Hopping Pilot Pattern for Interference Mitigation in OFDM 1

Afif Osseiran1 and Jiann-Ching Guey2

Ericsson Research, Stockholm, Sweden, 2 Ericsson Research, Research Triangle Park, NC, USA {Afif.Osseiran, Jiann-Ching.Guey }@ericsson.com

Abstract—In an OFDM system, known symbols referred to as pilot are transmitted across the time-frequency plane for the receiving device to estimate the channel’s time-frequency response in order to perform coherent demodulation of data symbols. The placement of these pilot symbols largely falls into two categories, namely, the regular and irregular patterns. Inspired by synchronization techniques used in radars, [4] derived a time-frequency hoping pattern, called Costas Array which provides a better frequency offset estimation and accommodates substantially higher number of unique patterns that can be used for Base Stations (BSs) and/or antenna identifications. In this paper, we investigate the link and system performance of both pilot designs. From a link perspective we examine if there is a need to boost the pilot signals in order to achieve an adequate Signal to Noise Ratio (SNR). From the radio network perspective we analyze the impact of power pilot boosting. Further we explore an alternative method to reduce the interference perceived by the pilot signals, by introducing a data frequency reuse at interfering BSs. Our results show that a pilot boosting of 9 dB is required and data frequency reuse yields minor SINR improvement for the pilot signals. Furthermore the Costas Array, in addition to having lower peak power, yields substantially better SINR statistics compared to the regular pilot patterns. Key Words: Costas Array, OFDM, Pilot, Regular Patterns, Performance.

I. I NTRODUCTION In a radio transmission, the propagation channel will modify the phase and the amplitude of the signal. Hence in order to recover the original signal it is crucial to estimate the channel. The channel estimation is either based on pilots i.e. known transmitted signals, or blind i.e. based on exploiting certain properties of the transmitted signal. While blind channel estimation schemes require little or no pilot overhead, their application may critically depend on the assumptions of the chosen transmission scheme. In an Orthogonal Frequency Division Multiplexing (OFDM) system, known symbols referred to as pilot are transmitted across the time-frequency plane for the receiving device to estimate the channel’s time-frequency response in order to perform coherent demodulation of data symbols. Since the channel’s time-frequency response is a slow-varying twodimensional process, the pilot symbols essentially sample this process and therefore need to have a density that is high enough for the receiving device to reconstruct (or interpolate) the full response. From the sampling theory point of view, the pilot symbols essentially sample the channel’s time-frequency response and its density is thus determined by the channel’s maximal delay

and Doppler spreads, τmax and νmax 1 , respectively. Asymptotically, as long as the channel’s time-frequency response is sampled at a rate greater than νmax in time and τmax in frequency, the channel’s response can be reconstructed free of aliasing. This suggests a regularly spaced pilot symbol pattern with a time spacing of at most 1/νmax sec. and frequency spacing of at most 1/τmax Hz. The channel at the pilot signals positions can be estimated using classical pilot-assisted channel estimation techniques, such as zero-forcing, Minimum Mean Square Error (MMSE), etc. The channel estimation for the data signals is done by various prediction methods, such as linear interpolation and MMSE interpolation techniques. Channel estimation by interpolation in time and frequency based on a scattered pilot grid is considered to be an efficient solution for an OFDM-based radio interface [1], [2]. The placement of these pilot symbols (or pilot sub-carriers) largely falls into two categories, namely, the regular and irregular patterns. The former allocates the pilot symbols onto an evenly spaced subset of the OFDM sub-carriers (resp. symbols) across all symbols (resp. sub-carriers) whereas the latter allocates them in an irregular fashion across symbol and/or sub-carriers. These regular patterns are acceptable for systems in which pilot overhead is not of primary concern since the uninterrupted distribution of pilot symbols across time or frequency may be excessive. For future cellular systems employing multiple antennas, however, the number of pilot patterns observed at a given location may easily be in the order of 10 and the pilot’s density should therefore be as low as possible. Another disadvantage of the regularly spaced pattern is that it lacks the uniqueness to identify the transmitting device. Unlike a broadcast system such as DVB [3] where there is no need to identify the source devices and all broadcast stations transmit the same pilot pattern, the multiple base stations in a cellular system need to be individually identified. For instance, when the system is not synchronized in time, the number of unique patterns is equal to M , the number of subcarriers between two nearest pilot sub-carriers. Moreover, the OFDM symbol in which the pilots sub-carriers are inserted has much higher power than symbols carrying only data since the pilots are generally transmitted at higher power [3]. Therefore, the power amplifier is less efficient. The concentration of the pilot sub-carriers in one OFDM symbol also limit the pilot signal’s time support to one OFDM symbol duration, making its Doppler resolution inadequate for fast frequency offset 1 It

