two in tandem) is about 22 dB. This is clearly not a negligible value [85].

5.2.10. Penetration Loss Values When millimetre-waves are propagation through materials, they are more or less strongly attenuated. Table 5.4 gives attenuation (also: “penetration loss”, L pen ) values from the literature for a great variety of materials, where σ Lpen is the penetration loss standard deviation. Table 5.4: Penetration losses resp. additional path losses measured for common building materials and contents. Material

Thickness

Freq.

[cm]

[GHz]

Aluminium Sheet

0.32

60

Aluminium Sheet Brick Brick wall Chipboard Clipboard wall Clutter* Composite wall with studs in the path Composite wall with studs not in the path Concrete Concrete Concrete Concrete pillar Concrete wall Concrete wall Concrete wall Concrete wall, 1 week after concreting Concrete wall, 14 months after concreting Concrete wall, 2 weeks after concreting Concrete wall, 5 weeks after concreting Concrete, aerated Concrete, aerated

0.32 11 12 ------1.0 5.0 30.0 --15.0 3.0 3.0 -3.0 1.0 5.0

57.6 60 60 60 60 60 60 60 60 60 60 60 60 60 60 57.5 57.5 57.5 57.5 60 60

Polar.

Lpen

σ Lpen

[dB] 51.9 42.3 53 17 >20 --1.2 35.5 8.8 71.5 6.7 >30 >20 -27 36.0 73.6 28.1 68.4 46.5 3.7 18.9

[dB]

vert. horiz. ----------------------

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Normalised Average Attenuation [dB/cm]

--

--

-----1.8 ----------------

---5.2 5.15 ----6.7 --6.67 -2.4 24.5 9.4 -15.5 3.7 3.8

Reference

[89] [89] (from [241]) [291]/[293] (from [167]) [200] [14] (from [50]) [291] (from [167] and/or [50]) [14][15][16] [291][293] [291][293] [89] [14] (from [50]) [14][291][293] (from [167]) [200], [14] (from [200]) [291] (from [167] and/or [50]) [126] (from [270]) [14] (from [205]) [14][291][293] (from [181] [242]) [14][291][293] from ([181][242]) [291]/[293] (from [181]/[242]) [14][291][293] (from [181][242]) [14][291] (from [50]) [14] (from [167])

BROADWAY, IST-2001-32686 Drywall (2 sheets of sheetrock wallboard) Glass Glass Glass door Glass door with wire mesh Glass wool with plywood surfaces Glass, acrylic

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60 60 60 60 60 60 60

-6.0 3.4 2.4 [14][15][16] ---6.05 [14][291] (from [50]) -1.7 … 4.5 --[291][293] (from [167]) -2.5 -6.3 [291][293], [14] (from [291]) -4.2 --[200], [14] (from [200]) -9.2 … 10.1 --[291][293] (from [243]) ---1.03 [291] (from [167] and/or [50]) vert. 1.8 Glass, clear 0.4 60 --[89] horiz. 2.2 Glass, clear (untextured and unreinforced) 0.32 60 -3.6 2.2 11.3 [14][15][16] vert. 4.3 Glass, meshed 0.5 60 --[89] horiz. 0.6 Glass, meshed** 0.32 60 -10.2 2.1 31.9 [14][15][16] Glass, metallised -60 ->30 --[291] [293] (from [167]) Glass, rough 0.4 60 -4.5 -11.3 [14] from [167] Glass, smooth & clear 0.2 60 -1.7 -8.5 [14] from [167] Glass, smooth & clear 0.4 60 -2.4 -6.0 [14] from [167] Glass, smooth & clear 0.6 60 -3.1 -5.2 [14] from [167] Glass, smooth & clear 0.8 60 -3.1 -3.9 [14] from [167] Granite 3 60 ->30 --[291][293] (from [167]) Limestone 3 60 ->30 --[291][293] (from [167]) Marble wall -60 ---1.25 [291] (from [167] and/or [50]) Metal filing cabinet -60 ->20 --[200] Moveable hardboard office partition -60 -4.7 --[200] Person -60 -14.6 --[200] Plasterboard -60 ---1.5 [14][15] (from [50]) Plasterboard 1.0 60 -2.1 -2.1 [14][15] (from [167]) Plasterboard 1.4 60 -2.8 -2.0 [14][15] (from [167]) Plasterboard 2.4 60 -6.5 -2.7 [14][15] (from [243]) vert. 0.8 Plasterboard 0.64 60 --[89] horiz. 2.6 Plasterboard stud partition wall -60 -13.2 --[200] Plasterboard wall -60 ---1.51 [291] (from [167] and/or [50]) Plasterboard wall -60 -5.4 … 8.1 --[291][293] (from [243]) vert. 5.4-8.1 Plasterboard, 2 sheets -57.6 --[89] (from [243]) horiz. 5.1-7.8 vert. 7.3 Plasterboard, 2 sheets 1.0 60 --[89] horiz. 6.4 vert. 12.7 --[89] Plywood 1.91 60 horiz. 10.9 Plywood, cloth-covered -60 -3.9 … 8.7 --[291][293] (from [243]) Plywood, dry 1.9 57.6 -8.0 -4.2 [14][15] (from [229]) Plywood, dry 3.8 57.6 -14.0 -3.7 [14][15] (from [229]) Plywood, dry 1.91 57.6 -8 --[89] (from [241]) Plywood, wet 1.91 57.6 -59 --[89] (from [241]) Sheetrock 1.9 57.6 -5.0 -2.6 [14][15] (from [229]) Sheetrock 2 sheets 0.95 57.6 -5 --[89] (from [241]) Stone wall -60 ---5.73 [291] (from [167] and/or [50]) vert. 56.8 Thermolite Block 10.0 60 --[89] horiz. 51.4 Tiles -60 ---7.81 [291] (from [167] and/or [50]) Whiteboard*** 1.91 60 -9.6 1.3 5.0 [14][15][16] Wood -60 ---4.2 [14][15] (from [50]) Wood Fibreboard 1.2 60 -3.4 -2.8 [14] (from [167]) Wood wall -60 ---4.22 [291] (from [167] and/or [50]) Wooden Chipboard 1.3 60 -6.2 -4.8 [14] (from [167]) Wooden Chipboard 1.6 60 -8.3 -5.2 [14] (from [167]) Wooden door -60 -9.6 --[200] Wooden door -60 -7 --[126] (from [270]) Wooden Joint Panel 1.6 60 -7.6 -4.8 [14][15] (from [167]) Wooden Panel 1.2 60 -7.6 -6.3 [14][15] (from [167]) Wooden Panel 1.9 60 -8.6 -4.5 [14][15] (from [167]) Wooden panels -60 -6.2 … 8.6 --[291][293] (from [167]) * Objects that encroached into the first FRESNEL zone but did not directly block the LOS signal from transmitter to receiver. Clutter includes office furniture such as chairs, desks, bookcases, and filing cabinets, in addition to soft partitions that did not extend to the ceiling ** clear glass that has been reinforced with interlacing 24 gauge wires configured in a rectangular grid with openings of ½ inch × ½ inch *** Standard office dry-erase melamine whiteboard, attached to ½ inch thick plywood backing

Comments: The results from [293] indicate that the quantity and position of the metallic studs within a composite wall are important factors to determine the penetration loss (no blocking by studs: 8.8 dB, with blocking: 35.5 dB). Obviously, the water content of the materials has a dominant influence onto the frequency dependence of the propagation loss of a wave propagating within them [29], as it can be seen, e.g., for concrete walls in different stages of drying.

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5.2.11. Reflection and Scatter Loss Especially when performing detailed ray-tracing simulations of exactly defined environments, diffraction and scattering properties of materials are of certain interest. In [253] the significance of diffraction and scatter effects is examined as part of the deterministic modelling. Typically, the diffracted power does not yield a significant contribution to the total received power. The surface roughness of building materials that typically can be found in indoor environments is such that the resulting scattering (diffuse reflection) does not contribute significantly to the total received power either. The dominant contributions are expected to come from specular reflections. These contributions can be calculated based on the electrical characteristics of the material (as well as the material thickness and a factor that accounts for scatter loss). The performed simulations indicate that the results are mainly determined by the superstructure of the indoor environment. A selection of references containing information that is more detailed can be found in Table 5.5. Table 5.5: Selected references on diffraction, scattering and dielectric properties at 60 GHz. Reference • • • • • • • • • • •

[29]

[58] [89] [243] [284] [291]

• •

Topics surface roughness, FRESNEL zone extensions, FRESNEL’s reflection and reflection coefficients, penetration loss through building materials, attenuation due to reflection, atmospheric effects, free-space and two-path propagation, knife-edge diffraction, shadowing dielectric constants of building materials extensive measurements of reflections coefficients and complex refractive indices of different materials with varying thicknesses are reported for 60 GHz. reflection and transmission coefficients of various construction materials used in modern office buildings at 60 GHz reflection loss of different materials

5.2.12. Frequency Diversity Frequency diversity does not seem to be a real topic in the 60 GHz carrier frequency range. As (outdoor) frequency diversity measurements for vertical polarisation described in [177] show, at least for an unobstructed LOS radio link with extremely directional antennas, the 60 GHz band of frequencies does not exhibit any frequency selectivity in the absence of multipath components. The maximum difference between received signal power levels at all carrier frequencies measured there was limited to 0.7 dB.

5.3 Shadowing 5.3.1. Introduction Slow variation of the local mean signal strength is called slow fading or shadowing. It is caused by the dynamic evolution of propagation paths where new paths arise and old paths disappear as the mobile terminal moves. The term shadowing is descriptive since typically these changes are due to the appearance or disappearance of shadowing objects on signal paths. [165] At 60 GHz the radio signal barely passes through wall (cf. Table 5.4) and coverage is basically confined to a single room. The environment around transmitters and receivers, i.e. the room geometry, furniture and people walking inside the room, has a considerable impact on the wireless channel. However, there must also paid attention to the impact of human body shadowing, because persons walking across a 60 GHz communication link cause severe performance degradation. The attenuation by furniture (8.2 dB, [200]) or persons (4.2 dB, [200]) blocking the direct path is not always as severe as might be predicted from the material losses measured at close range (see section 5.2.10). NOBLES [200] concludes that in these cases only a fraction of possible multipaths is obstructed by the item of furniture or the person and thus reflected paths contribute markedly to the received signal. The authors of [130] came to similar results: For a configuration with significant multipath the power only decreased of about 3 dB in the area shadowed by a person, because in this situation a decisive contribution to the received power came from the echoes. 58/160

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5.3.2. Effects of Furnishing According to [64], the effect of the furnishings can be looked at in two ways. Firstly, objects in the room can be sources for extra reflections, but these new echoes are likely to be within a time window defined by the dimensions of the room and so will have little effect on the measured RMS delay spreads. The other point is that the extra objects can act as barriers to existing echo paths. In this instance, the blocking is dominant and has the effect of reducing the RMS delay spreads measured. The results presented in [63] for an empty room show that the multipath effects are larger than in the case of furnished rooms. In [62] ray-tracing results are presented. In the LOS case the long-term received power in a furnished room is found practically coincident with what is received in the empty room situation. The multipath component is found lower due to spatial filtering of obstacles; this determines an increase in the RICE K . In the NLOS state the long-term received power is enormously smaller with respect to the LOS state (at least 10-20 dB). The statistical characterisation is not easy because the NLOS component shows a strong dependence on the specific topology of the medium-scale NLOS area.

5.3.3. Effects of Human Body Shadowing For indoor wireless LAN applications, one of the main sources of channel variation is the movement of people in the vicinity of the fixed terminals [291]. XU [291] refers to measurement results at 30 GHz presented in [186]. These results show that the effects of human motion on the time average received power depend highly on the spatial fading state that the receiver was in when the environment was free from movement. When the receiver is located in a spatial crest, i.e. the received signal power is higher than the local average, the movement of people (1-4) has little effect on the mean signal level. However, when the receiver is located in a deep fade, the movement of people will significantly increase the mean signal level. As the number of people increases, this dependence becomes less important. Measurement results show that the coherent time with correlation of 50 % is no greater than 3 ms or a walking speed of 0.9 m/s to 1.5 m/s. In measurements reported in [130], the effect of moving a human between transmitter and receiver was explored (see configuration 2 in Figure 6.4). The Tx antenna (biconical horn) was placed at a height of 2.5 m, the Rx antenna (monopole) was at a height of 1 m. See section 6.1.1 for further details on the measurement campaign. Figure 5.10 from [130] gives a vivid impression of the shadowing effect. It is found, that the direct path is additionally attenuated. The exact value depends on the exact position of the disturbing object. A mean attenuation of 20 dB is measured (see also [131]). The temporary shadowing of a LOS link by a person in an empty room significantly increases the mean excess delay τ from about 25 ns up to 35 ns, while the RMS delay spread σ τ doesn’t change noticeably as can be seen in Figure 5.11. τ στ

Figure 5.10: Temporary shaded wave rays measured with configuration 2 (Bild 9 from [130]).

Figure 5.11: Average delay and RMS delay spread measured with configuration 2 (Bild 11 from [130]).

FLAMENT presents in [90] and [91] an extensive study on issues related with human body shadowing. The essential results are given in the following. According to FLAMENT [90] [91], previous studies have showed that a person walking through the LOS of a communication link at 60 GHz can cause attenuation to the received power of 18 dB. Achieving coverage in a crowded room is therefore a potential problem. Furthermore, the statistical properties of the multipath fading change rapidly from RICE to RAYLEIGH. 59/160

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Two aspects should also be considered [91]: 1. Nowadays, a range of computing and communication devices is sold directly to the customer, who installs all equipment in a “do-it-yourself” fashion. Therefore, it cannot be assumed that devices are always installed appropriately. In fact, it seems more likely that APs for wireless LANs will be fixed on the wall rather (e.g., in a height of 2 m) than mounted on the ceiling to avoid extensive new cabling. The resulting small height difference between transmitters and receivers makes wireless links particularly susceptible to shadowing caused by persons walking inside rooms. 2. If the communication device is attached to the belt or placed in a pocket, another issue is the selfshadowing created by the user itself. The effect will basically cause a shadowing of all rays crossing the user’s body. In the simulations performed by FLAMENT [91] a rather large room of 20 m × 20 m was assumed, representing e.g. office or conference venue environments, which are often densely populated. The AP was installed in a corner of the room at a height of 2 m in order to model a typical ad-hoc WLAN installation. To simulate the shadowing, 0.8 m diameter column obstacles were uniformly placed in the room and allowed to move with a random direction, speed and acceleration. Each crossing of an obstacle yielded a 9 dB attenuation of the amplitude. At the APs, specially adapted antennas for corner-placement were used with an approximately 90-degree antenna lobe in the horizontal plane and 8 dBi gain. This guaranteed a relatively homogenous illumination of the room. The mobile terminals were equipped with a π/4-monopole over a ground plane. The density of people (i.e. shadowing objects) in each room was chosen to represent typical situations in office environments and public hot-spot areas, such as shopping centres, railway stations or airports. Appropriate values are proposed in [77]. A maximum density of 1 person per 20 m² was assumed for office spaces and maximal 1 person per 1.5 m² for public hot-spots.

Figure 5.12: Typical shadowing situation for indoor Wireless LAN systems (Figure 6.9 from [90], Figure 4.9 from [91]).

The situation of a person walking through the LOS can conveniently be modelled by attenuating the affected rays as shown in Figure 5.12. Following the SALEH and VALENZUELA propagation model (see section 7.2), we expect that the rays within a cluster are likely to arrive within a short time period and from the same direction. A person walking past the receiver will therefore obstruct not only a single ray, but also a whole cluster of rays. Consequently, several non-zero channel taps will fade during the shadowing event. The resulting effect is two-fold: the total received power will be reduced, and the statistical properties of the Channel Impulse Response (CIR) will change. From the results, it can be seen that the fading becomes more intense since the shadowing removes a significant number of non-zero channel taps from the CIR. The shadowing increases the variance of the frequency-selective fading. In some cases, some sub-carriers gain from the suppressed multipath reflections. Indeed, it is more likely that sub-carriers produce excessive bit errors, due to the non-linear dependency of the BER on the energy-per-bit to noise ratio. Hence, the average system performance will degrade. For high shadowing densities, the performance effect can be interpreted as an irreducible error floor for FDDM-DQPSK-OFDM. As the simulation results in [91] also show, as more persons are moving inside the room, the probability of rays being attenuated increases. This affects not only the direct LOS rays, but also reflected rays. The results show that, even for moderate shadowing densities (1 person per 20 m²), a user will experience more than 6 dB power loss for 10 % of time. A very high shadow density is likely to push the received signal below the noise floor if the terminal is not close enough to the AP. As a principle solution to handle the problem and to avoid excessive hand-over between APs, the VCN concept (virtual cellular network) is proposed by FLAMENT [91], where the same signal is simulcasted by several APs and the receiver accumulates all signal contributions. This leads to the channel model scenario of the Single Frequency Network, which is discussed in section 7.10. 60/160

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5.3.4. Modelling of Shadowing According to the Power Exponent Model given in Eqn. (5.19), the receiver always experiences the same signal power at two different locations, each having the same Tx-Rx distance. As the measurements show, this is not a realistic model, because it does not consider the fact that the surrounding environment may be vastly different at two locations having the same Tx-Rx separation [25] [156]. Moreover, this type of variations tends to be unpredictable [25]. Whereas the Power Exponent Model is more or less merely applicable for zones with LOS conditions, the other zones are (according to [63]) characterised by the absence of the line-of-sight component (=> NLOS). In this case, the large-scale received power is much smaller with respect to the LOS zone (at least 10-20 dB). In the NLOS state the large-scale received power seems to assume, with a low dispersion, a discrete set of values that weekly depend on distance. This suggested in [63] the consideration of different zones (“lighting zones”), where large-scale received power shows small fluctuations around a mean value characterising the zone. Each zone is defined by the locus of points lightened by the same set of reflectors. Thus, slow fading (large-scale fading) results from the shadowing of the propagating wave by obstacles [29] [89]. While moving from one obstacle into another, the signal power by a mobile station varies due to the alternate interruption and release of line of sight between transmitter and receiver. Therefore, the large-scale normalised power (in dB) in the NLOS receiver positions can be modelled as the sum of a deterministic contribution, dependent on the zone in the rooms, and a random contribution that takes into account fluctuations inside the zone. Referring to [15], [25], [89], [126], [156], [200], it has been well documented in the literature that the shadowing effects at a particular location are random and they are described by a log-normal distribution (the GAUSS distribution in logarithmic scale) about the distance-dependant local median of the path loss [28] [29] [44] [110] [228] [229] [244] [274] or the mean value of the large-scale normalised received power in the zone [63]. The shadowing component Lsf (often also denoted X σ ) describing the large-scale power variations when moving inside the zone is defined as a GAUSS random variable as Lsf = f x ( x = 0, σ = σ L ) (5.38) where f x is a GAUSS distribution, with zero mean ( x = 0 ), and standard deviation equal to the location variability σ L (in dB). More information about the lognormal distribution can be found in subsection 5.5.4.6. The shadowing component Lsf is often also denoted X σ ; hence, one can find often in the literature the formula (e.g. [139]) d (5.39) L[ dB ] ( d ) = L fs ,[ dB ] ( d 0 ) + 10n log   + X σ d  0 The location variability σ L is normally found from measurements. σ L varies with frequency, antenna heights and environment [89]. The shadowing component of measurements is obtained by subtracting the median path loss from the measurements [89]. Measurement and simulations results for σ L taken from literature can be found in Table 6.7.

5.4 Antenna Influence 5.4.1. Antenna Gain, Aperture and EIRP The gain G of an antenna is related to its effective aperture (also: effective area) Ae , which is related to the physical size of the antenna, by [156] [302]: 4π G = Ae 2 (5.40)

λ

Antenna gains are normally given in units of dBi (dB gain with respect to an isotropic antenna) or sometimes in units of dBd (dB gain with respect to a half-wave dipole antenna). An isotropic radiator is an ideal antenna that radiates power with unity gain uniformly in all directions, used as the reference antenna in wireless systems. The effective area Ae,iso of an isotropic radiator is [29]

Ae,iso =

λ2 4π

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When the transmit antenna is considered to be at the centre of a sphere with radius d , the total power density on the sphere (also referred to as flux density) may be expressed as: EIRP (5.42) PD = 4π r 2 where EIRP is the effective radiated power from an isotropic source and 4π r 2 is the surface area of the sphere. The effective isotropic radiated power (EIRP) is defined as: EIRP = PTx ⋅ GTx (5.43) where PTx and GTx are the power supplied to and the gain of the transmitting antenna, respectively.

5.4.2. Passive Repeater Passive repeaters are typically metallic, strong reflectors that can be used to redirect (reflect) micro- or millimetre-wave signals over or around obstructions. Passive repeaters are used at microwave frequencies to increase the received signal power level in obstructed regions and increase the system coverage area [291]. Passive repeater gain is defined as the difference (in dB) of the power density at a distant point due to the passive repeater to the power density which should exist at the same point if the passive repeater were replaced by a matched, isotropic antenna of 100 % ohmic efficiency and fed with RF power equal to that accepted by the passive repeater ([291] from [191]). The repeater gain G pr is the given by [291]

G pr = 20log ( 4π A cos α λ 2 )

were A is the repeater area, α is the incident angle, and λ is the wavelength. The repeater loss is given by ([291] from [191]) L pr[ dB ] = PTx[ dB ] + GTx[ dB ] + GRx[ dB ] + G pr[ dB ] − PRx[ dB ] − L fs[ dB ] ( d1 ) − L fs[ dB ] ( d 2 )

(5.44)

(5.45)

were L pr is the passive repeater loss, PRx is the received power, PTx is the transmitted power, GTx is the transmitter antenna gain, GRx is the receiver antenna gain, L fs ( d1 ) and L fs ( d1 ) are the free space path losses from the Tx to the passive repeater and from the passive repeater to the Rx, respectively. Some measurement results regarding passive repeaters at 28.8 GHz are given in [208]. For a 1.2 m² aluminium reflector they found 4-6 dB repeater loss.

5.4.3. Antenna Pattern Model The patterns of transmitter and receiver antennas, needed, e.g., for ray tracing, are modelled as [89]: Pant = GdBi + P ( φ ,θ , dBi ) (5.46) where GdBi is the maximum gain, P is in dBi with 0 dBi as maximum value, and φ and θ are the azimuth and elevation, respectively.

5.4.4. Directivity and Alignment It is conceptually well known that the directivities of transmitting and receiving antennas have a considerable influence not only on received power but also on channel distortion caused by multipath reception. The suppression of delayed components is found to be more effective for antennas with narrower bandwidths [180]. This is supported by [293]: When transmitter and receiver antennas are aligned, the main multipath component is the LOS component. Other multipath components are largely attenuated by the directional antenna, forcing the excess delay to be close to zero. In [178] it is concluded from the measurement results, that the use of relatively high-directivity antennas (antenna beamwidth 100°) [178]. E.g., the amplitude of the indirect path signals reduced in the measurements reported in [178] by about 10 dB. In comparison to linear polarisation, the consequences are manifold: • The RMS delay spread may become significantly (about a factor 2) smaller when applying circular polarisation, as indicated in [28], [140], [181], [182], [258] • There is a drastical decrease in fading depth (typically by 20 dB) and ISI, which may greatly improve the link budget for high data rate communications [178]. • According to [110], which refers to [180], [182], [192], [241], [258], the coverage may be improved. Referring to [178], with linear polarisation, the contribution of indirect path signals is significant and OFDM-DQPSK is attractive. However, using circular polarisation, which strongly decreases ISI, the simple QPSK modulation scheme appears to be the best choice with a BER lower than 10-5 for a normalised signalto-noise ratio >12 dB. In this case, according to [178], the more complex OFDM technique suffers from system nonlinearities and oscillator phase noise, despite the fact that OFDM remains an efficient technique for hard propagation conditions. These results have been experimentally checked in [178] for a 12 m transmission in a typical metallic furnished room for data rates up to 100 Mbit/s. Of course, when having a closer look at these statements, it becomes evident, that they are only appropriate for guaranteed LOS conditions. As soon as we have circular polarisation confronted with NLOS, things will change dramatically. Communication in NLOS situation “lives” from multipath contributions due to reflections. However, as circular polarisation is contra-productive in this case, we are forced to use linear polarisation in combination with a high NLOS-probability and OFDM.

5.4.6. Cross-Polarisation In cellular systems, an AP’s Tx typically uses a linearly polarised antenna (e.g. vertically polarised). On the signal path from the AP to the MT, reflections, diffraction and scattering caused by, e.g., rain drops and vegetation, give rise to a cross-polar component (e.g. horizontally polarised) [165] [209]. A statistical parameter that describes the extent of cross-polarisation is the cross-polarisation power ratio XPR [165] or cross-polarisation discrimination XPD [209], given by [165] [209] [291]  P  (5.47) XPR[ dB ] = XPD[ dB ] = 10lg    P⊥  where P and P⊥ are the co- and cross-polarised received power [165] [209] [291], respectively, averaged over a random route in a given environment [266]. PAPAZIAN et al [209] give some exemplary XPD values for the 30 GHz band. Accordingly depolarisation due to rain causes XPD values above 24 dB, whereas vegetation caused a XPD reduction to 9…14 dB. For a 1.2 m² aluminium reflector at 28.8 GHz values of 16-24 dB are given in [208]. The above power ratio evaluated at a given receiver location is called the instantaneous XPR. The XPR is an important parameter for mobile antenna development [266].

5.4.7. Coverage We will not detail on coverage calculations neither in this subsection nor in other parts of this study. As we have seen from the path loss contemplations, 60 GHz indoor coverage basically is limited to single rooms. In [66], omnidirectional antennas vertically polarised are used, and good coverage is shown mainly in the room where the transmitter is located. To a certain extent, coverage is achieved in other rooms, with propagation through plaster walls, glass windows (low attenuation) [66]. 64/160

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With biconical horn antennas (which have an omnidirectional radiation pattern in the azimuth plane, and a torroidal beam in the elevation plane [256]) for Tx and Rx (Rx at ceiling centre), almost uniform coverage of rooms can be achieved (zero power decay), as shown in [53] and [256]; similar results are given in [258]. This is due to that owing the radiation pattern of the biconical horn antennas the path loss is partially compensated by the antenna radiation pattern in elevation. Hence, the received power does not depend significantly on the horizontal position of the remote antenna [256]. In [212], a typical office environment was measured using omnidirectional AP antenna and omnidirectional/directional MT antennas, all of them circular polarised. Placing the AP antenna at the centre of the ceiling is superior to placing it at an edge in terms of BER and received power. In [91] it is shown, that for a DQPSK-OFDM system (1024 sub-carriers, 200 MHz bandwidth) the possible range can be roughly approximated to be 20 m (assumptions: noise floor power –116 dBm, receiver noise figure 5 dB, emitted power 20 dBm, E B / N 0 ≥ 12 dB ). Thus, in an office environment, this range is not likely to be exceeded unless the LOS disappears under the margin due to shadowing. The system will be interference limited. On the other hand, we will need three or four antennas to provide a reasonable coverage in a typical shopping mall. In this case, coverage is the limiting factor. According to [110], assuming low gain antennas, the propagation losses at 60 GHz enable to have good coverage in small cells, with low co-channel interference (cells with radius smaller than 200 m, typically “inroom” in indoor environments where attenuation due to walls is also significant) [53] [64] [256] [282]. This result is illustrated by reference [282], under specific assumptions of a 1-D urban scenario at 60 GHz, and bit-rates below 2 Mbs. It shows that there is an optimal cell radius, around 150 m, minimising the outage probability, and that the corresponding outage value is inferior to what can be obtained at 5.8 GHz (no optimum for 5.8 GHz). Reference [110] also states, that it is expected that advanced receiver techniques, such as adaptive antennas, can increase the coverage.

5.5 Small-scale Fading 5.5.1. Introduction As we have already expressed in section 5.1, the term small-scale fading denotes the rapid (and partially dramatic) variations in the amplitude and phase of a received signal in a local area within a short period of time and/or when a MT moves over small distances (in the order of a wavelength) in a time- or space-variant multipath channel. Since the mean amplitude or power remains approximately constant over these small distances [213], the small scale fading can be considered as superimposed on large scale fading for largescale movements [28]. As XU [291] states, when adding the multipath components, the enhancement or reduction in the amplitude of the resulting received signal depends on the phase differences of the multipath components. Due to the rapid phase change of each multipath component along the wave propagation path, multipath components interfere with each other constructively and destructively along the receiver path in space. Received signal power not only experiences large-scale attenuation due to the increase in distance, but also undergoes rapid fluctuation in a small local area, i.e. small-scale fading [45] [102]. Note that small scale fading is the result of the vector summation of the multipath components. Therefore, if the bandwidth of a system is wide enough to resolve each multipath component, the system does not undergo small scale fading. Practical wideband systems have finite bandwidths, and the signal pulse may still contain several multipath components. In this case, the small scale fading behaviour of the wideband pulse is determined by the multipath components that arrive within the pulse duration [74]. Time-varying received power, spreading of the signal spectrum caused by DOPPLER spreading, and time dispersion are known as small-scale fading effects, caused by two or more interfering multipath signals arriving at the receiver with slightly different amplitudes and propagation times. These signals will then combine as vectors to yield fluctuations in received amplitude and phase. These effects are considered smallscale because they characterise the channel when the motion of the receiver is on the order of ½ wavelengths during a short period of time [14] [229]. Thus, e.g., small displacements of one of the antennas can lead to dramatic changes in the signal reception due to multipath propagation [25]. It is quite possible in a small-scale fading channel to experience near-zero received power levels at points in space even if the large-scale power level is high. This type of dip in the power level is called a null. Conversely, a point in space that leads to maxima in the received power levels is called a peak [76]. 65/160

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Usually the displacement over a portion of a wavelength is neither a reason of a change in a number of multipath components, nor in their amplitudes. However, it can lead to the dramatic changes in the relative phases of path signals, since even a small displacement leads to the significant change in the phases of signals. Consequently, after the superposition of all path signals, it affects the resulting overall received signal. An example of this phenomenon is presented in Figure 5.14 [25].

Figure 5.14: The origin of the small-scale fading effect. The superposition of the path causes the fading depending on the mutual relations between the phases of path signals (Figure 1-6 from [25]).

Figure 5.15: Classification of the channels (Figure 1-10 from [25]).

The classification of channels according to their fading behaviour was already presented in section 4.9.2 from the coherence time point of view and in section 4.9.3 from the coherence bandwidth point of view. In summary, the channels can be classified into the following groups: time-flat, frequency-flat, flat-flat and non-flat. The channel is considered to be time-flat when it remains constant during at least the transmission time of one symbol. In other words, the channel is time-invariant. By analogy, the channel is referred to as frequency-flat when the bandwidth of the transmitted signal is smaller than the coherence bandwidth of the channel. This also means that the channel is frequency non-selective [25]. When the channel is flat in both time and frequency, it is called a flat-flat channel. In such a case, the transmitted signal bandwidth undergoes the same attenuation at each frequency and the channel remains unchanged during the transmission of one symbol. As a last type, we consider a non-flat channel. The channel is called non-flat when it is both time-variant and frequency selective. The introduced types of channels are summarised in Figure 5.15 [25].

Figure 5.16: Wideband and narrowband channel models (Figure 8 from [291]).

As already stated before, due to multipath propagation the radio channel will be time-dispersive and spacedispersive. This means that the channel impulse response will not be a single echo, but a sequence of pulses spread in time and space [28]. The difference between wideband and narrowband fading models is the resolution of the different multipath components [109]. For narrowband signals, the multipath components have a time resolution that is less than the inverse of the signal bandwidth (in other words, if the time of arrival between the first and last significant echoes is much smaller than the duration of a digital symbol [28]), so the multipath components of Eqn. (3.39) are combined into one signal with random amplitude and 66/160

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phase [109], the system is defined to be a narrowband system [28]. However, this is not the case with wideband signals, where each of the different multipath components can be resolved at the receiver [109], and the system is defined as a wideband system [28]. This resolution allows the multipath channel to be characterised in more detail using correlation functions and power spectral density functions [109]. Hence, the statement whether a system is narrowband or wideband, depends on both the duration of a symbol and the channel characteristics [28]. In the next sections we will further detail on narrowband and wideband fading.

5.5.2. Narrowband Fading Models Following XU [291], in narrowband communication systems, the pulse duration is large relative to the channel time delay spread. The received signal is the vector summation of all the multipath components. The narrowband channel model can be achieved by assigning delays to zero in the channel wideband impulse response, resulting in the following [291]

h( t ) =

N −1

∑ βi ( t ) e jϕ ( t ) i

(5.48)

i =0

The time variable is added to account for the channel time variations due to the transmitter/receiver motion, or any other changes in the channel [291]. In a narrowband system, the received signal power may change rapidly due to small scale fading [291]. Therefore, the received signal power is of major concern. The distributions of the received signal envelope in small scale fading channels are described by probability density functions (PDFs) such as RICE distribution, RAYLEIGH distribution and TIP (Two-Wave with Incoherent Power) distribution (see [74] [232] [234]). We will further detail on PDFs in section 5.5.4. In [45], CLARKE proposed a classical model for small-scale fading signal. The received signal is modelled as the vector summation of coherent field and incoherent field components. The incoherent fields are the results of diffuse scattering, and their phase terms are completely random. The coherent fields are the field components that have constant phase terms such as the LOS field component and specular reflected field components. When the received signal consists of numerous incoherent field components and none of them has a dominant power, the signal envelope follows the RAYLEIGH distribution (see [20] [214] [228] [232]). When received signal is the sum of a strong coherent field component and numerous small incoherent field components, the signal envelope obeys the RICE distribution (see [235] [236] [234]). The class of PDFs is extended by DURGIN [74] to TIP, which describes the envelope of the received signal, consisting of two coherent waves and numerous incoherent waves [291]. Besides signal PDFs, parameters such as average received power, fading depth, level-crossing rate and fade duration are used to describe the power level and rate of change of the received signal (see [45] [233]) [291].

5.5.3. Wideband Fading Models As to XU [291], in practice, a system is considered wideband12 if the transmitted signal has a pulse duration less than the relative delay between any two multipath components. In other words, the receiver has a bandwidth wide enough to distinguish each multipath component by its delay [291]. The received signal would be a sequence of multipath components spaced by their TOA. The time- or space-variant channel impulse response (CIR) consists of discrete impulses of multipath components as shown in Figure 5.16 [28] [291]: h ( t ,τ ) = ∑ β i ( t ) e jϕi ( t )δ ( τ − τ i ( t ) ) (5.49) i

The time-dependent amplitude β and phase ϕ from multipath components i arriving at τ i are added together for a particular time t [28]. From the impulse response (or from the power delay profile), a number of parameters can be extracted to characterise the time dispersion of the channel. These are the mean excess delay, RMS delay spread, maximum excess delay and coherence bandwidth [228]. If the impulse response is given for a number of antenna elements on an array, it is also possible to determine parameters that characterise the spatial dispersion (angular power spectrum) of the channel. Examples are the mean angular

12

According to XU [291] it must be mentioned that terminology “wideband” is defined differently in RF circuit design or antenna design, where wideband or narrowband is determined based on the ration of signal bandwidth with respect to the carrier frequency. For example, a system with a 2 GHz RF bandwidth centered at 60 GHz, operating in a channel with a minimum relative delay larger than 1 ns, will be wideband by the poropagation definition, since it can resolve 1 ns of time delay. But it will be narrowband in antenna design terminology, because the bandwidth represents only 3 % of the carrier frequency [291].

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direction and angular spread [28]. For details on the definition of the several parameters just mentioned the reader is referred to the corresponding sections in this study. Opposite to the narrowband channel model, a wideband channel model is composed of a large number of frequency components that can fade independently (frequency selective fading). In such a case, the CIR will consist of a series of paths received at different time delays [28]. It is quite common to treat each of these paths as a narrowband channel and thus characterising the large scale fading of each path with the lognormal distribution (see [300] [301]) [28] or other PDFs (see section 5.5.4). The wideband model can also be extended with information on the angle of incidence, e.g. for directional modelling (see [99]) and polarisation (see [127]) [28]. As mentioned earlier, the large-scale variations are often caused by changes in delay time of paths and appearance and disappearance of paths arriving at the moving MT in the propagation scenario (see [127] [300]) [28]. Therefore, channel models based on the geometric positions of clusters of scatterers (see [99]) should also consider the appearance and disappearance of these clusters as a large-scale effect (see [262], [17]) [28].

5.5.4. Probability Density Functions 5.5.4.1. General In this section the distribution of path amplitudes is investigated. In a randomly varying small-scale channel, the distribution of received signal power or envelope will dramatically affect the performance of a receiver. These fluctuations are best described using a probability density function or PDF, which characterises all of the first-order statistics of a channel [76]. In a multipath environment if the difference in time delay of a number of “paths” (echoes) is much less than the reciprocal of the transmission bandwidth, the paths cannot be resolved as distinct pulses. These unresolvable “subpaths” add vectorially (according to their relative strengths and phases) [126], thus each channel tap contains an aggregate of paths, with the delays smoothed out by the baseband signal bandwidth [100] and the envelope of their sum is observed. Fortunately, the taps often contain a sufficient path aggregation so that a statistical model might have a chance of success [100]; the envelope value is therefore a random variable [126]. This is illustrated in Figure 5.17.

Figure 5.17: A multipath component and its associated subpaths (Fig. 8 from [126]).

Mathematically, if τ ki − τ k j < 1 B , i, j = 1,2,

, n , where B is the transmission bandwidth, then the

resolved multipath component is [126]

ak e

jθ k

n

=

∑ ak e jθ i =1

i

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With proper interpretation, the definition of r may be extended to the narrow-band or wide-band temporal fading (i.e., variations in the signal amplitude when both antennas are fixed; such variations are due to the motion of people and equipment in the environment). If the latter definition is adopted, “spatial” separation between data points in this section should be replaced with “temporal” separations [126]. Amplitude fading in a multipath environment may follow different distributions depending on the area covered by measurements, presence or absence of a dominating strong component, and some other conditions [126]. These distributions will be detailed on in the next subsections.

Remark: As described earlier, small-scale fading in multipath channels occurs due to the coherent superposition of a great number of multipath components, each having a different phase variation over time or frequency. The basic and probably mostly well known model for time-variant multipath channels, which has often been called RAYLEIGH- or RICE-fading model, describes the time-variant fluctuations of the amplitude and phase values by statistical distribution functions. This model originally referred to fluctuations of a continuous wave (CW) signal received via a time-variant multipath channel and, thus, basically, it is a narrowband model. For frequency selective (i.e., wideband) channels, a commonly accepted extension of the RAYLEIGHor RICE-fading model is the assumption of RAYLEIGH or RICE fading for contributions at different delay times in the time-variant impulse response, which results in a tapped delay line model with RAYLEIGH- or RICE-fading taps [145]. Thus for channel models of the tapped delay line style it is necessary to know the RICE factor K tap for every tap (see for example the HIPERLAN/2 models in section 7.2.2). Measurements in the literature, however, often give only the RICE factor KCIR of a complete impulse response and not for the single taps. So one should be very careful about the RICE factor. Therefore, in this study we will explicitly distinguish between K tap and KCIR where necessary.

5.5.4.2. RAYLEIGH Distribution RAYLEIGH fading is a well-accepted model for small-scale fading which describes the received signal envelope distribution for channels, where all the components are non-LOS: i.e. there is no line-of–sight (LOS) component, all multipath power is non-specular ([25] [28] [76] [126] [156] [298]). ZHANG [298] states, that a large number of scatters or obstacles (reflecting, diffracting, and scattering radios) contributes to the received signal at a receiver in the shadow region and that it is assumed that at least at the receiver end an omni-directional antenna is used. The probabilistic RAYLEIGH model for the channel filter taps is based on the assumption that there is a large number of statistically independent uncorrelated rotating vectors with random amplitudes of the same order of magnitude and uniformly distributed phases in the delay window corresponding to a single tap [28] [100]. According to HASHEMI [126], the RAYLEIGH distribution is widely used to describe multipath fading because of its elegant theoretical explanation and occasional empirical justifications. To describe it theoretically, one can use the model of CLARKE [45] for the mobile channel. In this model it is assumed that the transmitted signal reaches the receiver via N directions, the i -th path having a complex strength ri e jϕi that can be described by a phasor with an envelope ri and a phase ϕ i . At the receiver these signals are added vectorially and the resultant phasor is given by: r ⋅ e jϕ = ∑ ri e jϕi (5.51) i

CLARKE (according to HASHEMI [126]) assumed that over small areas and in absence of a line-of-sight path, the ri s are approximately equal ( ri = r ′ , i = 1,2, , N ), and hence r ⋅ e jϕ = r ′∑ e jϕi

(5.52)

i

Since the reflectors are far away relative to the carrier wavelength (a typical radio wave travels a long distance to reach a local area – usually the distance of hundreds or thousands of wavelengths) and the path phase is very sensitive to the path length, changing by 2π when the path length changes by a wavelength, it is also reasonable to assume that the phase for each path is uniformly distributed over [ 0,2π ) and that these phases are independent [76] [100] [126]. In other words: since all effects of phase are periodic, only the 2π modulus of the phase is essential for characterising a propagating wave, but the 2π -modulus of a very large

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absolute phase value is unpredictable and, therefore, may be treated as a uniformly-distributed random variable [76]. Thus, the problem reduces to obtaining the distribution of the envelope sum of a large number of sinusoids with constant amplitude and uniformly distributed random phases. In such a case, the central limit theorem can be applied, which leads to the description of the channel as a complex GAUSS, zero-mean random process. This type of processes can be represented by the sum of two independent, uncorrelated zero-mean, i.i.d. jointly GAUSS processes with the same variance σ 2 in the complex plane (see Figure 5.18), thus the parameter σ represents the RMS value of the received signal (most probable value, RAYLEIGH parameter) [25] [100] [126] [142].

Figure 5.18: The complex plane (Figure 1-7 from [25]).

Following GALLAGER [100], this model, which is called RAYLEIGH fading, is quite reasonable for scattering mechanisms where there are many small reflectors, but is adopted primarily for its simplicity in typical cellular situations with a relatively small number of reflectors. The word RAYLEIGH is almost universally used for this model, but the assumption is that the tap gains are circularly symmetric complex GAUSS random variables. The joint distribution of the random variables R = X 12 + X 22 and Φ = arctan ( X 2 X 1 ) (with X 1 = I and X 2 = Q ) was – according to HASHEMI [126] – first investigated by Lord RAYLEIGH [231] with the result that R and Φ are independent, R being RAYLEIGH-distributed and Φ having a uniform [ 0,2π ) distribution. A short derivation can be found in [210]. The PDF, CDF, and k -th moment of the generalisation R =

∑ i =1 X i2 n

(with X i being statistically independent, identically distributed zero mean

GAUSS random variables) are given by PROAKIS [224]. The GAUSS random process n ( t ) from Figure 5.18 can be expressed in polar coordinates leading to the formula for the RAYLEIGH probability density function (PDF) of magnitude R and phase Φ (of the tap or the channel) [25] [28] [76] [83] [100] [109] [126] [139] [142] [156] [165] [224] [288] [298] 2π

fR ( r ) =

∫

f RΦ ( r ,ϕ ) dϕ =

0

 r 2  2r  r2 − = exp exp  2σ 2  σ 2  −σ 2 σ2    r r r

∞

fΦ ( ϕ ) =

1

∫ f RΦ ( r,ϕ ) dr = 2π ,

  , r ∈ [ 0, ∞ ) 

ϕ ∈ [ 0,2π )

(5.53) (5.54)

0

Unlike the purely specular wave PDF’s the RAYLEIGH PDF is non-zero over the entire range of 0 ≤ r < ∞ [76]. The substitution, σ r2 = 2σ 2 (i.e., rrms = σ r = 2σ ) was made to give the PDF a more physical meaning. The value σ r2 (sometimes denoted as Ω p ) is the mean power of the non-specular voltage component (the power of the complex process), and is less nebulous than the value σ . The probability that the envelope of the received signal does not exceed a specified value of r is given by the cumulative distribution function (CDF) [156] [224] r

 r2  = − ( ) 1 exp f x dx R  − 2σ 2 , r ≥ 0 ∫   0 In general the moments of a RAYLEIGH distributed R are [224] FR ( r ) =

E { R k } = ( 2σ 2 )

k 2

Γ ( 1 + 12 k )

(5.55)

(5.56)

Mean and median value of the RAYLEIGH-distributed amplitude are [154] [156] ∞

r = E { R } = ∫ r ⋅ f R ( r ) dr = σ 0

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rmedian = 1.177σ found by solving

1 = 2

rmedian

∫

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f R ( r ) dr

(5.58)

0

For the variance we have [154] [224]

π V { R } =  2 −  σ r2 2  The probability of the most probable value σ is [156] 1 0.6065 fR ( σ ) = ≈ σ e ⋅σ The level crossing rate for level r is calculated as [109]   r 2  r LR ( r ) = 2π ⋅ ν max ⋅ ⋅ exp  −    σr   σr   The average fade duration is given as [109] exp  ( r σ r )2  − 1 1 ⋅ TR ( r ) = r σr 2π ⋅ ν max Finally, the power distribution is given by [109] 2 2 1 f R2 ( r 2 ) = 2 e −r σ r

(5.59)

(5.60)

(5.61)

(5.62)

(5.63)

σr

Thus, the received signal power is exponentially distributed. 0.7

0.6065/σ 0.6

mean = 1.2533σ median = 1.177σ variance = 0.4292σ2

0.5

0.4

0.3

0.2

0.1

0 0

Figure 5.19: RAYLEIGH distribution (Abbildung 2.7 from [154]).

σ1

2 2σ

3 3σ

4 4σ

5 5σ

Figure 5.20: RAYLEIGH distribution (from [156]).