is assumed a one sided spectrum.

estimation. Inspired by synchronization techniques used in radars, [4] derived alternative patterns to the regular ones. These patterns, the Costas Arrays, preserve the non-aliasing, provide excellent synchronization signals in an OFDM system, and accommodate substantially higher number of unique patterns that can be used for BSs and/or antenna identifications. Moreover, the periodic Costas Array based solution has good ambiguity properties in both local and global scale. The local properties enable the quick initial acquisition of timing and frequency offset with very short observation. The global properties allow for the identification of a large number of devices using unique cyclic delay-Doppler shifts of an original pattern. In this paper, we investigate the link and system level performance of regular and irregular pilot designs. From the link we examine if there is a need to boost the pilot signals. From the radio network perspective we analyze the impact of power pilot boosting. Further we explore an alternative method to reduce the interference perceived by the pilot signals by introducing a data frequency reuse at interfering BSs. The rest of this paper is organized as follows. Section II presents the regular and Costas pilot patterns. In Section III, our network deployment model is explained. The link-level assumptions and results are briefly given in Section IV. The system-level simulation results are presented in Section V. Lastly, conclusions are given in Section VI. II. P ILOT PATTERNS : R EGULAR & I RREGULAR Let fs be the sub-carrier spacing and Ts be the OFDM symbol duration including the guard interval. Let us assume that the pilot symbols are transmitted with interval of fp = M fs and Tp = N Ts in frequency and time directions, respectively. M and N are simply the pilots spacing in terms of sub-carrier and OFDM symbol, respectively. From the sampling theory point of view, the channel’s two-dimensional delay-Doppler response h(τ, ν) can be fully represented only if its timefrequency transform domain equivalent H(t, f ) is sampled at or above the Nyquist rate. In other words, the time domain sampling frequency 1/Tp must be no less than νmax , the channel’s maximal Doppler spread; and the frequency domain sampling rate 1/fp must be no less than τmax , the channel’s maximal delay spread. But in general the pilot signals are over-sampled in order to ensure a good trade off between performance and overhead. Hence, M and N depend on the maximum Doppler frequency, fD = 1/νmax , the maximum delay of the channel τmax , and must satisfy the following relation:     1 1 1 1 M≤ and N ≤ , (1) βf τmax fs βt fD Ts where βf and βt denote the over-sampling factors in frequency and time, respectively. According to [5], an over-sampling factor of βf βt ≈ 2 provides a good compromise between performance and overhead due to pilots. It should be noted that the pilot density can be easily obtained by using (1). In the regularly spaced pilot pattern, the pilot symbols are evenly spaced in frequency and in time. Figure 1(a) illustrates

a regularly spaced two-dimensional pilot pattern in the timefrequency domain where N = 6 and M = 4. In the figure, two regularly spaced pilot signatures are shown: the first signature represented by the grey plain squares and the second one where the pilot signals, represented by the cross squares, are all shifted by one sub-carrier compared to the first signature. On the other hand, in the irregular pilot patterns case, the pilots symbols can be irregularly placed in time, in frequency or in both. An example of irregularly spaced pilots is shown in Fig. 1(b), where the two pilots are irregularly placed in frequency. In that figure as in the above regularly spaced pilot example two pilot signatures are shown. The irregular patterns can be chosen according to a certain criteria, yielding a specific signature (i.e. sequence). In [4], it was suggested to use the pilot sequences according to the Costas array. In the following we will describe the properties of Costas sequences. Let the collection of all the pilot probes be expressed as a repetitive signal in both time and frequency [4]: s(t) =