Remark 1: Magnitude and number of paths The assumption that the ri are equal is – according to HASHEMI [126] – unrealistic since it implies the same attenuation for each path. It has been shown, however, that if the magnitudes are not equal but any single of them does not contribute a major fraction of the received power (i.e., if ri2 ∑ ri2 , i = 1,2, , N ), then the RAYLEIGH distribution can still be used to describe variations of the resulting amplitude [126]. Moreover it has been shown that even when as few as 6 sine waves with uniformly distributed and independently fluctuating phases are combined, the resulting amplitude and phase follows very closely the RAYLEIGH and uniform distributions, respectively ([165] ref. to [214], [126] ref. to [252]).

Remark 2: Temporal RAYLEIGH fading According to DURGIN [76], for fixed, narrowband receivers, temporal fading in a wireless channel is due to the motion of scatterers. RAYLEIGH fading as a function of time requires temporally diffuse propagation, which physically means that the propagation environment consists of numerous scatterers, all of which are in motion. One such scenario occurs often for mm-wave propagation through a rainstorm, where drops of water scatter radio waves to the receiver. However, most cases of temporal RAYLEIGH fading in terrestrial wireless propagation are due to receivers moving through small-scale spatial RAYLEIGH fading. Recognise, therefore, that temporal RAYLEIGH fading in the absence of receiver (or transmitter) motion, is much more rare than frequency or spatial RAYLEIGH fading. 71/160

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5.5.4.3. RICE Distribution As we have seen before, the RAYLEIGH fading describes well extreme multipath situations. In practice, however, there is occasionally a dominant incoming wave which can be a LOS component or a strong specular component. In these situations, the RICE PDF (also named “Ricean” or “Rician” PDF) describes the fading of non-specular power (the fluctuations of the signal envelope in narrowband multipath fading channels) if a strong dominant, non-fluctuating (stationary, non-fading, coherent, direct) multipath component (resp. path), i.e. signal parts with constant amplitude and phase exists in addition to the low level scattered paths; this strong component may be a line-of-sight (LOS) path or a path that goes through much less attenuation compared to other arriving random components, assumed to be a large number of uncorrelated rotating vectors with amplitudes of the same order of magnitude and uniformly distributed phase [2] [28] [76] [89] [91] [126] [142] [156] [165] [226] [234] [275]. According to HASHEMI [126], TURIN ([272]) calls the dominant component a “fixed path”. When such a strong path exists, the received signal vector can be considered the sum of two vectors: a scattered RAYLEIGH vector w with random amplitude and phase, and a vector s that is deterministic in amplitude and phase, representing the fixed path. If w = w ⋅ e jα is the random component, with w being RAYLEIGH and α uniformly distributed, and s = s ⋅ e jβ is the fixed component (thus s represents the magnitude of the constant component; s and β are not random), then the received signal vector r = r ⋅ e jϕ is the phasor sum of the above two signals (see Figure 5.21).

r

β

ϕ

w

α

s

Figure 5.22: RICE phase PDF ( ψ ≡ ϕ )

Figure 5.21: Superposition of the paths after RICE (after Abbildung 2.8 from [154]).

RICE [235] [236] has shown the joint PDF of the random variables R and Φ to be r  r 2 + s 2 − 2rs cos ( ϕ − β )  f RΦ ( r,ϕ ) = exp −  , r ≥ 0, − π ≤ ( ϕ − β ) ≤ π 2πσ 2 2σ 2  

(5.64)

where σ 2 is proportional to the power of the “scatter” RAYLEIGH component. Furthermore, since – according to HASHEMI – the length and phase of the fixed path usually changes, β is itself a random variable uniformly distributed over [ 0,2π ) , and randomising β causes R and Φ to become independent. Thus R has a RICE distribution given by the PDF [25] [28] [76] [109] [126] [139] [168] [214] [224] [226] [280] [298] r  r 2 + s 2   r ⋅ s  2r  r 2 + s 2   2r ⋅ s  (5.65) = f R ( r ) = 2 exp  − I exp  0  − σ 2  I 0  σ 2  , r ∈ [ 0, ∞ ) σ 2σ 2   σ 2  σ u2     u  u where I n ( ⋅ ) denotes the modified BESSEL function of the first kind and n-th order. The substitution

σ u2 = 2σ 2 gives the PDF a more physical meaning because 2σ 2 is the mean power of the sum of the nonspecular (i.e. non-LOS) voltage components (which are described by the RAYLEIGH distribution). The PDFs of the received signal phase is described by [25] 1 π s ⋅ cosϕ s ⋅ cos ϕ    s2    r 2 ⋅ cos2 ϕ    (5.66) fΦ ( ϕ ) = exp  − 2   1 + exp  1 + erf     2  2π 2 σ  σ 2    2σ    2σ  Obviously the phase is not longer equally distributed for RICE fading [142]. For increasing RICE direct component, the phase ϕ ( t ) varies in increasingly narrower limits (see Figure 5.22). 72/160

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As the formulas (5.65) and (5.66) describe the RICE distribution, the channel is called RICE channel [25]. The PDF, CDF, and k -th moment of the generalisation R =

∑ i =1 X i2 n

(with X i being statistically

independent GAUSS random variables with [different] means and equal variances) are given by PROAKIS [224]. The cumulative distribution function (CDF) is given by [168] [224] ∞

 s 2 + r 2   s k  sr  FR ( r ) = 1 − exp  − ∑   Ik  σ 2  2σ 2  k = 0  r   The shape and behaviour of the RICE PDF and CDF are illustrated in the Figure 5.23.

(5.67)

Figure 5.23: Examples of PDFs and CDFs of the RICE distribution ( σ 2 = 1 , rlos ≡ s ) (Figure 1-8 from [25]).

The mean value µ Ri for the RICE distribution is given by [25]

π

s2   s2  s2    I0 ⋅ exp  − 2  ⋅   1 + 2 2σ 2   4σ 2  4σ    According to [168], the mean value can also be expressed as π 2  s2  ⋅ σ ⋅ L1  − 2  2 2  2σ  E{ R } =

µR = E{ R } = σ

 s2  s2   I + 2 1 2   2σ  4σ  

(5.68)

(5.69)

σ

where Ln ( x ) is the LAGUERRE function satisfying the equation [168] d2y dy + ( 1 − x ) + ny = 0 2 dx dx The mean square value resp. the average power in the RICE fading is given by [109] [168] Ω p = E { R 2 } = s 2 + 2σ 2 x

(5.70) (5.71)

The variance for the RICE distribution is given by [25]

π  s2 exp ⋅  − 2σ 2 8σ 2 

2   2  s2   2 2  s s σ s 2 I I ⋅ + + ( ) 0 1   2  2     4σ   4σ   VASCONCELOS and CORREIA [280] introduced the normalised magnitudes [280] r s , y= x= 2 ⋅σ 2 ⋅σ Thus, they obtained for the PDF of the RICE distribution ([280] from [214]) f X ( x ) = 2 x exp  − ( x 2 + y 2 )  I 0 ( 2 xy )

σ R2 = V { R 2 } = s 2 + 2σ 2 −

2

(5.72)

(5.73) (5.74)

These definitions might be useful when one has no information regarding the individual values of s and σ if during measurements only the total power was registered [280]. Hence, to adjust the theoretical distribution to the measured data, the signal has been normalised to the RMS value of its total power, which can be expressed as [280] r r x x u= = = = (5.75) 2 2 2 Ωp 1+ K s + 2σ 1+ y

where the RICE parameter K has been introduced. 73/160

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The RICE factor K (“Ricean K ”, shape parameter) is defined as the ratio of the power of the dominant multipath component to the (average fading) power of the remaining, non-specular multipath (which is the total scattered power 2σ 2 = σ u2 ) [2] [25] [62] [76] [89] [109] [142] [165] [226] [275] [280] s2 s2 = = y2 (5.76) 2 2 2σ σu It is a measure of fading whose estimate is important in link budget calculations [2]. Another, more theoretical definition of the model RICE factor K as the quotient between the summation of all deterministic parts and the summation of all scattered parts of one complete scattering-function is [35] K=

+ν max τ MED

K=

∫ ∫

−ν max 0 +ν max τ MED

∫ ∫

−ν max

Sd ( τ ,ν ) dτ dν (5.77) S s ( τ ,ν ) dτ dν

0

where Sd ( τ ,ν ) and S s ( τ ,ν ) denote the deterministic and the scattered parts of the scattering function. Using the RICE parameter K we can express the RICE distribution as [142] [165] 2r 2r   r2  f R ( r ) = 2 ⋅ exp  −  2 + K   ⋅ I 0  K  σ σu  u    σu  (5.78) r ≥ 0, K ≥ 0 2 2 Kr r  2 Kr     = 2 ⋅ exp  − K  1 + 2   ⋅ I 0   s s   s    and with the definition of the scale parameter Ω p = E { R 2 } we obtain [2] [109] 2( K + 1) r K ( K + 1)   ( K + 1 ) r2   exp  − K − I0  2r   , r ≥ 0, K ≥ 0, Ω p ≥ 0 (5.79) Ωp Ωp Ωp     The RICE distribution can be rewritten in terms of the fast varying instantaneously received signal power p . The PDF is then modified to [25] [275] K +1 p p   fP ( p ) = exp  − ( K + 1 ) − K  ⋅ I 0  2 K ( K + 1 )  (5.80) P0 P0 P0     fR ( r ) =

where P0 denotes the local mean power. It should be noticed that when the dominant component fades away (i.e., when if s → 0 resp. K → 0 ), the amplitude distribution Eqn. (5.65) transforms to the RAYLEIGH distribution ([25] [28] [89] [126] [156] [165] [298]), whereas in formula (5.66) the phase tends to the uniform distribution (as it is the case in the RAYLEIGH distribution) [25]. Therefore, the RICE distribution contains the RAYLEIGH distribution as a special case. [28] [126] On the other hand, if the fixed path vector has a length considerably longer than the RAYLEIGH vector (power in the stable path is considerably higher than the combined random paths, i.e., if K 1 ), r and ϕ are both approximately GAUSS, r having a mean equal to s and ϕ having zero mean [126] [165]. That is, in this case, the RICE distribution is well approximated around its mode by a GAUSS distribution [126]. The K -factor (for each tap) can be estimated from a collected data set using the following definitions for µ R ,rel [2] [203] [226] and σ R2 ,rel [2] (there denoted as γ )

µ R ,rel =

E{ R } E{ R

2

}

=

π

K K K ⋅ exp  −  ⋅  ( K + 1 ) I 0   + K I1     4( K + 1)  2   2  2  

σ R2 ,rel

=

V{ R2 }

( E{ R2 } )

2

=

2K + 1

( K + 1 )2

(5.81) (5.82)

Note that both µ R ,rel and σ R2 ,rel depend only on K , and the effect of Ω p is cancelled out by the proper definitions of the ratio of the moments, which enables a separate estimation of K and Ω p [2]. Based on the sample estimate of µ R ,rel , an estimate of K can be obtained by solving the nonlinear equation in (5.81)

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numerically. Figure 5.24 shows this dependence (5.81) graphically. However, K can be expressed in terms of σ R2 ,rel explicitly as [2] K=

1 − σ R2 ,rel 1 − 1 − σ R2 ,rel

(5.83)

According to ABDI et al [2], σ R2 ,rel turns out to be a useful quantity as it also provides a reliable and simple moment-based estimator for the m parameter of NAKAGAMI fading distribution, which is m = 1 σ R2 ,rel .

Figure 5.24: The relationship between the statistics of the received amplitude and the RICE factor K (Figure 5 from [226]).

The level crossing rate of the RICE distribution, LR ( ⋅ ) , for crossing of envelope level r is given by [50] r⋅s  r2 + s2  (5.84) ⋅ exp  − ⋅ I 0  2   2 σ 2σ  σ   where ν max is the maximum DOPPLER shift experienced by the mobile terminal. Using the normalised variables described earlier one gets [50] [109]: LX ( x ) = 2π ⋅ ν max ⋅ x ⋅ exp ( − ( x 2 + y 2 ) ) ⋅ I 0 ( 2 xy ) (5.85) LR ( r ) = π ⋅ ν max ⋅

LU ( u ) =

r

2π ( K + 1 ) ⋅ ν max ⋅ u ⋅ exp ( − ( u 2 ( K + 1 ) + K ) ) ⋅ I 0 ( 2u K ( 1 + K ) )

(5.86)

Eqn. (5.86) can then be used to analyse experimental data, once the value of K is known. For the average fade duration, GOLDSMITH [109] refers to Eqn. 2.93 in [263]. The usage of the RICE distribution for 60 GHz channels is justified in several references: • In [62] it has been checked for the indoor case that the fluctuations of short-term power are due to phase changes only and that they can be modelled by means of a RICE distribution. • The results for a canyon-like urban street presented in [280] and [281] show, that the small-scale (fast) fading was well described by the RICE distribution in ~90% of the cases; the RICE parameter along the street had a GAUSS distribution. • Following GOSSE et al [110], it is in general accepted that the best approximation of small-scale distributions is always the RICE distribution, both for indoor and outdoor propagation [66]. Indeed, the high amplitude of the LOS and specular reflected components swamp the randomly scattered component of the received signal and change the distribution of the envelope from a nominal RAYLEIGH distribution to a RICE distribution [271]. In outdoor environments, the simple sum of the direct ray plus a reflected one is often enough to describe the channel [53] [282]. • However, GOSSE et al [110] also state, that some references adopt other assumptions, closer to what is classically used for the 2GHz band. o RAYLEIGH distribution for all channel taps, except the first one, which is RICE distributed (LOS component in the assumed indoor environment) [114], o RAYLEIGH distribution for all channel taps, in the indoor environment [256]. • The small-scale fading caused by multipath is typically modelled with a RICE distribution for LOS and RALEIGH for non-LOS, the RICE K-factor is found to be highly variable over a large range, with the highest values in LOS conditions [29]. • According to NOBLES ([200]), small-scale (less than a wavelength) signal variations are typically modelled with a RICE distribution for line-of-sight (LOS) and RALEIGH for non-LOS. 75/160

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5.5.4.4. NAKAGAMI m-Distribution The NAKAGAMI m-distribution (proposed by NAKAGAMI in [197]) is frequently used in the modelling of radio channels; it applies to cases where there is a large number of multi-path components as well as to cases where this number is limited [298]. In addition, it does not require the use of omni-directional antennas [298]. Physically speaking the NAKAGAMI m-distribution is obtained when many (scatter) component vectors are summed, which are not only random in phase ϕi but also random in length ri ; it is therefore a more general (and more realistic) model than RAYLEIGH [28] [126] where the length of the scatter vectors were assumed to be equal and their phases to be random. The NAKAGAMI m-distribution offers an advantage when analysing combinations of multiple signals (e.g. diversity, Rake receivers, Smart-antennas) in that it is easier to use than the RICE distribution [28]. In [298] it is expected, that the NAKAGAMI m-distribution is well suited for describing the LMDS channel at 28 GHz. According to [298], it is indicated by the study [209], that the RICE distribution may fail to characterise LMDS radio channels, because the use of high-gain antennas limits the number of propagation paths. The NAKAGAMI-derived formula for the PDF of r = ∑ ri e jϕi is written as [28] [109] [126] [154] [168] [224] [298]

where Ω p = E { R 2 }

m

2  m   m 2 ⋅ ⋅ r 2 m −1 ⋅ exp  − r  , r ≥ 0, m ≥ 0.5 Γ ( m )  Ω p   Ωp  is the average power [109] [224], m is the fading figure defined as [224] fR ( r ) =

( E{ R2 } ) m= V{ R2 }

2

=

E

{( R

Ω2p 2

− Ωp )

2

}

, m≥

1 2

(5.87)

(5.88)

And Γ ( x ) is the Gamma function given here as [154] ∞

Γ ( x ) = ∫ e −ϑϑ x −1dϑ

with

x>0 .

(5.89)

0

For the cumulative distribution function one obtains the incomplete Gamma function [168] 1 m 2 m 2   FR ( r ) = r = P  m, r  ⋅ γ m, Γ ( m )  Ω p  Ω p  

(5.90)

Figure 5.25: NAKAGAMI distribution (Abbildung 2.10 from [154]).

The n -th moment of a NAKAGAMI-distributed R is [224] n

Γ ( m + 12 n )  Ω p  2 E{ R } = Γ ( m )  m  Thus, the mean value and mean square value are, resp., [168] n

(5.91)

1

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resulting in a variance [168] 2  1  Γ ( m + 12 )   V{ R } = Ω p ⋅  1 −    m  Γ ( m )     For the power distribution holds [109]

f R2 ( r 2 ) =

(5.94)

m

1  m   m 2 r  ⋅ ⋅ r 2( m −1 ) ⋅ exp  − Γ ( m )  Ω p   Ωp 

(5.95)

The NAKAGAMI distribution is a general fading distribution that contains many other distributions as special cases [126]. It reduces to a RAYLEIGH distribution for m = 1 [28] [109] [126] [197] [298] and to the onesided GAUSS distribution for m = 1 2 [126]. It also approximates, with high accuracy, the RICE distribution [25] [126] for higher values of the parameter m [28] (for m = ( K + 1 )2 ( 2 K + 1 ) the distribution reduces to RICE fading with parameter K [109]). For m → ∞ we get an AWGN channel [109]. The NAKAGAMI distribution also approaches the lognormal distribution under certain conditions [126]. Note that the m parameter can be less than one, in which case the fading is “worse than RAYLEIGH” [109].

5.5.4.5. WEIBULL Distribution The WEIBULL fading distribution for a random variable R has a PDF given by [126] [154]  br α  α b  br α −1 ⋅ exp  −    , r ≥ 0 fR ( r ) =   r0  r0    r0  

(5.96)

where α is a shape parameter, r0 is the RMS value of r , and b = [ ( 2 α ) Γ ( 2 α ) ]1 2 is the normalisation factor [1] [154].

Figure 5.26: WEIBULL distribution for constant r0 = 1.0 and varying shape parameter α (Abbildung 2.11 from [154]).

Figure 5.27: WEIBULL distribution for constant r0 = 2.0 and varying shape parameter α (Abbildung 2.12 from [154]).

A slightly different definition is given in [168], and [237] referring to [38]. Thus, a continuous random variable X has a WEIBULL distribution if its PDF has the form  β x β −1 x β ⋅ exp  −    ; x ≥ 0; σ , β > 0 f X ( x, σ , β ) =   (5.97) σ σ   σ   This model has a scale structure, that is, σ is a scale parameter, while β is a shape parameter [168] [237]. The CDF is [168], [237]:  x β FX ( x, σ , β ) = 1 − exp  −    (5.98)  σ   For mean value, mean square value, and variance, resp., we have [168] 1 E { X } = σ ⋅ Γ  1 +  (5.99) β  2 E { X 2 } = σ 2 ⋅ Γ  1 +  (5.100) β  77/160

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 2 1 2 V { X } = σ 2 ⋅  Γ  1 +  −  Γ  1 +    (5.101) β   β     According to HASHEMI [126], there is no theoretical explanation for encountering this type of distribution. However, it contains the RAYLEIGH distribution as a special case (for α = 1 2 ). It also reduces to the exponential distribution for α = 1 . Following [126], the WEIBULL distribution has provided good fit to some mobile radio fading data as given in [248]. E.g., for the first bin of the NLOS channel model at 17 GHz developed within the WINDFLEX project (see [237]), a combination of exponential and WEIBULL PDF is used.

5.5.4.6. Lognormal Distribution According to HASHEMI [126], the lognormal distribution has often been used to explain large-scale variations of the signal amplitudes in a multipath fading environment. Following ZHANG [298], the lognormal distribution applies if an LOS propagation path exists, along with a limited number of multi-path components. The PDF of a lognormally distributed random variable R is given by [83] [126] [154] [155] [165] [224] [298]  ( ln r − µ )2  1 1  ln 2 ( r r )  fR ( r ) = exp  − exp (5.102) = − , r ≥ 0 2πσ r 2πσ r 2σ 2  2σ 2   

where µ = ln r is the mean of the random variable ln r , which has a normal (GAUSS) distribution and

represents the amplitude of overall received signal, and σ 2 is the variance of this ln r . Again referring to HASHEMI [126], there is overwhelming empirical justification for this distribution in urban and ionospheric propagation. A heuristic theoretical explanation for encountering this distribution is as follows: due to multiple reflections in a multipath environment, the fading phenomenon can be characterised as a multiplicative process. Multiplication of the signal amplitude gives rise to a lognormal distribution, in the same manner than an additive process results in a normal distribution (the central limit theorem). In [298] it is proposed, that for a propagation environment including both LOS and non-LOS propagation paths, a hybrid of lognormal and RAYLEIGH distributions should be applied to the LMDS radio channel at 28 GHz. In [83] a quite similar model is proposed: The authors introduce a gradual transition from a completely log-normal state (no severe multipath fading) to a state where the average power is again determined by a log-normal variable but, similar to the case in [48], there exists also a multipath fading component that can be modelled by RAYLEIGH distribution. In other words, as soon as there is shadowing in the LOS path, mainly due to the presence of foliage, the propagation regime will change from a lossy one to a scattering regime due to leaves and branches. This is a hybrid model where a lognormal shadowing attenuation is multiplied by extra terms that are introduced to take into account dispersion caused by scatterers.

Figure 5.28: Lognormal distribution (Abbildung 2.13 from [154]).

For a discussion of the lognormal distribution in the context of shadowing see section 5.3.4.

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5.5.4.7. FRECHET Distribution According to [237] which refers to [38], a continuous random variable R has a FRECHET distribution if its PDF has the form:  σ β β σ β +1 f R ( r, σ , β ) =   ⋅ exp  −    ; r ≥ 0; σ , β > 0 (5.103) σ r    r   A FRECHET variable R has the CDF [237]  σ β FR ( r , σ , β ) = 1 − exp  −      r   This model has a scale structure, with σ a scale parameter and β a shape parameter [237].

(5.104)

E.g., for the first bin of the LOS channel model at 17 GHz developed within the WINDFLEX project (see [237]), a FRECHET PDF is used.

5.5.4.8. Exponential Distribution According to [237] which refers to [38], a continuous random variable R has an exponential distribution if its PDF has the form: 1 r−µ f R ( r, µ ) = ⋅ exp −  (5.105)  ; r ≥ 0; µ ,σ > 0 σ  σ  This PDF has location-scale structure, with a location parameter, µ , and a scale one, σ [237]. The CDF of the exponentially distributed variable R is [237] r−µ FR ( r , µ ) = 1 − exp −  (5.106)   σ 

{

}

{

}

E.g., in WINDFLEX [237] an exponential PDF is used for all bins except the first in both the 17 GHz LOS and the NLOS channel model.

5.5.4.9. SUZUKI Distribution According to HASHEMI [126], this distribution was first proposed by SUZUKI [265] to describe the mobile channel. It is a mixture of the RAYLEIGH and lognormal distributions. The SUZUKI distribution for a random variable R has the PDF [126] [154] ∞

 ( ln σ − µ )2   r2  1 exp exp (5.107) − ∫ σ 2  2σ 2  2πσλ  − 2λ 2  dσ 0 Following HASHEMI [126], this distribution, although complicated in form, has an elegant theoretical explanation: one or more relatively strong signals arrive at the general location of the portable. The main wave, which has a lognormal distribution due to multiple reflections or refractions, is broken up into subpaths at the portable site due to scattering by local objects. Each subpath is assumed to have approximately equal amplitudes and random uniformly distributed phases. Furthermore, they arrive at the portable with approximately the same delay. The envelope sum of these components has a RAYLEIGH distribution with a lognormally distributed parameter σ , giving rise to the mixture distribution of Eqn. (5.107). The SUZUKI distribution phenomenologically explains the transition from the local RAYLEIGH distribution to the global lognormal distribution. It is, however, complicated for data reduction since its PDF is given in an integral form [126]. fR ( r ) =

r

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6. Measurement and Simulation Results This section intends to present briefly the main characteristics of the propagation conditions in the 60 GHz band. The results presented hereby were found in the literature for measurements and simulations performed in indoor as well as outdoor environments. It must be noted that channel measurements in the literature are often very specific.

6.1 Indoor 6.1.1. TU DRESDEN Measurements and IMST Simulations In an empty room (12.40 m × 8.05 m × 3.5 m) at DRESDEN University of Technology (TUD) which is illustrated in Figure 6.4 measurements13 of mm-wave indoor radio channels were accomplished for several configurations; see [130] and [131]. All measurements were performed with a bandwidth of 2 GHz for LOS and NLOS around a centre frequency of 60 GHz, 61 GHz, or 62 GHz. Impulse responses were calculated from the measured frequency transfer functions using inverse FOURIER transformation. Within this study we want to refer to two measurement scenarios. In both cases, the transmitter antenna is a biconical horn antenna with 6 dBi gain (see Figure 6.1) and the receiving antenna is a shaped monopole with 4 dBi (see Figure 6.3), respectively. Both antennas have an omni-directional antenna characteristic in the horizontal plane. Scenario 1 Here Tx and Rx antenna were placed in a height of 1.50 m above the floor, and the receiver was moved during the measurements step by step from position 1 to position 3 (see Figure 6.4). The results served as basis for the TUD-LOS1 and TUD-NLOS1 channel models presented in section 7.2.3. Scenario 2 Here the Tx antenna was placed 2.5 m above the floor at the same position, and the Rx antenna was at a height of 1.0 m fixed on position 1. A person sitting on a table was stepwise moved through the direct path to explore the effect of human shadowing. It should be mentioned that in both scenarios because of the directivity of the antennas and the room geometry no measurable reflections from floor or ceiling occurred [130]. Within BROADWAY, KUNISCH and PAMP from IMST performed simulations (see [31]) using an electromagnetic modelling tool based on ray-tracing (Wireless Insite from Remcom, Inc.) for scenario 1 to endorse the TUD measurement results.

Figure 6.1: Biconical horn (part of Bild 3 from [130]).

Figure 6.2: Monopole with shaped metal ground plane (part of Bild 3 from [130]).

13

Figure 6.3: Waveguide fed dielectrical lens antenna (part of Bild 3 from [130]).

The work was partly funded by the Deutsche Forschungsgemeinschaft (DFG) under contract INK13, by the Free State of SAXONY, and by the European Commission, DG XIII, as ACTS project AC006 MEDIAN.

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Figure 6.4: Measurement environment at Dresden University of Technology (after Bild 1 from [130] and Fig. 1 from [131]).

A very vivid impression of the ray expansion in the room under consideration, which was gained in the raytracing simulations ([31]), gives Figure 6.5, which shows the 10 strongest paths between the transmitter and the receiver (at position 3).

Figure 6.5: The 10 strongest paths between Tx and Rx position 3 (Fig. 2 from [31]).

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In order to obtain below presented impulse responses Figure 6.10, Figure 6.12 and Figure 6.14, measurements were done at indicated positions 1, 2 and 3, respectively. Figure 6.6 presents the average of all 3,000 calculated impulse responses for scenario 1, whereas Figure 6.7 presents the average of the 301 simulated impulse responses from [31].

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Figure 6.7: Average of simulated impulse response magnitudes (top of Fig. 3 from [31]).

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The average impulse response can be described with three clusters: 1. direct path, 2. first order reflected paths from side walls, 3. second order reflected path from sidewalls and first order reflected path from window front. Since the receiver is moved towards the transmitter, the arrival time of the direct path is decreased for each new measurement. Therefore, the cluster of the direct component looks broad but is actually small for each separate impulse response. This effect occurs for each wave arriving at the receiver. Whereas Figure 6.6 showed the average PDP for configuration 1, Figure 6.8 gives a vivid overview about the behaviour of the PDP on the way from position 1 ( x = 0 m ) via position 2 ( x = 1.5 m ) to position 3 ( x = 3 m ). Figure 6.9 shows a PDP with approximately mean received power, average delay and RMS delay spread.

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Figure 6.8: Measured 60 GHz impulse responses with scenario 1.

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In Figure 6.10/Figure 6.11, Figure 6.12/Figure 6.13 and Figure 6.14/Figure 6.15 the clusters described above can be found again. Only the relative positions of the clusters with respect to each other and their power level differences are changed. These impulse responses are typical for LOS conditions in the considered environment. The simulation results from [31] are given in parallel to the measurement results from TUD. As it becomes evident, measurement and simulation results match to a high degree for scenario 1, thus confirming one another.

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Figure 6.10: Measured impulse response magnitude at position 1 (Fig. 3a from [131], bottom of Fig. 4 from [31]).

Figure 6.11: Simulated impulse response magnitude at position 1 (top of Fig. 4 from [31]).

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Figure 6.12: Measured impulse response magnitude at position 2 (Fig. 3b from [131], bottom of Fig. 5 from [31]).

Figure 6.13: Simulated impulse response magnitude at position 2 (top of Fig. 5 from [31]).

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Figure 6.14: Measured impulse response magnitude at position 3 (Fig. 3c from [131], bottom of Fig. 6 from [31]).

Figure 6.15: Measured impulse response magnitude at position 3 (top of Fig. 6 from [31]).

Whereas the results presented up to here did belong to scenario 1, now some results from scenario 2 shall be presented. Figure 6.16 shows the measured PDP when the person was about 1 m alongside the direct path, that is, no blocking occurred. The corresponding frequency response can be seen in Figure 6.18. Figure 6.17 shows the PDP for the case that a person is fully blocking the direct path; Figure 6.19 shows the corresponding frequency response. As it can be seen, the direct path’s contributions are strongly attenuated, whereas the structure and the power of the multipath contributions hardly change. Some more results regarding received power, RMS delay spread and mean delay are presented in section 5.3.3.

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6.1.2. IMST MEDIAN Measurements 6.1.2.1. Environment In [29] and [162] 60 GHz channel measurements by IMST (Institut für Mobil- und Satellitenfunktechnik, which is a partner in BROADWAY) are described, which were carried out within the framework of the ECfunded ACTS AC006 MEDIAN project.

Figure 6.20: Floor plan of the library. Shaded areas indicate bookshelves (various desks and chairs are not shown) (from [162]).

The measurements were performed with a bandwidth of 960 MHz in a library at IMST premises (Figure 6.20). The room is approx. 13 m × 5 m × 2.6 m in size. Four metal bookshelves of 2 m height and 2.5 m to 5 m length are standing parallel to the shorter wall, while a 6 m × 2 m metal bookshelf stands along the 84/160

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longer wall. Bookshelves are almost completely filled with books, magazines, etc. Some tables and chairs are interspersed within the shelves. One long side of the room is made of concrete and has windows. The observed indoor environment with large metal reflectors (book shelves) was supposed to cause large multipath contributions, resulting in a kind of worst case LOS scenario. Emphasis was put on LOS or almost LOS conditions (i.e., no strict LOS, but with still a dominant path e.g. by diffraction), which was felt to be the most relevant practical application case. The AP antenna was an almost vertically polarised omnidirectional waveguide fed dielectric lens antenna designed for a constant power flux density in a height of approx. 1.5 m below the antenna within a radius of approx. 6 m (same as in [26]; see also Figure 6.3); the gain is 8 dBi (in directions 76° from vertical). For the measurements reported here, two types of MT antenna were used: a 20 dBi standard gain horn (same as in [26]) and a wideband printed array of 8×8 pentagonal dipoles with a total gain of 22 dBi. The MT antennas were used in both polarisation orientations. The MT antenna and the down-converter were positioned on a linear rail to facilitate precise sampling of distance. For a number of measuring positions, the antenna was moved along the rail at a constant height of approx. 1 m. The rail was oriented perpendicular to the respective line of sight (LOS) or parallel to a wall of the room. The measuring positions were selected such as to cover different typical situations. The horizontal separation of the measuring points and the AP antenna was varied between 1.5 m and 4.5 m.

6.1.2.2. Measurement Results Figure 6.21 shows two sets of measured impulse responses at two LOS positions. Note that due to the constant power flux design of the AP antenna, the gain is comparable for both positions despite the different distance between MT and AP. Multipath decay is slower for position farer from the AP. The effect of mispointing at short distances is clearly visible in Figure 6.21 (b). Moving the AP antenna 25 cm here results in a 10 dB drop of the direct path signal, and, as the multipath is approximately constant, a corresponding degradation of the C/M ratio [29] [162].

Figure 6.21: Measured impulse responses at two positions: (left) far from and (right) near to AP (from [29] [162]).

In Figure 6.22 two averaged power delay profiles (PDP) for two LOS positions far (a) and near (b) the AP are given. Multipath contributions are visible approx. 30 dB below the LOS level. The envelope of the multipath shows a linear (on dB scale) decay behaviour. Some additional peaks are visible indicating the existence of additional discrete echoes. [29] [162] For these two positions, a comparison of the empirical probability density function (PDF) of the PDP amplitude and the maximum likelihood estimate (MLE) of a RICE PDF for a 5 ns delay window of 501 PDP’s is shown in Figure 6.23. In both cases, the power ratio of the constant and stochastic part, the K factor, is sufficiently low to effectively reduce the RICE to a RAYLEIGH PDF, i.e., real and imaginary parts of the complex impulse response essentially follow a GAUSS distribution, confirming the proposition in [26]. The match between the empirical and MLE RICE PDF is significantly better for the position near the AP. This may be due to the fact that the spread of multipath directions-of-arrival may be much higher for the nearer position than for the remote position. At that position, multipath contributions are supposedly more likely to arrive from the general direction to the AP. [29] [162]

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Figure 6.22: Averaged power delay profiles at two LOS positions: (left) far from and (right) near to AP. The vertical lines denote the 50 % - 99 % energy window of the noise normalised PDP (from [29] [162]).

Figure 6.23: Empirical PDF and maximum likelihood estimate of RICE PDF for a 5 ns delay window in the multi-path region of 501 PDP’s for two LOS positions: (left) far from and (right) near to AP (from [29] [162]).

6.1.3. SMULDERS Measurements at TU/e 6.1.3.1. Environments SMULDERS describes in [253] and [256] results of an extensive indoor measurement campaign in the 5759 GHz frequency band carried out at the Technical University of EINDHOVEN (TU/e). Bandwidth was 2 GHz and time-domain resolution 1 ns. A part of these measurements was dedicated to collect power delay profiles (PDP) in different indoor environments using several antennas and antenna positions. The PDP measurements in [253] were performed in 8 different environments: Environment A (Reception Room in the Auditorium Building) is an empty, almost perfectly rectangular room with dimensions 24.3x11.2x4.5 m³. One (long) long side is completely windowed with double thermo pane glass in a steel framework from floor to ceiling. The walls are mainly made of wood. The concrete floor is covered with a carpet. The ceiling is a complex structure made of plastic. Environment B (Large Room in the Auditorium Building) is an amphi-theatre-shaped room with approximate dimensions of 30x21x6 m³. The walls and the ceiling are made of wood covered by acoustically soft material (rock wool). The central floor on which the measurement equipment was located is made of wood. A number of chairs are also lined up on the central floor. The transmitter was moved randomly among them. The ceiling is covered with plastic panelling with lighting holders and spotlights. Environment C (Large Hall in the Auditorium Building) has a complex structure with approximate dimensions 43x41x7 m³. Dominant objects are four staircases that lead to the balustrade of the second floor. The walls and the ceiling consist of plastered concrete. The floor consists of linoleum glued on concrete. Some tables and chairs are placed throughout the hall. Environment D (Vax Room in the Computing Center) has a complex structure with dimensions of 33.5x32.2x3.1 m³. The room has a bare concrete wall, one metal wall and two glass sides. The floor is linoleum glued on concrete. Many large mainframe computer and filing cabinets are dominant objects in this room.

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Environment E (Corridor in the Computer-Center Building) is a straight, empty corridor with dimensions 44.7x2.4x3.1 m³. The long sides are smooth metallic walls up to a height of 2.5 m and windows above. Swivelling doors with glass in a wooden frame are located half way down the corridor. These doors were open during the measurements. The floor is covered with thin carpeting and the ceiling is made of aluminium profiles with lighting holders. Environment F (Computer Room in the Computer-Center Building) is a rectangular room with dimensions 9.9x8.7x3.1 m³. One (long) side consists of large floor to ceiling double-glazed windows encased in a steel frame while the other sides are smooth metallic walls. Some 20 personal computers are lined up against these walls. Wooden chairs and tables with metal legs are lined up through the room. Environment G (Lecture Room in the Auditorium Building) is a typical rectangular classroom with dimensions 12.9x8.9x4.0 m³. One (long) side consists of large windows in a steel framework from 1 m height to ceiling. Up to 1 m height there is concrete. The other sides are walls that are completely covered with wooden lathing. The concrete floor is covered with linoleum. The ceiling is covered with lighting holders. Tables and chairs are lined up throughout the room. Environment H (Laboratory Room in the Faculty Building of Electrical Engineering) is rectangular with dimensions 11.3x7.3x3.1 m³. One (short) side consists of a window from 1 m height to the ceiling and a metal heating radiator case below. The other walls consist of smoothly plastered concrete. The floor is linoleum on concrete. Four square (0.5x0.5 m²) concrete pillars and a metal cupboard in a corner are dominant objects in this room. A number of large wooden benches with wooden shelves on top are located in this room. The ceiling consists of aluminium plates and lighting holders.

6.1.3.2. Antennas For the PDP measurements in [253], two different antennas were used: • an omni-directional biconical-horn antenna with 9 dBi antenna gain (see Figure 6.24) • a directional circular-horn antenna with 15 dBi antenna gain (see Figure 6.25 and Figure 6.26)

Figure 6.24: Co- and cross polarisation radiation pattern in the azimuth plane of a 57-59 GHz biconical-horn antenna (Fig. 3.6 from [253]).

Figure 6.25: Measured co-polarisation radiation patterns of the 57-59 GHz circular-horn antenna for the azimuth plane (Fig. 3.9a from [253]).

Figure 6.26: Measured co-polarisation radiation patterns of the 57-59 GHz circular-horn antenna for the elevation plane (Fig. 3.9b from [253]).

6.1.3.3. Configurations For the PDP measurements in [253], the antennas described in section 6.1.3.2 were located in three different configurations within the environments described in section 6.1.3.1. The configurations are illustrated in Figure 6.27. Configuration A: The directional (15 dBi) circular-horn antenna was used as the transmit antenna. It was placed at 20 randomly chosen (horizontal) positions 1.4 m above the floor. The receive antenna was 9 dBi omnidirectional biconical-horn antenna positioned in the middle of the room at 3 m height. At each measurement position, the directional horn was pointing in the horizontal plane towards the receive antenna. Configuration B: The directional antenna was used as the receive antenna. However, it was not located in the middle of the room but in a corner at 3 m height. The boresight direction was horizontal towards the opposite corner of the (rectangular) room. The receive antenna was a 9 dBi biconical-horn antenna. It was placed at 20 randomly chosen horizontal positions 1.4 m above the floor. Configuration S: Tx and Rx antennas were biconical-horn antennas (9 dBi). The transmit antenna was located at 1.4 m above the floor at a number of randomly chosen (horizontal) positions. The receive antenna was placed in the centre of the environment under test at 3 m height.

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Figure 6.27: Measurement configurations (Fig. 3.17 from [253]).

6.1.3.4. Exemplary Results The following figures show exemplary results gained from the measurements in [253]. Other results like RMS delay spread can be found in sections 6.4 and 7.5.2.

Figure 6.28: Typical impulse response obtained in environment A, configuration S (Fig. 4.1 from [253], Fig. 3 from [256]).

Figure 6.29: Average power delay profile in Environment B (Fig. 4.3 from [253]).

6.1.4. Normalised Received Power vs. Distance The following was taken from [28]. Path loss measurements have been performed by the Radio Communication Group of the TU/e in a room with dimensions 7.2×6×3.1 m3 [104]. The sides of the room consist of glass window and smoothly plastered concrete walls whereas the floor is linoleum on concrete. The ceiling consists of aluminium plates and light holders. The transmitting antenna was located in a corner of the room at a height of 2.5 m. This antenna has an antenna gain of 16.5 dBi and produces a fan-beam that is wide in azimuth and narrow in elevation. Its beam was aiming towards the middle of the room. A similar fan-beam antenna was applied at the receiving station, which was positioned at various places in the room at 1.4 m above the ground. For comparison, additional measurements have been performed with the fan-beam antenna at the receiver replaced by an omnidirectional antenna. 88/160

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Figure 6.30 shows the received power normalised on the transmitted power (NRP) in dB measured in the 5859 GHz band as function of the separation distance between transmitter and receiver. The upper solid curve in Figure 6.30 shows the NRP in case the beam of the receiving antenna is pointing exactly towards the transmitting antenna. The dotted curve represents the situation in which the fan beam at the receiver has an azimuth pointing deviation of 35°.

Figure 6.30: Normalised received power under LOS conditions (Figure 4-1 from [28]).

Figure 6.31: NRP [dB] vs. distance [m] under non-LOS conditions (Figure 4-2 from [28]).

The lower solid curve represents the situation in which the fan-beam antenna at the receiver is replaced by an antenna that has an antenna gain of 6.5 dBi and that radiates omni-directional in the horizontal plane. As a reference, the dashed curves are added which represent the respective theoretical results according to the free-space law of FRIIS, i.e., a 6 dB decrease per doubling of distance. The curvature of both solid NRP curves is typical for indoor situations in which antenna patterns are not well pointed towards each other at short distances. In that area, the NRP increases with distance. This is because the increased free space loss is more than compensated by antenna gain since the antennas are better directed towards each other. If the separation distance is increased further, these curves tend to become higher than the free-space curves because the reflections from walls etc. contribute effectively to the received power. The dotted curve remains lower because of the fixed 35° antenna mispointing at all distances. All curves in Figure 6.30 refer to the situation of a LOS path between transmitter and receiver. Figure 6.31 shows the curves for NLOS conditions. With application of the fan-beam antenna the average drop of NRP due to LOS path obstruction is about 11 dB for 0° as well as 35° pointing deviation. With the omnidirectional antenna this drop is about 4 dB. For the exact definition of θ d see [104]. The results in Figure 6.30 and Figure 6.31 are representative for other indoor environments in the sense that the free-space law can be considered as a reliable lower bound of NRP at relatively large distances.

6.1.5. ANDERSON Indoor Measurements at VIRGINIA TECH ANDERSON describes in [14] (summary in [15]) an extensive indoor measurement campaign at 60 GHz on the 4th floor of DURHAM HALL at VIRGINIA TECH. The measurement sites were chosen to be representative of a broad range of typical femtocellular propagation environments in a work setting, where a low power transmitter will serve a single room or portion of a floor. Figure 6.32 illustrates the building floor plan and identifies transmitter and receiver locations. More detailed plans can be found in Figures 7.4, 7.6, 7.7, 7.8, 7.9, and 7.10 from [14]. • Location 1: NLOS from room to room and from room to hallway (separation by drywall with studs) • Location 2: LOS, Tx at the end of a hallway • Location 3: LOS, Tx in the middle of a hallway • Location 4: medium sized room containing standard office cubicles (NLOS and cluttered propagation) • Location 5: NLOS, typical office reception area containing a single cubicle, chairs and office plants • Location 6: propagation through glass doors, glass reinforced with wire mesh • Location 7: propagation through glass doors, glass reinforced with wire mesh • Location 8: propagation through glass doors, clear glass 89/160

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Figure 6.32: Map of the 4th floor of DURHAM HALL at VIRGINIA TECH, wit Tx and Rx locations identified (Fig. 1 from [15]).

Tx and Rx utilised vertically polarised pyramidal horn antennas (25 dBi, first-null beamwidths of 50°, for elevation patterns see Figure 6.33 and Figure 6.34), this should emulate sectored antenna systems proposed for mm-wavelength indoor applications. The Tx and Rx antenna heights were always 1.2 m with the only exception of the Tx antenna height in location 4, which was 2.4 m. The measurement equipment provided a multipath resolution of 2.5 ns.

Figure 6.33: Azimuth antenna pattern (part of Fig. 7.1 of [14]).

Figure 6.34: Elevation antenna pattern (part of Fig. 7.1 of [14]).

On the next pages, impulse responses from the several locations can be seen. Typical local area PDPs, e.g. from locations 3.1 and 4.3, show that most multipath components arrive very soon after the direct path component, which results in not very long excess path lengths [14]. Propagation in a hallway with directional antennas is very ray-like, however, at location 4.3 soft partitions and office furniture introduce clutter into the propagation environment and create several strong multipath signals [14]. The channel is – for the environments under test – limited in time often to about 25 to 50 ns and can even degenerate to a one-tap channel. The given PDPs give a good insight into the 60 GHz indoor channel structure when applying highly directional antennas, especially when keeping an eye on the floor plan given in Figure 6.32.

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.35: Location 1.1 Power Delay Profiles (Figure B.23 from [14]).

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Figure 6.36: Location 1.2 Power Delay Profiles (Figure B.24 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.37: Location 1.3 Power Delay Profiles (Figure B.25 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.38: Location 1.4 Power Delay Profiles (Figure B.26 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.39: Location 2.1 Power Delay Profiles (Figure B.27 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.40: Location 2.2 Power Delay Profiles (Figure B.28 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.41: Location 2.3 Power Delay Profiles (Figure B.29 from [14]).

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Figure 6.42: Location 3.1 Power Delay Profiles (Figure B.30 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.43: Location 3.2 Power Delay Profiles (Figure B.31 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.44: Location 4.1 Power Delay Profiles (Figure B.32 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.45: Location 4.2 Power Delay Profiles (Figure B.33 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.46: Location 4.3 Power Delay Profiles (Figure B.34 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.47: Location 4.4 Power Delay Profiles (Figure B.35 from [14]).

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Figure 6.48: Location 5.1 Power Delay Profiles (Figure B.36 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.49: Location 5.2 Power Delay Profiles (Figure B.37 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.50: Location 5.3 Power Delay Profiles (Figure B.38 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.51: Location 5.4 Power Delay Profiles (Figure B.39 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.52: Location 6.1 Power Delay Profiles (Figure B.40 from [14]).

10λ parallel local average PDP

10λ perpendicular local average PDP

½ metre track parallel local average PDP

½ metre track perpendicular local average PDP

Figure 6.53: Location 6.2 Power Delay Profiles (Figure B.41 from [14]).

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½ metre track perpendicular local average PDP

Figure 6.54: Location 7.1 Power Delay Profiles (Figure B.42 from [14]).

10λ parallel local average PDP

½ metre track parallel local average PDP

10λ perpendicular local average PDP

½ metre track perpendicular local average PDP

Figure 6.55: Location 7.2 Power Delay Profiles (Figure B.43 from [14]).