∞ 

∞ 

c(t − nTp )ej2πmFp t ,

(2)

m=−∞ n=−∞

where c(t) is an arbitrary base signal, Fp = Lfp is the frequency domain period and Tp is the time domain period, which is also the pilot insertion period. Note that the periodicity definitions here are different from these of the regularly spaced pattern described previously. Consider now a base signal c(t) =

L−1 

p(t − τl Ts )ej2πlfp t ,

(3)

l=0

where p(t) is a narrowband pulse shaping function with a certain time support. In the case of conventional OFDM, it is a rectangular pulse of the length of the symbol. τl are distinct integers ranging from 0 to L − 1. In other words, the delay hopping pattern {τ0 , τ1 , · · · , τL−1 } is one of the L! permutations of the integer set {0, 1, · · · , L − 1}. A length-L Costas sequence [6] is a permutation of the integer set {0, 1, · · · , L − 1} with the special property such that for any given 0 < |n| < L, τm − τm−n are distinct for all valid m. This property ensures that the signal shifted in time and frequency by (nTs , mfp ) has at most one coincidence with the original signal in the time-frequency plane except for n = m = 0. Take L = 6 for example, the sequence {τ0 , τ1 , · · · , τ5 } = {0, 2, 1, 5, 3, 4}

(4)

is a Costas sequence. The former example is illustrated by the plain grey squares in Fig. 1(b) where (L, M, N ) = (6, 4, 6), and the Costas sequence is defined according to (4). Note that when a Costas sequence is displayed in the delayDoppler plane by markings at (τn , n) in an L × L array, it is sometimes referred to as a Costas Array [7]. In the same figure another Costas array pilot sequence, {τ0 , τ1 , · · · , τ5 } = {4, 0, 2, 1, 5, 3}, is plotted (and represented by the cross squares). It is interesting to mention that Costas arrays have been shown to exist (through both exhaustive search and algebraic construction) for all L ≤ 31 and for any arbitrarily large values of L related to the occurrence of prime numbers and prime powers [7]. Based on the above observation, we can

design the pilot pattern with a time domain insertion period of N = L + 1 instead of N = L while using the Costas sequence of length L as the base signal. In other words, in the last symbol duration of each period, no pilot sub-carrier is transmitted. The interesting property of Costas array is that for a unsynchronized system in time, different time shifts can not be used for identification. Therefore, the total number of unique patterns for a perfect Costas array is M × L, in contrary to M patterns for the regularly spaced pattern. If the system is synchronized in time, the numbers of unique patterns become M × L × N and M × N for the perfect Costas array and regularly spaced pattern, respectively. With patterns that are orthogonal and nearly orthogonal, the assignment strategy is then to exhaust the orthogonal patterns first in a close proximity and reuse the nonorthogonal patterns far away. III. N ETWORK DEPLOYMENT MODEL A network deployment with seven sites where each site comprises three sectors is considered. The network is assumed to operate at a carrier frequency of 3.5 GHz and OFDM with 128 sub-carriers is used within the 5 MHz transmission bandwidth. Table I provides a summary of the assumed system parameters.

(a) Regular.

TABLE I S YSTEM AND S IMULATIONS PARAMETERS . Parameter Number of sites Inter-site distance [m] Number of sectors per site Sector output power BS receiver noise figure Carrier frequency Transmission bandwidth Sub-carrier bandwidth Number of sub-carriers Cyclic prefix length

Value 7 1000 m 3 36.5 dBm 5 dB 3.5 GHz 5 MHz 39.0 kHz 128 3.2 μs

A. Radio Channel Model The C2 metropolitan area pathloss and channel model from [8] are used in the evaluations. The model is applicable to a scenario with macro BS installation above rooftops and User Terminal (UTs) located outdoors on street level. None line of sight propagation is assumed between the BS antennas and the UTs. Shadow fading is modeled as a log-normally distributed random variable with a standard deviation of 8 dB. The ray-based channel model is an extension to the 3GPP spatial channel model (SCM) [9] with correlated shadow fading, delay spread and angular spread. B. Radio Network Algorithms UTs connect to the sector with the lowest path-loss, shadowing and antenna gain. Signals are transmitted using a fixed output power and the modulation order and channel code rate are selected to maximize the data rate. Round-robin transmission scheduling is employed.