10λ parallel local average PDP

½ metre track parallel local average PDP

10λ perpendicular local average PDP

½ metre track perpendicular local average PDP

Figure 6.56: Location 8.1 Power Delay Profiles (Figure B.44 from [14]).

In Table 6.1 numerical results for the measurement campaign are given. Table 6.1: Summary of measurement results for local areas (Table 7.3 from [14], see also Table II from [15]). Link L fs Location Distance [dB] [m]

1.1 1.2 1.3 1.4 2.1 2.2 2.3 3.1 3.2 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 6.1 6.2 7.1 7.2 8.1

5.4 9.2 4.7 3.5 7.8 16.2 22.9 18.2 27.4 6.0 13.0 13.6 4.7 4.5 12.2 7.7 3.9 7.6 17.1 5.5 10.4 5.5

83 87 81 79 86 92 95 93 97 84 90 91 81 81 90 86 80 86 93 83 88 83

L path

στ

[dB] (excluding antenna gains)

Min 97 101 91 81 72 76 95 88 97 89 97 89 88 76 94 85 73 88 97 93 97 84

Avg 98 103 93 82 73 78 98 89 99 94 99 91 89 81 96 87 80 89 103 94 99 85

Max 99 105 94 83 74 87 104 90 100 98 101 97 90 83 97 87 83 91 107 95 99 86

τ max

[ns]

Min 14.8 17.9 15.7 1.0 2.5 7.2 6.0 11.0 7.7 9.8 9.1 10.2 5.5 5.8 2.9 5.2 2.9 2.0 19.2 8.9 6.2 16.9

Avg 17.5 20.2 16.8 2.5 5.6 7.9 7.5 13.8 9.4 11.4 13.6 14.5 12.9 7.9 7.8 8.0 3.9 5.8 25.3 11.9 9.2 19.1

[ns]

Max 20.2 22.0 18.3 3.7 7.6 8.5 9.1 16.5 11.6 15.8 17.9 18.8 22.4 11.5 11.5 10.4 5.9 12.0 30.0 14.2 12.1 24.1

Min 35 24 30 5 3 3 3 3 3 3 12 18 3 3 3 3 3 3 37 3 3 37

Max 51 80 60 5 5 13 28 3 12 3 25 26 13 15 12 13 17 4 75 22 20 73

Remark: We can't emphasise strongly and often enough that all these measurements were done with Tx and Rx antennas aligned. Results would dramatically change if this wouldn’t be the case (see also section 5.4.4).

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6.1.6. XU Indoor Measurements at VIRGINIA TECH 6.1.6.1. Environment and Antennas XU describes (among other things) in [291] an extensive measurement campaign at 60 GHz that was performed in 8 different indoor locations at VIRGINIA TECH. The locations were as follows (for more details like photos see [291]): • • • • •

• • •

Location 1: typical hallway (L×W×H = 102×2.1×4.3m), Tx fixed at one end, always LOS Location 2: typical hallway (54.7×2.9×4.3m), Tx fixed at one end, always LOS Location 3: conference room (6.7×5.9×4.3m). Tx fixed in one corner, Rx in the opposite corner or centre of the room Location 4: classroom (8.4×7.1×4.3 m), Tx fixed in one corner, Rx in the centre and the other three corners of the room Location 5: NLOS propagation; Rx in a laboratory (11.7×5.1×4.3m), Tx in hallway; two different positions (Tx and Rx separated by a composite wall with metallic studs inside; Tx and Rx separated by a glass door) Location 6: NLOS propagation, adjacent rooms (11.7×5.1×4.3m; 5.1×4.3×4.2m) separated by a composite wall with 40 cm separated metallic studs inside Location 7: outdoor parking lot with no cars, only possible scatterers were lamp posts Location 8: outdoor location near an exterior stone wall, Tx and Rx placed along the wall with a separation of 2 m to 5 m from each other and 3.5 m from the wall

Figure 6.57: Receiver and transmitter antenna patterns used in the measurement campaign (Figure 61 from [291]).

For this measurement campaign, and open-ended waveguide with 90° half-power beamwidth (HPBW) and 6.7 dBi gain was used as the transmitter antenna, and a horn antenna with 7° HPBW and 29 dBi gain was used as the receiver antenna (see also Figure 6.57). These antennas were chosen to emulate typical antenna systems that are proposed for millimetre-wave indoor applications, where a sector antenna is used at the transmitter and a highly directional antenna is used at the receiver. [291]

6.1.6.2. Power Angle Profiles A very instructive part of the results – as the authors of this BROADWAY study think – are power angle profiles (PAP), which were measured to investigate the correlation between the propagation environment and the multipath AOA. The measured PAPs were imported into the site-map to identify the origin of each multipath component. Examples of XU’s [291] PAP results are shown in Figure 6.58 for propagation within a room, in Figure 6.60 for propagation in a hallway, and in Figure 6.59 for propagation into rooms. The PAPs exhibit strong correlation with the propagation environments. The following observations were made from the recorded PAPs: •

Propagation within a room [291]: As shown in Figure 6.58, when the LOS path exists, the maximum multipath component is always from the LOS direction. The value of the maximum multipath power is given as P in dBm in the legend. Powers of the other small multipath components are given in dB in the figure relative to the maximum power. LOS and first-order reflected waves contribute the majority of the multipath components (the order of reflection is referring to the number of reflections that a multipath component goes though before is reaches the receiver). In the centre location 4.2, there are only three strong multipath components: one is the LOS component, the other two are first-order waves from the sidewalls. The reflected wave from “wall 2” is 19 dB below the LOS component. The blackboard appears to be a strong reflector. The reflected wave from the blackboard is only 8 dB below the LOS path. There are more multipath components in the corner locations of the room. In location 4.4, the multipath components consists of LOS component, first-order reflected waves from “wall 2” and the blackboard, and the second-order reflected wave from “wall 2” and the blackboard. Similar analysis can be performed for locations 4.1 and 4.3. At location 4.1, the strong reflection of the blackboard resulted in a multipath component with comparable power with the LOS component.

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Figure 6.58: AOA measurements for propagation with a room (location 4), relative power levels given in polar plots and peak multipath power (P) given in text. Rays are shown only for locations 4.2 and 4.4 in the figure, similar procedure can be performed for all the locations (Figure 62 from [291]).

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Figure 6.59: AOA measurements for propagation into rooms (locations 5 and 6), relative power levels given in polar plots and peak multipath power (P) given in text (Figure 64 from [291]).

Figure 6.60: AOA measurements for propagation along a hallway (location 2), relative power levels given in polar plots and peak multipath power (P) given in text (Figure 63 from [291]). •

Propagation through walls [291]: Figure 6.59 shows the measurement results for NLOS propagation into rooms. In both locations, the radio wave propagates through a composite wall with metallic studs. Results indicate that the metallic studs have strong impact on the millimetre-wave propagation. In location 5, the metallic studs do not obstructs the LOS path. Measurement results show that the penetration loss is 9 dB through the wall between the room and the hallway. The strongest multipath component is still from the transmitter direction. Other major multipath components are reflected waves from the metallic bookshelves. The multipath energy seems to be more diffuse in their AOAs in this NLOS case as compared to the LOS propagation within a room (Figure 6.58). Reflections/scattering of the radio wave from the studs also contribute to the

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multipath components. In location 6, the metallic stud obstructs the LOS path, and the measurement results show that the penetration loss through the wall and the blackboard is as high a 35.5 dB. Since the LOS path was highly attenuated, the maximum multipath power came from the reflected path through two glass doors. Other strong multipath components might come from the reflection/scattering from the metallic plotter of the studs. Propagation in a hallway [291]: Figure 6.60 shows the measurement results of location 2 in the hallway. For all the measurement positions, the strongest multipath component came from the LOS direction. For location 2.1, the main multipath components are LOS and the reflected waves from the sidewalls. Location 2.2 is near the intersection of 2 hallways. The LOS component and reflected waves from sidewalls are still strong, but became more diffusive. A strong multipath component came from the corner of room 257. As shown in locations 2.3, 2.4 and 2.5, when the separation further increases, the reflections from the sidewalls became insignificant. The reflection from the other end of the hallway became stronger. Results from location 2.5 clearly show the LOS and the reflected wave components.

These measurement results clearly demonstrate a strong correlation between the propagation environments and the multipath channel structure. The following general conclusions can be made from all the measurement results [291]: •

•

For LOS applications, free space propagation and reflection are the dominant propagation mechanisms. When there are no strong reflectors in the propagation environment, the reflected multipath components are at least 10 dB below the LOS component. LOS component and first-order reflected waves contribute majority of the received signal power. Strong multipath components can results from strong reflectors, such as metallic furniture. When strong reflectors are present, the reflected waves can be comparable to the LOS component. For NLOS applications, the direct path can be highly attenuated and become comparable to reflected multipath components. As a result, the multipath channel structure may become more diffuse than in LOS environments. When radio waves propagate through composite walls, metallic studs within the wall must be considered. Penetration loss through the composite wall depends on the position and orientation of the studs with the wall.

6.1.6.3. Results for TOA Statistics Channel measurements are highly dependent on the propagation environments and the measurement system setup [291]. Table 6.2 provides channel parameters both for systems with aligned antennas (“track”) and for systems with antennas pointing in arbitrary directions (“spin”) such as in a mobile environment (for more detailed results see Table 14 and Table 15 in [291]). Table 6.2: Measured time dispersion parameters from track and spin measurements (Tx-Rx separation: d Rx −Tx ) (part of Table 14 and Table 15 from [291]). Site info

LOS, hallway NEB

LOS, hallway Whittemore

LOS, room NEB

LOS, room Whittemore

Hallway to room Room to room LOS, outdoor parking lot LOS, outdoor

loc-#

1.1 1.2 1.3 1.4 1.5 1.6 1.7 2.1 2.2 2.3 2.4 2.5 3.1 3.2 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 6.1 7.1 7.2 8.1

Comments

open area

intersection

corner centre corner centre corner, ⊥ to Tx corner, ⊥ to Tx LOS through wall LOS through glass through wall Tx pattern Rx pattern near NEB

d Rx −Tx [m]

τ track

τ spin

στ ,track

[ns]

[ns]

[ns]

στ , spin [ns]

5.0 10.0 20.0 30.0 40.0 50.0 60.0 5.0 10.0 20.0 30.0 40.0 4.2 3.3 7.1 3.8 5.2 4.2 2.4 2.4 2.4 2.4 3.0 1.9 1.9 2.0

1.20 6.16 32.61 15.50 27.60 46.42 6.38 2.22 2.78 2.30 22.02 77.30 0.74 0.92 2.74 2.40 12.88 21.30 0.83 2.46 0.71 1.16 14.82 7.63

80.0 52.0 85.9 116.6 84.9 52.1 53.2 51.0 62.1 90.7 41.2 83.7 42.6 47.7 46.6 64.3 66.3 77.8 49.1 41.6 95.8 80.3 42.7 41.3 56.6 24.4

6.95 5.88 47.25 31.15 37.04 28.17 22.57 6.24 6.48 4.56 33.87 45.07 4.85 4.95 4.72 4.98 31.10 33.94 5.50 7.41 5.36 5.19 21.78 24.59

14.7 18.8 40.1 38.7 60.0 26.1 30.3 20.7 29.4 14.6 12.3 53.8 16.2 17.5 13.0 13.3 17.7 13.3 21.4 18.1 14.6 16.0 16.6 17.4 16.1 7.7

Results from Table 6.2 show a significant decrease of TOA delay statistics obtained from the track measurements compared to the spin measurements: •

RMS delay spread [291]: When the receiver antenna was pointed to different directions, the RMS delay spread was in the range of 7.5 ns to 76.5 ns for hallways, and 10.9 ns to 41.0 ns for rooms. When the receiver antenna was fixed, the RMS delay spread was significantly smaller. Typical ranges are from 4.6 ns to 47.3 ns in the hallways, and from 4.7 ns to 33.9 ns in the rooms.

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Mean excess delay [291]: When the receiver antenna was rotating, the measured τ was in the range of 41.2 ns to 116.6 ns for hallways, 42.6 ns to 77.8 ns for rooms, 41.6 ns to 91.8 ns for propagation from room to hallway and from room to room, and 24.4 ns to 56.3 ns for short distance outdoor measurements. In the hallway measurements, τ increased significantly in the open area near the elevator, such as in location 1.4. Significant reduction of delay was also observed when the antennas were aligned and fixed. Antenna alignment [291]: For example, the mean excess delay from the track measurement in location 1.1 is only 1.2 ns, while it is 80.0 ns from the spin measurements. When transmitter and receiver antennas are aligned, such as track measurement at location 1.1, the main multipath component is the LOS component. Other multipath components are largely attenuated by the directional antenna, forcing the excess delay to be close to zero. However, if the antennas are not aligned and pointing into different directions, such as in spin measurements, the LOS path is attenuated and becomes comparable to the reflected multipath components, resulting in a significant increase of time delay parameters.

6.1.6.4. Results for AOA Statistics The following results were gained from the spin measurements (for more detailed results see Table 14 in [291]): •

•

• • •

Angular distribution of multipath power [291]: Measurement results show that the angular spread, Λθ , ranges from 0.36 to 0.78 for hallway measurements, 0.62 to 0.84 for room measurements, from 0.63 to 0.81 for indoor NLOS propagation, and 0.12 to 0.49 for outdoor measurements with few nearby obstructions. These measurement results show a clear increase of the angular spread from the least cluttered outdoor environments to obstructed NLOS indoor environments. In the hallway where multipath components are mainly constrained along the path, the angular spread is smaller than in rooms. Also, with the increase of distance along the hallway, the angular spread increases, indicating more multipath coming from different directions which have powers comparable to the LOS component. These angular spread values accurately reflect the correlation between the propagation environments and the multipath angle of arrival distributions. Angular constriction [291]: High angular constriction, γ θ , results were observed in close distances in the hallway measurements (up to 0.88 at location 2.1, but only 0.15 at location 2.4) and in the outdoor measurements near a building (0.76). This is the result of distribution of multipath energy between LOS and strong reflected wave components. Maximum fading angle [291]: In the far side of the corridor (locations 1.6 and 1.7, for example), the received signal consists of the LOS component along the corridor and the reflected component from the end of corridor. These two components have opposite directions, and the maximum fading angle is along the LOS path. Direction of maximum multipath power [291]: Measurement results show strong dependence of the maximum AOA, θ max , on the propagation environments. For all LOS locations, almost all maximum AOAs are close to the LOS path within ±5°. Peak to average power ratio [291]: Peak to average power ration characterises the power of strongest multipath as compared to the average received power from all directions. This ratio gauges the increase of the received signal power by pointing the directional antenna in the maximum AOA direction. Values between 8.5 dB and 14.7 dB were measured during spin measurements.

6.1.7. Single Frequency Network Results 6.1.7.1. Virtual Cellular Network It has been shown by FLAMENT [90] [91] that shadowing is a particular problem when considering imperfect installation of infrastructure (see also section 5.3.3). The strong attenuation of the human body at 60 GHz considerably decreases the received power and changes the character of the multipath fading statistics, so that the resulting BER as a function of the received SNR increases with the shadowing density. In [90] and [91] FLAMENT introduces the concept of Virtual Cellular Networks (VCN) in order to increase the DOA diversity at the receiver, to introduce channel macro-diversity, and thus to avoid excessive handover between APs. Diversity is defined as the fact that information repeats itself (or can be repeated) in a different manner along a certain dimension. There are three main dimensions for diversity that can be exploited: frequency, time, and space. Polarity is another dimension, but depolarisation often occurs in wireless mobile systems (for example with rough scattering), which makes it less attractive. Diversity schemes are commonly used to mitigate the impact of both slow and fast fading by exploiting the decorrelation of signal contributions in space, time, or frequency. The discussion in [90] [91] showed that the performance loss of the proposed OFDM wireless indoor LAN system is caused by a combination of both shadow and multipath fading. In this context, frequency diversity can only improve the multipath-fading problem but not the shadow power drops, whereas time diversity will require long interleaving intervals due to the relatively slow evolution of the shadowing situation. On the other hand, the modified SALEHVALENZUELA model in suggests that there the power of particular taps is coming from specific DOA with small angular dispersion. If this theory holds at 60 GHz, a diversity scheme in space appears to be appropriate. Space diversity schemes generally use a set of antennas. Antenna diversity at the receiver, i.e. the use of more than one antenna, is relatively easy to achieve at 60 GHz since an antenna separation of a few wavelengths ( λ = 5 mm ) can be implemented even for small devices. However, it cannot resolve the shadowing caused by the user carrying the device. Using multiple APs seems the most promising solution, since it provides decorrelation of the received signal from the different APs since we add diversity in the DOA for the received rays.

VCN uses distributed access points (AP) and Single Frequency Networks within one virtual cell in order to form an adaptive wireless communication architecture. The situation is depicted in Figure 6.61 that differs from Figure 5.12 because the two AP are sending the same signal. 98/160

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The idea of VCN, where the same signal is simulcasted by several APs and the receiver accumulates all signal contributions, originates from Single Frequency Network (SFN), such as DAB, but VCN uses adaptive resource allocation. A VCN system intelligently selects the APs forming a virtual cell for a particular user. 1. 2. 3.

In order to preserve capacity, APs only transmit if their received power contribution at the terminal exceeds a certain threshold. The number of APs in one virtual network cell is limited in order to avoid increasingly time dispersive channels. In the case of good quality of the different channels, the system tries to combine the contributions from each VCN AP in an optimum way to increase the diversity gain.

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Same OFDM symbol from AP1 and AP2

Figure 6.61: Typical shadowing situations for indoor wireless systems in the VCN case (Figure 7.1 from [90]).

In order to avoid that shadowing situations result in a dropped network connection, the network must be designed in a way that AP’s coverage areas overlap each other. Hence, the key requirement for the installation of APs is a sufficient angular separation, possibly on opposite sides of a room, and a sufficient synchronisation of the AP. The major motivation for VCN is the increased DOA diversity at the receiver but it also introduces more TOA diversity (frequency-selection). The VCN basically creates a cell for a particular user and follows him. The concept is very interesting because the handover procedure does not exist anymore on the terminal side. It is the network that is switching APs on and off in such a way that the signal is received by the user. It changes completely the way we think about cellular network and new rules and adaptive techniques need to be implemented. The use of VCN requires a centralised network unit (or eventually a common control channel) deciding how the virtual cells move with the user. This is a major drawback. It will be difficult to implement the system in public places where many APs belong to different wireless network owners. However, it is the solution that will give the best results for the interference problem. VCN is used jointly with OFDM based modulation in order to alleviate the propagation delay originating from different transmitting APs in a virtual cell. Since OFDM is already identified as an important feature in a 60 GHz wireless channel because of its time-dispersive nature, the additional complexity at the receiver due to VCN is negligible. Channel combination in VCN results in a new power delay profile. Whenever rays from different APs contribute to the same discrete tap, they might cancel each other due to phase differences resulting in power loss. This effect could be circumvented if one knows the two channels before we send the signal from the transmitting APs but would require having a fast and reliable feedback channel in order to provide this information at the transmitters. Within the simulations, FLAMENT considered the downlink where each AP emits the same power. Simulations were based on a single frequency network and omni-directional antennas, all APs were synchronised and the receiver virtually summed the complex multipath signal received from the different AP. The occurrence of shadowing events can be significantly reduced already with 2 APs. For instance, a power gain of approximately 15 dB can be achieved with 4 APs at 10 % outage level. More detailed results and diagrams can be found in [90] and [91]. It is important to take into consideration that the total transmitted power increases linearly with the number of AP. Since the total emitted power is increased in order to keep the same coverage, one could argue that VCN is not power efficient. However, for the same outage level we can effectively reduce the total transmitted power. Therefore, since we gain more in outage when we add APs, than we loose in transmit power, the solution is power efficient. The use of VCN decreases generally the BER. It is worth mentioning that the performance does not increase with the number of APs in a VCN. This can be explained by the fact that the combined signals from the APs increase the frequency-selectivity of the channel. From the results, FLAMENT realised that the use of only two APs presents the best BER performance. However, the choice of the number of simulcasting APs will depend on the goal of the system designer, whether he wants to trade probability of outage against higher BER error floor. Given that the error floor using proper error control coding is easier to mitigate than the loss of signal due to shadowing, VCN architecture remains a good solution. 99/160

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6.1.7.2. Overlapped-Spot Diversity According to KOBAYASHI et al [155], it has been found for high-speed WLANs at 60 GHz that shadowing is one of the most important problems to be combated to realise reliable communications. Since both transmission and diffraction effects are very small in the 60 GHz band due to its quasi-optical nature, a human body constitutes a practically insurmountable obstacle and produces large path loss around 20 dB when the human is inside the direct LOS path [131] (see also section 5.3.3). In a realistic indoor environment such as an office, shadowing may frequently occur by people walking around, and then new countermeasure should be introduced against shadowing due to human motion. In [155] an anti-shadowing scheme called “overlapped-spot diversity” employing site diversity combined with OFDM modulation is proposed to realise high-speed reliable communications under shadowing in the 60 GHz band. In the proposed system, multiple APs sufficiently separated on a ceiling cover a same terminal so that it can receive more than one direct LOS paths even under shadowing situation. To realise that, a terminal should be constantly covered with multiple APs whose coverages overlap completely. By using OFDM, multiple APs within a single cell can transmit identical information using an identical frequency band, while the terminal receiver can simply sum up all the signals arrived from those APs without any specific combining technique. Of course, when multiple APs are employed against shadowing, the number of arriving paths, both multiple direct and reflected paths, will increase in proportion to the number of APs. As to [155], the application of OFDM for transmitting identical signal by multiple antennas using identical frequency originally comes from broadcasting system, which is known as Single Frequency Network (SFN). In contrast to these systems that only partially overlap on cell boundaries the overlapped-spot diversity system focuses on an anti-shadowing scheme, which consists in complete overlapped coverage by multiple APs located within a single cell. The performance of the system was evaluated with 1 to 3 AP antennas at the ceiling using three-dimensional ray-tracing simulations considering up to two reflections and lognormal shadowing. A few values of relative dielectric constant ε were applied to an empty room (20m × 20m × 3m, smooth surfaces) assuming various types of practical indoor environment. The terminal was placed at a height of 1.5 m, it was assumed immobile during the operation; hence, the DOPPLER frequency shift of the terminal itself is considered null whereas that of surrounding in the typical indoor environment is 2 ~ 10 Hz . Thus, the channel is considered non-frequency selective slow fading where fluctuations can be neglected during a few symbols. All antennas were assumed to be half-sphere omnidirectional ( G ( θ ) = 1 for θ ≤ π 2 , elsewhere G ( θ ) = 0 ), the total transmission power per system was set to be equal for fair comparison between systems with different number of APs. The simulations results in terms of average BER and outage probability (defined as the percentage of number of received locations where BER exceeds a threshold of 10-3 to total number of locations considered) indicated the following [155]: • • • •

By using the features of OFDM, the proposed overlapped-spot diversity system achieves good robustness over a wide range of shadowing. The proposed system with 2 and 3 APs can achieve an average BER reduction of two orders compared to that with single AP when σ L is within 8 dB. In indoor environment where reflection is small due to wooden obstructions or open windows, the single AP system becomes extremely sensitive to shadowing. Thus, the proposed system is confirmed to be particular effective. In the case of light to heavy shadowing where the location variability σ L is from 2 to 8 dB, the 2 AP system is effective enough, while for very heave shadowing such that σ L is over 10 dB, at least 3 APs are needed.

The improvement can be considered mainly due to the multiple APs, which can decrease the probability of simultaneous shadowing on direct paths, in other words, increase path visibility. In case that one direct path is shadowed in this system, the remaining direct paths make it possible to stabilise the performance [155]. The results indicate also that the performance is dependent on the relative dielectric constant. Remember that the smaller ε the smaller reflection and vice versa. When ε is small (=2), the weight of reflected paths is relatively small and the received power depends largely on the power of direct paths. In such a situation, the single AP system that has only one direct path becomes very sensitive to shadowing. Thus the outage probability is significantly increased when σ L arrives at 6 dB, while the proposed system still shows its robustness due to its multiple direct paths which contribute to path visibility. On the other hand, when ε is large (=8), a fairly low outage probability can be obtained for all systems with 1 to 3 APs when σ L does not exceed 6 dB. This is because reflected paths with large power due to large reflection may serve to enlarge the power of desired signal [155]. As to the authors of this study, an issue that must be solved for such systems is the power control of the single APs and of the set of APs as a whole. 100/160

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6.2 Outdoor 6.2.1. Results from Urban Streets in OSLO LØVNES et al present in [177] results from multipath measurements, which were obtained at 59 GHz with a maximum bandwidth of 200 MHz (that is, 5 ns resolution) during a campaign in 7 different streets downtown Oslo. Only instantaneous CIRs were treated, no averaging was performed to remove fast fading. The stationary Tx antenna was a 90-degree horn, the movable Rx antenna was a biconical horn assumed being omnidirectional, both antennas were vertically polarised. During measurements the LOS path was never obstructed by large vehicles; weather was sunny and dry. Here we want to detail only on streets A and F, because for them selected typical impulse responses are given in [177]. Street A (see Figure 6.62) has a width of 36 m, trees without leafs were located along and in the middle of the street, thus sometimes blocking the LOS path; some cars were moving, cars were parking, isolated buildings were on one side of street A separated by 7-8 metres, the buildings were 4 to 7 storied buildings made of concrete. For this street, we only focus on route A2. Street F (see Figure 6.63) has a width of 13 m, no trees were located on the street, many cars were moving, cars were parking with a bus being significant, there were no open spaces between the buildings, the latter were modern buildings made of concrete and steel, often covered with glass.

In Table 6.3 TOA parameters for the two routes are given. Table 6.3: TOA parameters for route A2 and F (excerpt from Table 1 of [177]). Route

Max. RMS delay spread τ RMS,max [ns]

Mean Excess delay τ [ns]

Maximum excess delay τ MED ,9dB [ns]

A2 F

54.5 20.6

19.8 20.6

150 265

Figure 6.62: Transmitter positions and measurement routes for street A, the shaded areas represent buildings. The height of the transmitter is indicated (h), lengths along the streets are in metres (part of Figure 2 from [177]).

Fractional energy delay window τ FED ,90% [ns] 85 270

Figure 6.63: Transmitter positions and measurement routes for street F, the shaded areas represent buildings. The height of the transmitter is indicated (h), lengths along the streets are in metres (part of Figure 2 from [177]).

In Figure 6.64, Figure 6.65, Figure 6.66, and Figure 6.67 four typical impulse responses are shown. Many of the measured CIRs looked like Figure 6.64, i.e. with only one peak. This peak, however, may consist of several rays that were not resolvable due to measurement resolution. In Figure 6.67 the multipath components caused by the parking bus are clearly cognisable. According to LØVNES et al [177], putting the receiver quite close to the transmitter, while the antennas are not pointing towards each other, also represents a bad situation in terms of time dispersion.

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Figure 6.64: Typical PDP from Route A2 (from [177]).

Figure 6.65: Typical PDP from Route A2 (from [177]).

Figure 6.66: Typical PDP from Route A2 (from [177]).

Figure 6.67: Typical PDP from Route F (from [177]).

6.2.2. Influence of Street Width In [55] a ray-tracing analysis of a canyon-like urban street was performed. The street was composed of slightly rough concrete walls, was 300 m long and 10 m respectively 50 m wide with no crossings, with a base station 5 m high located in one of the extremes at the middle, and the mobile moving along the street (in the middle of it) with its antenna 1.8 m from the ground. Both antennas are isotropic, with linear (vertical polarisation, and the receiver had a bandwidth of 200 MHz around the 59 GHz carrier. Figure 6.68 presents the delay spread for two different street widths (10 and 50 m), where the difference is notorious: the median value for RMS delay spread στ differ around 20 ns, where the narrowest street presents values of circa 3 to 4 ns. It is confirmed then that an increase of the street width will augment the values of the parameters of the impulse response. The average impulse response, taken along the whole street, is shown in Figure 6.69, where, again, it is noticeable the difference between the two situations; the average values for στ calculated for this average impulse response are 7.1 ns and 35.3 ns respectively for the narrow and wide streets (a factor of 5.0 when the street is 5 times larger). One can observe that the average impulse responses can be approximated by the well-known negative exponential behaviour.

Figure 6.68: Delay Spread (Fig. 4 from [55]).

Figure 6.69: Comparison of average impulse responses for two different street widths (Fig. 5 from [55]).

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6.3 Results for Coherence Bandwidth In Table 6.4 measurement and simulation results for coherence bandwidth are given. Table 6.4: Results for coherence bandwidth at around 60 GHz from literature. Environment

Corridor: 41.00×1.91×2.68m Tx stationary at one end

Antennas

Tx: 10 dBi std horn Rx: 6 dBi omni

Bcoh ,0.5

Bcoh ,0.7

Bcoh ,0.75

Bcoh ,0.9

[MHz]

[MHz]

[MHz]

[MHz]

d= 1.50

481.22

278.48

58.70

d=18.09 d=37.80

204.01 105.22

72.85 27.97

7.63 1.28 min : 1.28 mean: 14.09 max : 84.51 min : 1.10 mean: 11.53 max : 105.33 min : 5.82 mean: 31.31 max : 75.59 min : 6.80 mean: 23.25 max : 82.58 65 116 87

Comment

Tx: 10 dBi horn Rx: 10 dBi horn Tx: 10 dBi horn Rx: 6 dBi omni

Room: 12.80×6.92×2.60m, Tx fixed in one corner

Tx: 10 dBi std horn Rx: 6 dBi omni

with furniture empty

Corridor: 44×2.20×2.75m³

isotropic omni-omni (8.5 dBi) horn-horn (20.8 dBi)

162 310 222

Corridor: 41×1.92×2.68 m Tx fixed at one end and Rx moving towards other end Irregular room (5×7m)

237.8 microstrip antennas

LOS NLOS

232 160

108 197 147 28.4

Reference

[250]

[195]

2.8

[291] (from [117])

41.6 28.0

[47]

In Figure 6.70 and Figure 6.71 measurement results from SIAMAROU et al [250] for a corridor are shown. It can be observed that the coherence bandwidth is highly variable with the location of the receiver with respect to the base station. Figure 6.72 and Figure 6.73, also taken from [250], show, that the layout of the furniture did not influence significantly the frequency correlation values. Again, it can be observed for both environments that the coherence bandwidth is highly variable with the location of the receiver with respect to the base station. In Figure 6.74 the relation between RMS delay spread στ and coherence bandwidth BC measurement results for the corridor environment in [250] is shown. From our point of view, the results endorse the principal relationship Bcoh ∼ 1 σ τ , which is included in almost all the different expressions for the coherence bandwidth given in section 4.9.3. GOSSE et al [110] refer to [271] when stating that, in general, a power increase in the LOS component relative to the power in the randomly scattered component will cause an effective narrowing of the delay distribution and hence an increase in Bcoh . The lower Bcoh values occur when the LOS component is partially or totally obstructed, or when there is a specularly reflected component of comparable magnitude to the LOS component incident on the receiver.

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Figure 6.70: Coherence bandwidth for 0.9 correlation level as a function of Rx-Tx distance for the corridor (horn-horn) (Figure 7 from [250]).

Figure 6.71: Coherence bandwidth for 0.9 correlation level as a function of receiver position for the corridor (horn-omni) (Figure 8 from [250]).

Figure 6.72: Correlation bandwidth function for 0.9 correlation level as a function of receiver position for the room with furniture (Figure 12a from [250]).

Figure 6.73: Correlation bandwidth function for 0.9 correlation level as a function of receiver position for the room without furniture (Figure 12b from [250]).

Figure 6.74: RMS delay spread versus coherence bandwidth for the corridor (horn-horn) (Figure 9 from [250]).

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office room office rooms almost empty conference room (13.51x7.81x2.6m)

empty room (12.50 x 8.05m x 3.50m)

indoor arched straight corridor L-shape corridor indoor empty room obstacles are present due to furnishing --NLOS case, furnished room LOS furnished room LOS empty room Communication Laboratory (open plan site consisting of three rooms) corridor (3x30 m) Teaching Laboratory (15x30m) laboratory (3 rooms forming a L, each 10x10m) corridor (3x30m) teaching room (15x30m) empty room rooms

indoor

large room, (30×15x3 m)

library, 13x5x2.6m with metal bookshelves office scenario with furniture (24.6 × 6.0 (10.4) × 3 m) L B H

Environment

6.4.1. Indoor

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20 dBi horn or omni

monopole, 1 m above floor

20 dBi horn

biconical horn, 1 m above floor biconical horn, 2.5 m above floor lense, 2.5 m above floor biconical horn, 2.5 m above floor

omni monopole

omni, main beam ~λ/2 dipole wide (scalar feed horn), ~60° 3-dB width, main beam ~GAUSS

biconical horn

biconical horn

biconical horn, 2.5 m above floor

half-wave dipole

standard gain horn, wideband printed array

Rx Antenna

half-wave dipole

dielectric lens

Tx Antenna

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LOS LOS LOS LOS shading by a non-moving person (NLOS)

LOS LOS NLOS

no windows windows are included significant amount of window area, different wall materials no windows

BS at the ceiling in the middle of the room

Comment

13.59 10.91

M S M S

15 18…20 18…20 18.08 15.35

M

3 13 4.5..28 3…13

M M S M

3 13

6

100 1.02 5.82 20..75

36, 45

100 40

< 12

avrg

18

11 24 8 18

13 35

14

13 35

14

9…12 2…3 40…50 12 3 12

15…20

max

70…100 70…100

21…35

10…16 27…50 11…13 23…27

109

135

74 63 27

70…90 (100…120)

[ns]

[ns]

[ns]

6

8 11 2 15

35

min

τ max

τ

τ RMS

M

M

S

S

S

Meas./ Simu.

Table 6.5: Measured and simulated values for delay parameters from the literature in indoor environments.

6.4 Results for TOA parameters

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τ FED (90 %) [ns]

[180]

[131] [65] (from [91])

[130]

[114] [126]

[64]

[63]

[62]

[53]

[43]

[12]

[62], [63]

[299]

Reference

microstrip

horn (29 dBi)

open-ended waveguide (6.7 dBi)

microstrip

biconical horn

medium (standard gain horn), ~10° 3-dB width, main beam pyramidal horn narrow (scalar lens horn), ~5° 3-dB width, main beam ~GAUSS narrow-beam scalar lens-horn (4.6°) isotropic omni (8.5 dBi) horn (20.8 dBi) omnidirect./direct.

LOS, Tx at end of hallway LOS, Tx at end of hallway LOS, Tx in corner of room LOS, Tx in corner of room NLOS, Tx hallway, Rx in lab NLOS, Tx and Rx in adjacent rooms LOS NLOS

circular polarised

vertical or horiz. polarisation circular polarisation

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biconical horn

isotropic omni (8.5 dBi) horn (20.8 dBi) omnidirectional

wide beam scalar horn (60°)

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M

M

M

M

S

21.78 4.12 5.46

14.72

100

100 100

35 (55) 10 12

60.0 53.8 17.5 33.94 21.4

15…45 30…70 55…80

4.89 7.81 15…45 30…70

5.88 4.56 4.85 4.72 5.19

15

1.05 0.79

M S 10…11 4.5…5.7 2.13 1.18 1.58

4.70 2.22

M S

5 1.2 4

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10.67…42.7

1.20…116.6 2.22…90.7 0.74…47.7 2.4…77.8 0.71…95.8

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GOSSE et al [110] summarised, that delay spread at 60 GHz typically varies from 5 ns to 75 ns. For more measured values of mean and maximum excess delay and delay spread see Table 6.1 on page 94 and Table 6.2 on page 97.

irregular formed room (5x7m)

typical office environment common room workshop small rooms large indoor environments indoor environments small rooms large rooms, hall corridor hallway (LxWxH = 102x2.1x4.3m) hallway (LxWxH = 54.7x2.9x4.3m) conference room (6.7x5.9x4.3m) classroom (8.7x7.1x4.3) hallway to laboratory (11.7x5.1x4.3m) room (11.7x5.1x4.3m) to room (5.1x4.3x4.2m)

long corridor 44x2.20x2.75m (LxWxH)

room (10.44 x 8.78 x 2.6 m)

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86 87

10

108

7 (90 %)

[47]

[293]

[256]

[226]

[212]

[195]

[182]

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open-ended waveguide 6.7 dBi horn, 29 dBi

LOS, Tx and Rx along the wall

LOS, nearly no scatterers

values for 90 % of all locations

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M

M

7.63

16.1

1.5..9 1.6 S M

horn, beamwidth 120°

18.5

7.7

17.4

124.1

0.02.. 6.8

24.4…24.59

41.3…56.6

8.0…20.6

0.7.. 26.3 2.7.. 6.3 0.6.. 27.2 2.7.. 3.3 3.3.. 3.7 3.3.. 4.9 3.5.. 4.1 2.1.. 3.3 0.01.. 3.3 3.3.. 3.7

7.5 35.1 7.4 26.0 6.1 6.6 7.4 6.7 6.2 6.1 6.4

0.9

0.1 2.1 5.4 1.8 4.9 6.1 6.1 6.2 4.6 0.1 6.1

max

35.1

avrg 7.1 35.3

τ FED

>=150

λτ , where τ is the delay required for the multipath echo amplitude β ( 0 ) to fall below the noise level under consideration.

Figure 7.35: One realisation of the channel based on the SALEH-VALENZUELA channel model (Figure 2.2 from [288]).

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MAVRAKIS [188] wrote that the parameter values of the SALEH-VALENZUELA model could be roughly calculated from the physical characteristics of the room to be simulated. The dimensions of a single wall will define the ray arrival rate within the cluster (since the rays do not arrive from different scatterers within the cluster, but from the same wall), while the mean distance of the antennas will define the cluster arrival rate. Based on all those theoretical descriptions, Figure 7.35 taken from [91]/[288] shows a vivid picture of a channel realisation at 60 GHz with a bandwidth of 200 MHz, which has been simulated based on the SALEHVALENZUELA channel model with a receiver speed of 5 m/s. Also shown are a plot of amplitude in a subchannel and the amplitude at a time instant across all the possible frequencies separately, see Figure 7.36 and Figure 7.37. By analysing more similar plots of each subcarrier and the amplitude at each time instant, WANG [288] states, that each subcarrier is a slow fading channel and seems to have a fixed distribution; however it is difficult to find a fixed distribution for the amplitude at each time instant.

Figure 7.36: Received amplitude in one sub-carrier (Figure 2.3 from [288]).

Figure 7.37: Received amplitude at one time instant (Figure 2.4 from [288]).

In [96] it is proposed to stop the cluster and ray arrival time determination when Tl > 10Γ and τ k ,l > 10γ , respectively. Another possibility would be to stop if the value for β k2,l (which in this case must be calculated after every cluster resp. ray time determination) falls below a given threshold (e.g., -30 dB) compared to the direct path.

7.3.2. Extension for DOA-Modelling SPENCER et al proposed in [259] an extension to the SALEH-VALENZUELA model and studied the DOA of their measured data sets at 5.2 GHz [91] [90]. The modelled impulse response of the channel with consideration of DOA statistics is then given by (7.7) [65]: h ( t ,θ ) =

∞

∞

∑ ∑ β k ,l e jφ δ ( t − Tl − τ k ,l ) δ ( θ − Θl − ωk ,l ) k ,l

(7.7)

l =0 k =0

where Θl is the mean DOA for the cluster l and ωk ,l is the mean DOA for the ray k within cluster l . Depending on the type of antenna, the power delay profiles have different properties; as the direction of arrival of the rays is correlated with the cluster, the rate of cluster arrival drops dramatically when the antenna gains increase [91]. SPENCER et al assumed in [260], that time and angle are statistically independent. If there were a correlation, it would be expected that a longer time delay would correspond to a larger angular variance from the mean of a cluster. This was not observed in their data, which were gained from measurement in the frequency range from 6.75 to 7.25 GHz. The consequence of this independence is that the complete impulse response with respect to both time and angle, h ( t ,θ ) , becomes a separable function: h ( t ,θ ) ≈ h ( t ) h ( θ ) (7.8) As a result, h ( θ ) can be addressed separately from h ( t ) . Thus, SPENCER et al [260] propose an independent angular impulse response of the system, similar to the time impulse response of the channel given in (7.2): 130/160

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∞

∑ ∑ β k ,lδ ( θ − Θl − ωk ,l )

(7.9)

l =0 k =0

where, as before, β k ,l is the ray amplitude for the k th arrival in the l th cluster, given in equation (7.5). Θl is the mean DOA of each cluster, which is uniformly distributed on the interval [ 0,2π ) [65] [91] [259] [288]. They also propose in [260] (also [65] [91] [288]), that the ray DOA (ray angle) within a cluster, ωk ,l , is modelled as a zero mean LAPLACE distribution with standard deviation σ : 1 − 2θ σ p(θ ) = e (7.10) 2σ They found values for σ of 25.5° and 21.5° from their measurements in [260] (at 7 GHz). FLAMENT [91] refers to [259] (5 GHz carrier frequency range) when he gives a variance of 0.3.

7.3.3. SAMSUNG and CHALMERS Indoor Parameter Sets PARK et al [212] from SAMSUNG/JAPAN obtained from their measurements model parameters for the SALEHVALENZUELA model (see section 7.3.1 for more details). The measurements were carried out in a typical furnished office environment. The AP antenna (omni-directional with 120° beamwidth) was placed in an upper edge of the room at the ceiling in a height of 2.6 m; the MT antenna (omni-directional with 60° beamwidth) was placed at different positions 1.3 m above the floor, always pointing towards the AP antenna (LOS). Circular polarisation was used. The gained model parameters are given in Table 7.22. Table 7.22: SAMS channel model specifications (from [212]). Parameter

Value

Mean time between clusters 1 Λ ( Λ : cluster arrival rate)

75 ns

Cluster decay time constant Γ

20 ns

Mean time between rays 1 λ ( λ : ray arrival rate)

5 ns

Ray decay time constant γ

9 ns

Sampling frequency

200 MHz

Impulse response length

40 taps (200 ns)

Modelled after this, DE SOUZA JÚNIOR [65] from CHALMERS UNIVERSITY OF TECHNOLOGY/GÖTEBORG generated impulse responses for the 60 GHz channel using the parameter set specified in Table 7.23. A threshold of –40 dB limits the number of taps. All the taps with power below the threshold were set to zero. Table 7.23: CHAL1 channel model specifications (from [65]). Parameter

Value

Mean time between clusters 1 Λ ( Λ : cluster arrival rate)

75 ns

Cluster decay time constant Γ

20 ns

Mean time between rays 1 λ ( λ : ray arrival rate)

5 ns

Ray decay time constant γ

9 ns

Sampling frequency

271 MHz

Impulse response length

39 taps (144 ns)

Number of clusters

10

Number of rays within a cluster

25

The channel used by DE SOUZA JÚNIOR for simulations has 39 taps with RMS delay spread στ ≈ 24 ns , speed was 1-2 m/s. The estimated power delay profile is displayed in Figure 7.38.

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Figure 7.38: Power delay profile for the 39-tap channel (Figure 21 from [65]).

The parameter set from PARK et al [212] was also used by LABOEUBE and DE GOUVILLE [164] in their investigations. They limited the impulse response to 10 taps (for which they give the channel coefficients), but as to the authors of this study this seems to be rather short (too short) when compared to PARK et al [212] and DE SOUZA JÚNIOR [65]. FLAMENT (also from CHALMERS UNIVERSITY OF TECHNOLOGY/GÖTEBORG) gives in [90] parameters for the SALEH-VALENZUELA model for an office room, which were derived from ray-tracing considerations. Table 7.24: CHAL2 channel model specifications (from [65]). Parameter

Value

Mean time between clusters 1 Λ ( Λ : cluster arrival rate)

15 ns

Cluster decay time constant Γ

20 ns

Mean time between rays 1 λ ( λ : ray arrival rate)

2 ns

Ray decay time constant γ

9 ns

7.3.4. IMST Indoor Model Parameters According to [29]/[162], the results of KUNISCH et al in [162] show (see section 6.1.2), that in LOS and almost LOS conditions, the channel is dominated by the direct path. Multipath contributions show an essentially GAUSS behaviour with an exponential amplitude decay that fits well into the framework of the statistical indoor model by SALEH and VALENZUELA (see section 7.3.1 for detailed description). A simplified one-cluster version of this model augmented by a direct path of free-space propagation is found to match the measurement results well, with modifications to the direct path required for almost LOS conditions. The model may be used to generate typical impulse responses for simulation purposes. In [29]/[162] it is assumed that blocking of the direct path e.g. by a person passing through the beam may be covered by the model as well by dropping the direct path. However, this assumption has not been backed up by measurements. Thus the multipath part is modelled as a single cluster SALEH-VALENZUELA model with the mean echo power following an exponential decay relationship β 2 ( τ ) = β 2 ( 0 ) ⋅ exp ( −τ γ ) and fading according to a RAYLEIGH distribution with variance β 2 ( τ ) , whereas the additional direct path is assumed to have a power of 0 dB and no RAYLEIGH fading. Hence, the impulse response component at τ = 0 is the sum of a constant part having a uniformly distributed phase and a RAYLEIGH distributed part 14. Table 7.25 summarises the parameters β ( 0 ) and γ . The values of β ( 0 ) are given in decibels relative to the maximum value in the averaged PDP (direct path amplitude). The extraction of β ( 0 ) and γ was based on linear regression within a particular energy window of the averaged PDP. The used window extended 14

Thus this model could also be seen as the model from section 7.5.2 with ∆ LOS = ∆ DEC = − β ( 0 )[ dB ] and τ 1 = 0 .

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from 50 % to 99 % of the averaged PDPs that have been normalised to the noise level. The approach is illustrated in Figure 6.22. According to the dimension rule in section 7.3.1, a value of λ = 1 ns −1 was chosen, because for the measurements reported in [29]/[162] theoretically ∆t = 1 960 MHz ≅ 1 ns . Table 7.25: IMST model parameters (selected values from [29]/[162]).

β ( 0 ) [dB]

Model

Comment

IMST-HM IMST-AM IMST-FA IMST-NA IMST-DY IMST-FZ IMST-M

MT horn, mean values MT dipole array, mean values MT far from AP MT near to AP MT horn, MT between bookshelves MT horn, MT behind bookshelf mean values over all measurements

-23.3 -31.1 -29.0 -28.5 -19.9 -17.6 -25.8

γ [ns]

λ [1/ns]

10.9 9.6 12.5 8.5 9.3 10.6 10.5

1.0 1.0 1.0 1.0 1.0 1.0 1.0

A comparison of a typical measured and modelled (direct path gain = -66 dB, β ( 0 ) = −28.5 dB (max) ,

γ = 8.5 ns , λ = 1 ns−1 , M = 150 ) impulse response is shown in Figure 7.39. White GAUSS noise (70 dB below direct path) has been added to the modelled impulse response. A HANN window has been applied to both responses. [29] [162]

Figure 7.39: Comparison of a measured (left) and a modelled (right) impulse response. White GAUSS noise has been added to the modelled impulse response (from [29] [162]).

7.4 DELIGNON et al Statistical Model DELIGNON et al [68] propose – starting from their indoor measurement results at 60 GHz – a modification of the original SALEH-VALENZUELA model ([239], see section 7.3.1) concerning the ray arrival within the clusters and the distribution of the channel coefficients. By taking into account the nature and layout varieties of the objects in the propagation environment, from a measurement location to another, they assume that gains and mean duration between successive arrival times of rays are random processes, which depend on reflecting surfaces and layouts of objects in the environment. Whereas for the SALEH-VALENZUELA model the ray arrival rate λ is constant from one cluster to another, here this is not assumed anymore, such that every cluster l has its own ray arrival rate λl , the ray (and also cluster) interarrival time still being POISSON distributed (see also Figure 7.40).

Figure 7.40: A schematic representation of a realisation of the impulse response (Fig. 1 from [68]).

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A digital communications system is considered where the duration of a symbol is T . The digital filter, which models the multipath channel, is built up by integrating h ( t ) on each elementary time symbol T . Therefore, tap coefficient n of the channel impulse response of the l th cluster is given by hl ( n ) =

N l −1

∑ β k ,l ( n ) e j( 2π f τ

c k , l ( n ) +θ k , l

)

(7.11)

k =0

Hence, the overall channel impulse response is h( n ) =

N

∑ hl ( n )

(7.12)

l =1

where N is the number of cluster by symbol duration and N l is the number of rays of the cluster l arriving in [ nT , ( n + 1 ) T ] . It should be remarked that the random number N of clusters by symbol duration is POISSON distributed with parameter ΛT . In the same way, the N l number of rays of a cluster l arriving in [ nT , ( n + 1 ) T ] is also a POISSON random variable with parameter λlT . Under these assumptions, although the number of rays per cluster is not constant but is a POISSON random variable with a large expected parameter, hl ( n ) converges in law toward a zero mean non-correlated complex GAUSS random variable (for proof see annex of the paper [68]). Therefore, each cluster is characterised for each tap coefficient n by an expected number of rays λl and a gain β l depending on n . The variances of the real and imaginary parts of hl ( n ) are the same, and they are function of n : T σ l2 ( n ) = β l2 ( n ) λl ( n ) with β l ( n ) = E { β k ,l ( n ) } (7.13) 2 Because any sum of zero mean circular complex GAUSS variables is still a zero mean circular GAUSS variable, h ( n ) is a zero mean complex circular GAUSS variable with the variance of the real and imaginary parts given by σ 2 ( n ) = Λ ( n ) T σ l2 ( n ) with σ l2 ( n ) = E {σ l2 ( n ) } (7.14) The expectation is taken with respect to the distribution of clusters in the time interval [ nT , ( n + 1 ) T ] . Note that σ 2 ( n ) is also the power gain of the channel in this interval. Thus, the assumption was made that clusters vary in number and in shape from one location of measurement to the other. Indeed, some clusters can disappear when they become hidden, some new clusters can appear and the shape of each cluster is subject to changes. Therefore, the σ 2 ( n ) parameter is a random variable. The choice of its distribution has mainly to take into account the flexibility of the probability density, in order to be adapted to various propagation environments. DELIGNON et al proposed the Gamma density because it is an L or bell shaped curve. fσ 2 ( n ) ( u ) =

uα ( n ) −1

κ ( n )α ( n ) Γ ( α ( n ) )

e

−

u

κ(n )

, u ≥ 0 (1)

(7.15)

where α ( n ) and κ ( n ) are the shape and the scale parameters of the Gamma distribution [46] [67]. Therefore, the amplitudes of the impulse channel coefficients are K-distributed. The probability density of h ( n ) is the following:

where Kα ( n ) −1

α ( n ) −1

2x   (7.16) ⋅ Kα ( n ) −1   , x ∈ [ 0, +∞ [  κ (n)  is the modified BESSEL function of the second kind of order α ( n ) − 1 . Since κ ( n ) is a

f h( n )

2  x  ⋅ (x) = κ ( n ) Γ ( α ( n ) )  2κ ( n ) 

2

scale parameter, the shape of the K-distribution PDF depends only on α ( n ) . In order to compare the impulse response coefficient distribution to this parametric model, they introduced two parameters functions of the moments of order 1, 2 and 3 of h ( n ) . These parameters, noted ρ1 and ρ 2 , are invariant with respect to κ ( n ) , so they depend only on α ( n ) .

ρ1 =

µ12 µ2

and ρ1 = 134/160

µ13 µ3

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where µ1 , µ2 and µ3 are respectively the k th order moments of h ( n ) , k ∈ {1,2,3} :

µ1 = E { h ( n ) }

=

πκ ( n ) Γ ( α ( n ) + 12 ) ⋅ 2 Γ(α ( n ) )

µ2 = E { h ( n ) 2 } = 2α ( n ) κ ( n ) µ3 = E { h ( n ) 3 } = 3 ⋅

(7.18)

πκ 3 ( n ) Γ ( α ( n ) + 23 ) ⋅ 2 Γ(α ( n ) )

The representation of the K-law in ( ρ1 , ρ 2 ) graph is a line (Figure 7.41) converging toward zero when α tends to infinity. Note that the RAYLEIGH law is the limit form of the K-law when α tends to zero. In the ( ρ1 , ρ 2 ) graph, the RAYLEIGH distribution is the point ( π / 4,π / 6 ) .

Figure 7.41: K law (line and points), RAYLEIGH law (cross) in (ρ1,ρ2) graph (Fig. 2 from [68]).

Figure 7.42: K law (line), RAYLEIGH law (cross) and channel impulse tap coefficients (stars) in (ρ1,ρ2) graph (Fig. 3 from [68]).

Figure 7.43: Comparison between the RAYLEIGH PDF (dotted curve) and K-PDF with α=50 (line) with the same variance (Fig. 4 from [68]).

From their measurements, for each coefficient h ( n ) the estimates of ( ρ1 , ρ 2 ) , noted ( ρˆ1 ( n ) , ρˆ 2 ( n ) ) , were calculated by using the empirical moments. Then, the ( ρˆ1 ( n ) , ρˆ 2 ( n ) ) were plotted in the ( ρ1 , ρ 2 ) graph and are compared to the line of the K-law. In Figure 7.42 point out the adequateness between the experimental data and the K-line. Almost all the coefficients are very close to the K line. In this graph, RAYLEIGH law is marked by a cross. The ( ρˆ1 ( n ) , ρˆ 2 ( n ) ) points are quite far from the RAYLEIGH point, so this later distribution is not adapted to describe variation of the stochastic channel impulse response coefficients. A comparison between the K-law for α equal to 50 and the RAYLEIGH distribution is shown in Figure 7.43. This figure shows the large skewness of the K-law compared to the RAYLEIGH law. As a consequence from their investigations, DELIGNON et al came to the conclusions that, by considering measurements in a vicinity of a location, the RAYLEIGH model is no more realistic because it doesn’t take into account the variation of the environment leading to variations of clusters of rays, and that the K model is appropriate to any indoor propagation and in particular it is a good candidate for modelling indoor propagation at 60 GHz, but Remark: It must be noted that no further details were given concerning the parameters that DELIGNON et al gained from their analysis; hence here we can not give any applicable parameter set for a 60 GHz channel model.

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7.5 SMULDERS Time-Domain Model 7.5.1. Original Model SMULDERS [253] developed a time-domain model for the 60-GHz indoor channel [253] [256] from his measurements. In [253] the relation between the model parameters and environment properties (dimensions and wall reflective figures) is described by first order approximations. The model can be interpreted as modified single-cluster SALEH-VALENZUELA model (see section 7.3.1). For a single cluster, the outer sum in Eqn. (7.2) disappears and with Tl = 0 = 0 we have: h( t ) =

∞

∑ β k e jϕ δ ( t − τ k )

(7.19)

k

k =0

The ray interarrival times, τ k ( k > 0 ), are modelled as independent random variables that are exponentially distributed (i.e. a POISSON process with fixed (mean) arrival rate λ ); this agrees with the SALEH-VALENZUELA model. The rays phases ϕ k are modelled as independent random variables that are uniformly distributed over [ 0, 2π ) ; this agrees with the SALEH-VALENZUELA model. The amplitude values of the LOS rays, β 0 , are not modelled since they can be determined easily based on the radio equation (see section 5.2.2); this agrees with the SALEH-VALENZUELA model. The amplitude values of reflected rays, β k ( k > 0 ), are modelled as independent random variables that are RAYLEIGH distributed, which agrees with the SALEH-VALENZUELA model. In contrast to the SALEH-VALENZUELA model, the normalisation parameter of this distribution is based on the observed mean delay power spectra (e.g., see Figure 6.29) and is modelled as a function of excess delay by a constant level part followed by a linear decrease (dB value) as shown in Figure 7.44. The level of the constant-level part as well as the slope parameter of the linearly decreasing part was related to the specific properties of the particular environment under consideration and the antennas used.

• • • •

∆ LOS

Power [dB]

Power [dB]

According to [253], the constant-level part is caused by the compensation of free-space losses by antenna gain compensation due to the elevation dependence of the antenna radiation patterns and the difference between the transmit antenna and receive antenna height. The pulses in a response that immediately follow the first pulse (LOS pulse) are likely to come from single reflected rays. Thus, the model is characterised by five parameters: 1. β 02 : power of the direct ray (LOS component), 2. ∆ LOS : difference between the LOS component and the constant-level part, 3. τ 1 : duration of the constant level part, 4. A : slope of the exponentially decaying part, 5. λ : ray arrival rate. Mathematically, the DPS can be (linearly) written as τ τ1  β 0 ∆ LOS ⋅ e  A[ dB ns ]  where the multipath power decay coefficient γ is calculated as γ = 1  ln10  .  10 

A resp. γ

τ1

∆ DEC

A resp. γ

τ1

Excess delay

Figure 7.44: Model of the DPS (Fig. 4.4 from [253]).

∆ LOS

Excess delay

Figure 7.45: Modified model of the delay power spectrum.

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7.5.2. TU/e Indoor Channel Parameters The parameter sets presented in this section are based on the measurements performed by SMULDERS [253] at the Technical University of EINDHOVEN (TU/e); for further details like environments and configurations see section 6.1.3. They parameterise the time-domain model of SMULDERS [253], which is presented in section 7.5.1. If we do not intend to account for path loss, β 02 = 1 can be assumed. In [253] the mean interarrival times 1 λ were listed for thresholds –40 dB, –30 db, and –20 dB. Regarding to SMULDERS [253], especially the values for the –40 dB threshold are comparable to the measurement resolution. This suggests that the discrete multipath process of mm-wave indoor radio channels converges towards a continuous RAYLEIGH model and, at every excess delay, the amplitude of the response is statistically characterised by a RAYLEIGH PDF. However, since according to [253] this threshold is in the order of the dynamic range of the applied measurement system also noise might contribute significantly to the result. In this respect, the results for the –20 dB threshold are considered most reliable by SMULDERS. As to us, a good compromise between noise influence and measured amplitude dynamics might be the usage of the values gained for the –30 dB threshold. Table 7.26: Parameters for TU/e indoor channels (adapted from Table 4.1, Table 4.2, Figure 3.13, and section 4.4.2 of [253]). Channel

Env.

Conf.

TUe-AA TUe-AB TUe-AS TUe-BS TUe-CS TUe-DS TUe-ES TUe-FB TUe-FS TUe-GS TUe-HS

A A A B C D E F F G H

A B S S S S S B S S S

στ [ns] measured 36…48 26…40 36…76 36…98 52…80 36…45 13…26 22…35

∆ LOS [dB] 12 12 7 8 5 4 10 3 1 10 4

A [dB/ns]

τ 1 [ns]

0.11 0.10 0.12 0.14 0.07 0.08 0.06 0.11 0.09 0.27 0.17

60 60 60 60 60 (70) 60 60 60 60 60 (50) 60

1 λ [ns] (-40 dB) 1.1 1.1 0.8 0.9 1.0 1.0 0.7 1.0 0.9 0.7 0.9

1 λ [ns] (-30 dB) 1.6 1.5 1.1 1.2 2.0 1.2 1.2 1.1 1.0 1.4 1.0

1 λ [ns] (-20 dB) 3.1 3.0 1.9 2.0 3.0 2.0 1.5 1.9 1.3 2.2 1.4

Remark: The channels described in this section can also be modelled using the FD-model (see section 7.5.4 and [289]). This might be recommendable if the simulator is anyhow mainly working in the frequency domain.

7.5.3. Modified Model To obtain a better fit for the measurement results of CORREIA et al (see section 6.2.2), we propose a slightly modified SMULDERS model for the DPS. The model is characterised by six parameters: 1. β 02 : power of the direct ray (LOS component), 2. ∆ LOS : difference between the LOS component and the constant-level part, 3. τ 1 : duration of the constant level part, 4. ∆ DEC : difference between the LOS component and the start of the exponentially decaying part, : multipath power decay coefficient, 5. γ : ray arrival rate. 6. λ Mathematically, it is written as τ τ1  β 0 ∆ DEC ⋅ e Figure 7.45 visualises this model. Hence, also this model is in principle a modified single-cluster SALEH-VALENZUELA model.

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7.5.4. Parameters for Urban Streets from CORREIA In section 6.2.2 average power profiles were presented for two urban streets with different widths under LOS conditions. For developing a channel model, the values for the average profiles were taken from the graphics in [55] (see also Figure 6.69). In order to obtain LOS channel models, some assumptions are made: • Basically, it is supposed that these channels can be modelled as (modified) single-cluster SALEHVALENZUELA model (see section 7.3.1), which seems to be a reasonable presumption for 60 GHz channels. • The value for λ (the ray arrival rate) is chosen according to the dimensioning hint of KUNISCH et al given in [162] (see also section 7.3.1). That is λ ≈ 1 ∆t = f S , where ∆t is the measurement or simulation resolution. CORREIA et al used in their study a bandwidth of 200 MHz, which leads to λ = 1 ( 5 ns ) . • Rays have independent RAYLEIGH distributed amplitudes whose variances (resp. envelope) decay according to the approximated profiles presented below. Thus, we use the model described in section 7.5.2. In Table 7.27 the model parameters are given. If we do not intend to account for path loss, β 02 = 1 can be assumed. The model Cor-10 for 10 m street width can also be seen as an original single-cluster SALEH-VALENZUELA model. Table 7.27: Parameters for modelling CORREIA outdoor channels. Channel

Cor-10 Cor-50

Env.

10 m street width 50 m street width

∆ LOS [dB] 0 3.73

∆ DEC [dB] 0 8.47

γ

τ1

[ns] 6.3 36.0

[ns] 0 60

1λ [ns] 5.0 5.0

Figure 7.46 and Figure 7.47 show the two modelled profiles in comparison with the measured profiles. [dB] 0

[dB]

Cor-10

-5

0

Cor-50

-5

measured profile

-10

-10

-15

-15

model

-20

-20

-25

-25

-30

model measured profile

-30

[ns] -35

[ns] -35

0

50

100

150

200

250

300

350

Figure 7.46: Av. PDP and model for 10 m street width.

0

50

100

150

200

250

300

350

Figure 7.47: Av. PDP and model for 50 m street width.

7.6 Frequency-Domain Modelling 7.6.1. WITRISAL et al Frequency-Domain Model WITRISAL et al present in [289] a frequency-domain model using frequency domain filtering and a HILBERT transformer. The model directly yields samples of the complex transfer function H ( f , t = tS ) . As to [25], for the frequency-domain model a frequency transfer function is used as a representation of the linear timevariant filters in the frequency domain. Having a frequency transfer function of the channel it is possible to make a transition to the time domain by applying FOURIER transform. The spaced-frequency, spaced-time correlation function φH ( ∆f , ∆t ) is a convenient description, since the function represents the frequency selectivity and the time variability of the channel transfer function. By shaping individually spaced-time and spaced-frequency correlation functions, the desired time-varying frequency selective transfer functions can be obtained assuming wide sense stationary uncorrelated scattering [25] [289]. In other words, according to [289]: The idea of frequency-domain (FD) channel modelling is to shape the spectrum of a GAUSS noise process in order to obtain the required spaced-frequency correlation function 138/160

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φH ( ∆f ) . The correlation function is specified by its FOURIER transform, which is the delay power spectrum φh ( τ ) The resulting coloured complex GAUSS sequence has the required spaced-time correlation function φH ( ∆t ) , which is specified by the DOPPLER power spectrum S H ( ν ) , the FOURIER transform of φH ( ∆t ) [225] (for the correlation and profile function relations see also section 4.10). Further details about the frequency domain modelling can be found in [289]. In agreement with measurements reported by SMULDERS in [253] (see also section 6.1.3), the shape of the DPS was defined in [289] as shown in Figure 7.48.

Figure 7.48: Model of the delay power spectrum (Figure 2 from [289], Figure 1 from [290], Figure 7 from [226]).

Figure 7.49: The impulse response of the FD-model obtained from the transfer function by IDFT (Figure 7 from [289]).

The DPS is characterised by four parameters [226]: 1. p ( 0 ) [dB] the normalised power of the direct ray (LOS component) 2. Π [1/ns], the normalised power density of the constant-level part 3. τ 1 [ns], the duration of the constant level part 4. γ [dB/ns], the slope of the exponentially decaying part. Mathematically, the DPS can be written as [289] 0  p ( 0 ) ⋅ δ (τ )  φh ( τ ) =  Π  Π ⋅ e −γ ( τ −τ1 ) A where γ is the decay exponent defined as γ = ln10 . 10

τ τ1

For the simulation system shown in Figure 7.50 the following description is given in [289]: “The independent FD-samples W ( f ) of the frequency response are generated by a real-valued, GAUSS noise source. The appropriate spaced-frequency correlation function is obtained by FD-filtering of W ( f ) with a filter g ( f ) . The output of this filter is the real-valued, coloured noise process H r ( f ) = W ( f ) ⊗ g ( f ) , where ⊗ denotes convolution. The inverse FT of H r ( f ) (the excess-timedomain representation) is complex valued and hermitean, i.e., symmetric with respect to the τ = 0 axis. It is not causal, in contrast to the impulse response of the real channel. The required causality in the time-domain is obtained by applying a HILBERT transform to H r ( f ) and adding the result H i ( f ) as H ( f ) = H r ( f ) − jH i ( f ) . Doing this, the negative part of the impulse response is cancelled.”

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Figure 7.50: Frequency-domain simulation of the frequency-selective radio channel (Figure 3 from [289], Figure 2 from [290]).

As WITRISAL et al [289] state, the amplitude distribution of the resulting transfer function H ( f ) is RAYLEIGH since H ( f ) is a complex GAUSS noise process; a RICE fading channel may be simulated by adding a complex constant h ( 0 ) to H ( f ) representing the direct path. The power of the direct path is thus defined as p ( 0 ) = h ( 0 ) 2 . The time variability may be implemented by filtering independent samples of the transfer function H ( f , t = nT ) , n = 1,2,3,… in the time domain using JAKES’ fading model. The transfer function of the filter to be used is defined by the DOPPLER power spectrum. According to [289], analytical expressions can be derived for the expected values of normalised received power (NRP), RICE factor KCIR and RMS delay spread στ from the continuous DPS φh ( τ ) . The reader is referred to [289] for these expressions. Examples that verify the model can be found in [289]. They show a good agreement with the measurement results from SMULDERS [253] (see also section 6.1.3). Figure 7.49 shows an exemplary impulse response.

7.6.2. KATTENBACH Directional Modelling KATTENBACH discusses in [145] the modelling of directional time-variant channels based on the time-variant transfer function. As we have already stated earlier using [145], it depends on the bandwidth which components actually superimpose for the different “paths” in the time-variant impulse response, the parameters for the tapped delay line models are however valid only for a certain bandwidth. Even more, since an increasing number of multipath components can be resolved in the time-variant impulse response with increased bandwidth, increasingly less multipath components superimpose and, thus, a statistical modelling of the time-variant fluctuations, which demands for the superposition of a great number of components, becomes questionable. For directional channel models, this problem even increases, since now the components are additionally resolved by their angle of incidence, and statistical modelling of temporal variations becomes even more questionable. For a reliable statistical modelling of small-scale variations, thus, another system function has to be taken into account. One approach to overcome these disadvantages is a statistical channel model based on the time-variant transfer function [145]. Basically, each of the system functions is equivalently applicable for modelling. Taking into account the properties of the system functions with respect to the different domains, it turns out that only in the timefrequency-aperture domain there is a superposition of multipath components with respect to all three quantities ( t , f , and x ), whereas for all other domains there is a resolution of components with respect to at least one quantity ( τ , ν , or θ ). Thus, the system function in the time-frequency-aperture domain, i.e., the time- and aperture-variant transfer function H ( t , f , x ) obviously is the most appropriate system function for statistical modelling. The time- and aperture-variant transfer function H ( t , f , x ) is the counterpart for directional channels to the time-variant transfer function H ( t , f ) for nondirectional channels [145]. Following KATTENBACH, there are mainly four arguments for using H ( t , f , x ) [145]: 1.

The strongest argument why to prefer H ( t , f , x ) for statistical modelling has already been give before: Since both with respect to t , f , and x , there is a superposition of components, at each point in the time-frequency-aperture domain the value of H ( t , f , x ) will consist of the superposition of all multipath components and, thus, the maximum available number, which in practice will be enough to permit a statistical modelling. Because at each point all components superimpose, the parameters will even be independent of the extent of H ( t , f , x ) with respect to t , f , and x , as far as large-scale effects (i.e., shadowing and frequency- or distance-dependence of path loss) are not taken into account.

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Another, more intuitive argument is closely related to the first one: Due to the great number of superimposing components a graphically displayed time- and aperture-variant transfer function looks like a “random function”, whereas all the other functions look somewhat more deterministic. However, the actual reason why the time- and aperture-variant transfer functions looks “random-like” is the superposition of a great number of (deterministic) components. The third argument is based on the fact that the statistical distribution functions usually taken into account for modelling (i.e., RAYLEIGH-, RICE-, or NAKAGAMI-distribution) originally have been applied to narrowband modelling. They have been derived from measurements of the time-selective fading for CW signals, i.e., for signals with zero bandwidth. This timedependent behaviour can be found as 2-D slice of the time-variant transfer function at the respective frequency of the CW signal and, thus, a modelling of the transfer function rather than the impulse response would be the consistent extension from narrowband statistical modelling to wideband statistical modelling. From the duality relations described in [145], the counterpart to “zero bandwidth” would be “zero aperture extent”. An aperture of extent zero can be identified with a point source, which has an omnidirectional radiation pattern and, thus, describes the nondirectional case. Extending the aperture will result in directional behaviour and, thus, a statistical modelling of the time- and aperture-variant transfer function obviously can be regarded as the consistent extension from narrowband nondirectional modelling to wideband directional modelling. This can be intuitively interpreted as using several conventional narrowband models for adjacent frequencies at each point on the aperture. The fourth argument directly results from the duality relations: Due to the time-frequency duality, the methods and distribution functions usually applied to statistical modelling of the time-selective fading can (and should) be applied as well to the frequency-selective fading. For directional channels the duality can be extended to “time-frequency-aperture duality”, since an analogous behaviour occurs with respect to the aperture as for time and frequency. According to that, the behaviour with respect to the aperture can meaningfully be denoted as “aperture-selective fading”, which consequently can (and should) be modelled by the same means as the time-selective fading.

The approach proposed in [145] can be described as following: A statistical modelling of the time- and aperture-variant transfer function initially would demand for a three-dimensional (3-D) joint probability density function. However, the approach simplifies, if the statistically independent random values are used, since the joint probability density function can be expressed by the product of the density functions for the time-selective fading, the frequency-selective fading and the aperture-selective fading. From the timefrequency-aperture duality, it can be expected that the distribution functions usually applied for the timeselective fading (i.e., RAYLEIGH-, RICE-, or NAKAGAMI-distribution) are as well applicable for the frequency-selective fading and the aperture-selective fading. For the application on a certain type of channel, the distribution functions and parameters can readily be determined from appropriate measurements by the same means as already used e.g., for nondirectional indoor radio channels. When using statistically independent random values they are also uncorrelated, which means that initially there is no correlation between adjacent (statistically generated) values of the time- and aperture-variant transfer function. This results in a time-frequency-aperture correlation function φH ( ∆t , ∆f , ∆x ) with the shape of a 3-D δ-function. The 3-D FOURIER transform yields a directional scattering function Sh ( ν ,τ ,θ ) that is constant for all values of τ , ν , and θ , that means, one has a 3-D white process. A white process can be coloured by filtering and, thus, in this case, the correlation can be induced straightforwardly by multiplying with a directional scattering function that describes the desired correlation properties of the channel. In fact, this may be regarded as a consistent extension of a method known from narrowband nondirectional statistical models, where the correlation of adjacent values in time is achieved by filtering with appropriate DOPPLER spectra (e.g., JAKES’ spectrum) [145]. Concluding one can say that the proposed extension is consistent with the nondirectional case, since this case is included for an aperture of zero extent, which can be identified as a point source with an omnidirectional radiation pattern. The distinction between time and space (i.e., the aperture) further helps to overcome the questions if, why or when a mobile radio channel should rather be interpreted to be time-variant or spacevariant [145]. An important finding in [145] is, that multipath components with different angles of incidence cause spacevariant fluctuations over the aperture even for a time-invariant channel (i.e., fixed mobile station and scatterers), whereas DOPPLER shifts occur even for a nondirectional channel if the channel is time-variant due to a moving mobile station or moving scatterers.

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7.7 ∆-K Model According to [96], the ∆-K model was proposed in [265]. A good fit to empirical indoor propagation data using the discrete time version of the model is reported in [125]. In the discrete time model, time axis is partitioned into bins with width ∆ . Denote the probability of having a path in bin k as Pk . If there is a path in the previous bin, bin k − 1 , Pk = K λk ; otherwise, Pk = λk where λk is given by [96] λ1 = r1 (7.23) rk , 2≤k λk = ( K − 1 ) ⋅ rk −1 + 1 where rk is the empirical bin occupancy rate for bin k . The path arrival process exhibits clustering for K > 1 , and the path arrival tends to be more evenly spaced for K < 1 . The impulse response of bin k is denoted as α k , and the path amplitude α k is lognormal distributed with an exponentially decaying multipath intensity profile (MIP). We add path polarity, pk , to the model to account for pulse inversions caused by channel reflections, where we assume pk is equiprobable +/-1. The following equations describe these relationships. [96] α k = pk α k (7.24) 20log10 ( α k ) ∝ Normal ( µk , σ 2 ) , or

(

E αk

α k = 10n 20 2

) = Ω0e−T

k

Γ

where n ∝ Normal ( µk , σ 2 )

(7.25) (7.26)

where Tk is the excess delay of bin k and Ω0 is the mean power of the first path of the first cluster. The µk is given by [96] 10ln ( Ω0 ) − 10 Tk Γ σ 2 ln ( 10 ) µk = − (7.27) ln ( 10 ) 20 As stated in [96], this model can also capture the multipath clustering phenomenon, similar to the SALEHVALENZUELA model. But as it is shown in [96], the model can’t fit both mean excess delay and RMS delay at the same time for either LOS or NLOS channels due to the limitation that only one exponential slope is available. The major difference between the double-exponential model and the single exponential model (embodied in the ∆-K model) is that the path amplitude in each subsequent cluster is not necessarily less than the one in the previous cluster in the double-exponential model [96].

7.8 HANSEN Stochastic Model HANSEN introduces in [120] a model for the stochastic millimetre-wave indoor radio channel. This model relates the stochastic properties of the radio channel to the underlying geometry of the investigated environment. The geometric simplicity of the millimetre-wave channel allows examining fundamental deterministic properties of the wave propagation behaviour in environments of predefined randomness, i.e., environments whose dimensions and properties are described by various probability distributions. The influence of the randomness on the radio channel is studied for the down-link of a wireless local area network at 60 GHz. Joint amplitudes of path lengths, angles of departure, and amplitudes, as well as spatial power densities, average power of the direct paths, and RICE KCIR -factors are investigated. HANSEN expands a ray-tracing algorithm to yield a stochastic CM in which geometric and electromagnetic side information about the environment is explicitly formulated. This side information can be easily varied; the randomness of the environments is well defined, since it is based on probability densities that uniquely determine its stochastic properties. Even though we will not further detail on this model, we give here two room definitions according on their wall material, which might be interesting for further investigations: • Modern office : 50 % glass, 30 % aerated concrete, 20 % concrete • Old-fashioned office : 20 % glass, 10 % aerated concrete, 70 % concrete

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7.9 KUNISCH-PAMP Ultra-Wideband Channel Model There is a growing interest in systems called “Ultra-Wideband (UWB)”, which have, according to [161], a fractional bandwidth greater than 0.2, or which occupy more than 500 MHz of spectrum. In [161], a radio channel model for indoor UWB environments is proposed which has been derived from measurements in an office environment under several conditions using omni-directional antennas. A distinguishing feature of the UWB indoor radio channel is that individual echoes are recognisable and resolvable in the measurements. The parameters that are given in [161] for the model presented there are – according to the authors – not usable for 60 GHz channels. Also according to verbal statements of the authors of [161] (who work at IMST which is a partner in BROADWAY) the model in principle has a good chance of being usable at 60 GHz, but unfortunately, there won’t be suitable parameters available in the near future. Therefore, we will not detail in this study on that sophisticated model.

7.10 NLOS CM Construction from LOS CM Practically all measurements presented by SMULDERS in [253] concerned line-of-sight (LOS) channels. Following SMULDERS, channels with obstructed LOS path (designated as obstructed channels – OBS) are derived from the impulse responses obtained under LOS conditions by mathematical removal of the direct ray. This method is – according to SMULDERS – justified by the experience that obstruction of the direct ray by a person, cabinet or piece of absorber caused a drop of the LOS ray in such way that the LOS component could not be recognised anymore in the measured response. The same quite simple but effective method was used by HÜBNER et al in [131] (see section 7.2.3).

7.11 Single-Frequency Network Model 7.11.1. SFN Model Principle As stated in BROADWAY deliverable WP3D7V1 [33], the idea behind a SFN scenario is that several transmission/reception antennas are distributed within a certain area, all transmitting/receiving the same signals. In function of the distance of the mobile terminals to the antennas within its range, the same signal is received with different delays and affected by different channel impulse responses. The advantages of OFDM are expected to be considerable in these so-called single frequency network (SFN) channels, because OFDM can cope with multipath impulse response (up to a certain length) and thus an important diversity gain is achieved. Figure 7.51 illustrates the idea by presenting a typical scenario. The corresponding differences in arrival times are given by Table 7.28, approximating the propagation speed of the signal by c0 = 3 ⋅ 108 m/s . The maximum range is assumed 25 m, a realistic value for 60 GHz applications as it is indicated by the OFDM reference parameter sets in [33]. It can be stated that the single frequency network scenario introduces significant and important signal delays.

540.80 sq. ft.

Distance 4: 12m

Table 7.28: Propagation delays in the example of a SFN (Table 4.3 from [33]).

Distance 6: 25m

Distance [m] Distance 1: 0m Distance 5: 18m

PC, Terminal

Distance 2: 3m

Distance 3: 5m

Figure 7.51: Typical example of a SFN scenario (Figure 4.3 from [33]).

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0

0.0

3

10.0

5

16.7

12

40.0

18

60.0

25

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Keeping this example in mind, in the following a simple but flexible model is presented which allows the simulation of single frequency networks in several environments. In the SFN being modelled the RF transmission and reception part of the access point (AP) consists of several (let’s say M ) identically equipped front-end sub-systems (FES), which are spatially distributed within the supply area with the aim to provide a good coverage at all locations within this area. Each sub-system is assumed to have its own power amplifier in the transmission branch and its own low noise amplifier in the reception branch. Transmission and reception antennas are supposed to have identical characteristics. The mobile terminal (MT) is only equipped with one Rx and one Tx antenna which again are supposed to have identical characteristics, this of course includes the case of using only one antenna both for transmission and reception in case of TDD (Time Division Duplex). Thus at the MT’s reception antenna a linear superposition of the multipath-influenced signals from the several FESs takes place. We assume for the downlink (AP Æ MT) that all M FESs are transmitting • the same signal at the same time (“simulcast”) • with the same power. This power might be • either the same power as a single-FES AP would transmit (Power Model PM1), • or 1 M of the power a single-FES AP would transmit (Power Model PM2). We assume for the uplink (MT Æ AP) that • all M FESs are used for reception, • the LNAs of all FESs amplify the particular received signal rm ( t ) , m = 1, , M with the same amplification, • the received and amplified signals from the several FESs will be linearly combined (summed) in the AP’s receiver, i.e. r ( t ) ∼

∑ m =1 rm ( t ) . M

With all these prerequisites, we can presume that the same channel model is valid for both up- and downlink and we only have to take care for the total transmission power in the downlink. The next prerequisite is a multipath channel model (CM) that represents the typical behaviour of the particular environment. Thus we assume that the CIR between every of the several FESs and the MT can be modelled by the same model. That is, the model must be typical for the environment. Because of the character of a SFN, it does not seem to be very close to reality if the utilised channel models originate from measurements or simulations with highly directive antennas. In every case, we have to have a pair of channel models for the environment under simulation: - a LOS CM, for which we assume that the model (not the single realisations) is normalised such that N m −1

∑i =0

hm,i

2

= 1 (that means the mean energy is fixed to 1),

- a corresponding NLOS CM for the same environment. The NLOS model can be obtained in two ways: - If the LOS channel model allows for, the direct path (e.g. the first tap) is switched off (or strongly attenuated) before generating the LOS channel realisation. The resulting NLOS must not be renormalised, thus we achieve automatically the necessary NLOS/LOS attenuation. - There might exist an extra NLOS CM for the particular environment, for which we assume that the model (not the single realisations) is normalised such that

N m −1

∑i =0

hm,i

2

= 1 (the mean energy is fixed to

1). The model’s realisations must be attenuated afterwards to obtain the necessary attenuation of NLOS compared to LOS. The direct path’s obstruction in multipath environments is often caused by shadowing (see section 5.3). Thus, the attenuation might also be modelled as a log-normally distributed random variable according to section 5.3.4. Because we want to construct a simple and handy model, we will not aim on specifying the particular environment as exact as possible (as it would be the case for ray-tracing simulations). We only will have to know roughly the dimensions of the environment.

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We propose two distance models (DM):

DM1:

The

position

ri = ( xi , yi , zi )T

for

every

of

the

M

FESs

is

fixed,

the

position

rMT = ( xMT , y MT , zMT )T of the MT is chosen randomly with x MT , y MT , and z MT being equally distributed between [ xMT ,lb , x MT ,ub ] , [ y MT ,lb , y MT ,ub ] , and [ z MT ,lb , z MT ,ub ] , respectively. From these values the particular Tx-Rx antenna distances d i = ri − rMT are calculated. There must be a mechanism for all d i , which ensures that always far-field conditions according to section 5.2.2 can be supposed. The simplest solution could be to choose the FES antenna heights zi and the MT antenna height z MT appropriately. DM2: The particular FES-MT antenna distances d i are chosen randomly with d i being equally distributed between [ d i ,lb , d i ,ub ] . I.e., what counts is not the true spatial positioning of FESs and MT but only the distances d i . For further simplification d i ,lb ≡ d lb might be assessed. Again, there must be guaranteed that all di ,lb ensure that always far-field conditions according to section 5.2.2 can be supposed. Of course, there is a variety of further distance models thinkable (other statistics, limited set of possible positions/distances, …). Another important modelling parameter is the decision whether the connection between a FES and the MT shall be treated as LOS or NLOS (Connection Type Selection – CTS). There exist several possibilities, among them always one should be selected by taking into account the environment type under simulation and the chosen distance model: CTS1: fixed number of LOS connections, CTS2: fixed probability pLOS for the connections being LOS (e.g. pLOS = 1 2 , pLOS = 1 M , or regarding to measurement or simulation results), CTS3: the classification could be done depending on the position of the MT (esp. useful for DM1), e.g. following measurement or ray-tracing results, There is no doubt that there are more options imaginable (e.g. soft transition between LOS and NLOS). What is also important is the decision what normalisation method (NM) shall be applied to the resulting final SFN CIR hSFN ( τ ) . It should be kept in mind that the M single channel’s CIRs were normalised according to

N m −1

∑i =0

{

E hm,i

2

} = 1 (for the LOS cases).

NM1: For this method we assume PM1 for the downlink, but do not perform any further normalisation. Thus, this method might be especially useful for simulations of the downlink performance without or slow power control. NM2: For this method we assume PM1 for the downlink again, but hSFN ( τ ) is normalised such that N SFN −1

∑i =0

hSFN ,i

2

= M . Thus, this procedure might be especially useful for simulations of the downlink

performance with fast (or optimum) power control. NM3: Here we assume PM2 for the downlink; therefore, the taps of hSFN ( τ ) are weighted by 1 M . Thus, this approach might be useful for performance simulations of both uplink and downlink, each without or slow power control.

NM4: Again we assume PM2 for the downlink, but hSFN ( τ ) is normalised such that

N SFN −1

∑i =0

hSFN ,i

2

= 1.

Thus, this approach might be useful for performance simulations of both uplink and downlink, each with fast (optimum) power control. We suggest the usage of NM2 and NM4. With all these preliminaries, we can now present the modelling steps (Figure 7.52 illustrates this): • Choice and definition of M , PM, CM (LOS, NLOS), DM and distance parameters, CTS and according parameter(s), and NM. • Generation of the positions of FESs and MT according to the chosen distance model, • Calculation of the distances d i and determination of their minimum d min = min ( d i ) . • Calculation of the normalised direct path delays Τi between the FESs and the MT according to Τi = ( di − d min ) c 0 (i.e. the normalised direct path delay of the FES being closest to the MT is forced to 0 ns). 145/160

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Calculation of the normalised relative path loss Li ,[ dB ] between the FESs and the MT for LOS conditions according to the path loss exponent model (see section 5.2.3) as Li ,[ dB ] = 10n lg ( d i d min )

•

(i.e. the normalised relative path loss for the FES being closest to the MT is forced to 0 dB); the value for the path loss exponent n should be chosen according to the particular environment, e.g. see Table 6.7. The path loss exponent model is applicable because we required the minimum distances to be within the far-field. Decision for every connections whether it is LOS or NLOS according to the chosen CTS model. Calculation of the CIRs for every of the M channels according to the selected channel model(s), to the LOS/NLOS decision, and to the normalisation method. Attenuation of every CIR according to its corresponding normalised relative path loss Li ,[ dB ] .

•

Path-delay corrected addition of all hi ( τ ) to obtain the combined impulse response (SFN-CIR)

• •

according to h ( τ ) = ∑ i =1 hi ( τ − Τi ) . M

•

Normalisation of the SFN-CIR according to the chosen NM.

Depending on the structure of the used simulator, finally it might be necessary to resample the obtained CIR to fit it to the sampling grid used within the simulations.

FOR i=1 TO M STEP 1 - calculation of di according to selected DM Determination of dmin FOR i=1 TO M STEP 1 - calculation of Ti - calculation of Li - decision for LOSi FOR i=1 TO M STEP 1 separate LOS/NLOS model? models ? False Falsch

Wahr True LOS(i) LOS(i)??

True Wahr

- generation of LOS realisation hLOS - hi=hLOS

- generation of LOS realisation hLOS

False Falsch - generation of NLOS realisation - attenuation - hi=hNLOS

True Wahr - hi=hLOS

LOS(i) LOS(i)??

False Falsch - attenuation of direct path - hi=hNLOS

- delay hi := hi(t-Ti) - hSFN := hSFN+hi - normalisation according to NM

Figure 7.52: Overview of SFN model.

Summary: For our SFN model, which is supposed to be a useful first order approximation for single frequency networks, it is assumed that the RF transmission and reception part of the access point consists of several identically equipped front-end sub-systems, which are either randomly distributed or at fixed positions within the supply, whereas the mobile terminal only has one antenna at its disposal and is located at a fixed position or randomly placed. An individual channel impulse response is associated with each front-end subsystem. Its basic delay coincides with the direct path distance. Therefore for every sub-channel an individual realisation of the underlying channel model (which is basically the same for all sub-channels) is generated which afterwards is weighted in power and delayed in time according to its individual distance. Finally, the individual sub-channel impulse responses are linearly superimposed.

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7.11.2. SFN Model Parameters Table 7.29 presents parameter sets for the SFN channel model, which was presented in section 7.10. There explanations can be found for the meaning of the several parameters. Table 7.29: Parameter sets for Single Frequency Networks. Parameter Type CM LOS CM NLOS M DM

n CTS NM

SFN-HL/2-TUe-CS large hall (43×41×7m³) BRAN D from LOS st (1 tap: -10 dB) 4 DM1 MT: x: 0.5…42.5m y: 0.5…40.5m z: 1.4m FES1: x: 0.0m y: 0.0m z: 3.0m FES2: x: 43.0m y: 0.0m z: 3.0m FES3: x: 0.0m y: 41.0m z: 3.0m FES4: x: 43.0m y: 41.0m z: 3.0m 1.3 CTS2: pLOS=1/2 NM4

SFN-TUe-CS large hall (43×41×7m³) TUe-CS from LOS st (1 tap: -5 dB) 4 DM1 MT: x: 0.5…42.5m y: 0.5…40.5m z: 1.4m FES1: x: 0.0m y: 0.0m z: 3.0m FES2: x: 43.0m y: 0.0m z: 3.0m FES3: x: 0.0m y: 41.0m z: 3.0m FES4: x: 43.0m y: 41.0m z: 3.0m 1.0 CTS2: pLOS=1/2 NM2 and NM4

SFN-TUe-ES corridor (44.7×2.4×3.1m³) TUe-ES from LOS st (1 tap: -10 dB) 2 DM1 MT: x: 0.5…44.2m y: 0.5 … 1.9m z: 1.4m FES1: x: 0.0m y: 1.2m z: 3.0m FES2: x: 44.7m y: 1.2m z: 3.0m

Model SFN-TUD2-1 room (12.4×8×3.5m³) TUD-LOS2 TUD-NLOS2 (3 dB atten.) 2 DM1 MT: x: 0.5…11.9m y: 0.5 … 7.5m z: 1.0m FES1: x: 0.0m y: 0.0m z: 2.5m FES2: x: 12.4m y: 8.0m z: 2.5m

SFN-TUD2-2 room (12.4×8×3.5m³) TUD-LOS2 TUD-NLOS2 (3 dB atten.) 2 DM1 MT: x: 0.5…11.9m y: 0.5 … 7.5m z: 1.0m FES1: x: 3.1m y: 4.0m z: 2.5m FES2: x: 9.3m y: 4.0m z: 2.5m

SFN-IMST library (13×5×2.6m³) IMST-FZ from LOS st (1 tap: -20 dB) 2 DM1 MT: x: 0.5…12.5m y: 0.5 … 4.5m z: 1.0m FES1: x: 3.3m y: 2.5m z: 2.6m FES2: x: 9.7m y: 2.5m z: 2.6m

SFN-Oslo-A2c street (162×36×15m³) Oslo-A2c-LOS from LOS (1st tap: -10 dB) 4 DM2 MT: d: 10…150m

1.2 CTS2: pLOS=1/2 NM2 and NM4

1.7 CTS2: pLOS=1/2 NM4

1.7 CTS2: pLOS=1/2 NM4

1.7 CTS2: pLOS=1/2 NM4

2.1 CTS2: pLOS=1/2 NM2 and NM4

The models are assumed to give a representative cross section of the possible environments and antenna arrangements. The model SFN-HL/2-TUe-CS using BRAN HL/2 channel models at 5.2 GHz is given for sake of comparative simulations within BROADWAY. We have chosen to decide for LOS or NLOS using the CTS2 principle with a LOS probability of pLOS = 1 2 for all FES. This value should make sense because it results on average in the probabilities for the number of LOS connections given in Table 7.30. Table 7.30: Probability for the number of LOS connections. Number of LOS connections 0 1 2 3 4

M=2 25 % 50 % 25 % -

M=4 6.25 % 25.00 % 37.50 % 25.00 % 6.25 %

The values for path loss exponent n were estimated from comparable (LOS) environments in section 1.1 in Table 6.7, except for the model SFN-HL/2-TUe-CS, where the value for HL/2 was taken from [153] (LOS, airport hall, 8-100 m, omni-omni).

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8. References The references are sorted alphabetically according to their first author’s surname.

[1]

“Received signal fading distributions”. IEEE Trans. Vehicular Techn., vol. 37, no. 1, Feb. 1988.

[2]

ABDI, A.; TEPEDELENLIOGLU, C.; KAVEH, M.; GIANNAKIS, G.: "On the Estimation of the K Parameter for the Rice Fading Distribution", IEEE Communication Letters, vol. 5, No 3, March 2001, pp. 92-94.

[3]

ABOURADDY, A.; SAID, S.: “Statistical modeling of the indoor radio channel at 10 GHz through propagation measurements—Part 1: Narrowband measurements and modeling,” IEEE Trans. Veh. Technol., vol. 49, pp. 1491–1507, Sept. 2000.

[4]

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