(b) Costas. Fig. 1.

An example of a Regular and an Irregular pilot pattern.

C. Data Reuse and Pilot signals setting 1) Pilot signals setting: In order to facilitate the comparison between different pilot designs, we will assume an infinite number of orthogonal pilot sequences. In fact the latter assumption will favor the regular pilot design in terms of performance since the number of unique sequences are substantially higher for the Costas array case compared to the regular design.

The power allocated to the pilot sub-carrier may be equal to or greater than the power allocated to the data sub-carriers. A power boosting factor, ρ, of 0, 6 or 9dB will be applied. Note that a power constraint, Pt , of 4W per OFDM symbol (per 5 MHz) is assumed. Let Np be the number of pilot sub-carriers allocated to an OFDM symbol, composed of Ns samples. Then the pilot sub-carrier power is given by: p=

Pt , Ns + Np (1 − ρ1 )

(5)

where equal power per pilot sub-carrier is assumed. From (5), it can be noticed that when ρ is greater than one2 , the allocated pilot power per sub-carrier is inversely proportional to the pilot density within the transmitted OFDM symbol. 2) Data Reuse: In order to study the impact of the interference on the pilot symbols from other cells (i.e. sectors), two data allocations are considered: • Data Reuse 1, where the pilot sub-carriers of a specific cell will be interfered by all other sectors. • Data Reuse 3, where the pilot sub-carriers of a specific cell will not be interfered by data or pilot signals from neighboring sectors (i.e. the pilot sub-carriers’ positions of the neighboring sectors are silent). An illustration of the Data Reuse 3 method is shown in Fig. 2, where for instance sector S3 will remain silent on pilot sub-carriers’ positions of sectors S1 and S2. Similarly, S1 and S2 will remain silent on the pilot sub-carriers’ positions of sector S3.

TABLE II L INK - LEVEL SIMULATION PARAMETERS Parameter N M Number of information bits delay profile Doppler profile modulation channel code

Value 12 (length-12 Costas sequence) 8 1152 exponential-decaying Jakes model QPSK rate 1/2 turbo code

both pilot designs require few decibels higher SNR compared to the ideal case in order to achieve the same FER. For instance there is a 4.2dB SNR gap between the ideal and both pilot patterns at a FER of 10% (see Fig. 3). When ρ = 9dB, the gap is decreased by 3dB, hence reaching 1.2dB. Moreover, for a FER of 1%, the pilot boosting further reduces the gap by almost 4dB. Consequently, according to the link results, a pilot boosting of at least 9dB is required in order to achieve an adequate SNR. Note that for a turbo code of rate 1/3, 1 to 2 dB Signal to Interference and Noise Ratio (SINR) is sufficient for adequate channel estimation; this result is not shown here due to space limitation. Rate 1/2, QPSK, 1× Nyquist

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Example of Data Reuse 3.

V. S YSTEM -L EVEL P ERFORMANCE R ESULTS IV. L INK -L EVEL P ERFORMANCE To evaluate the impact of pilot boosting on the link level performance, we consider the worst case scenario in which the channel’s delay-Doppler spread is at the pilot’s Nyquist rate. In other words, the channel’s time-frequency response is critically sampled by the pilot symbols. An MMSE channel estimator is used for all pilot patterns being studied. Table II summarizes the key parameters used in our simulation. Figure 3 shows the Frame Error Rate (FER) as a function of SNR for various pilot boosting power. The first interesting observation is that without any power pilot boosting (ρ = 0), 2 In

(5), ρ in taken in the linear scale.

A. Impact of Data Reuse Signal In case the pilot signals are interfered by all other cells (i.e. the Data Reuse 1 case) then barely 50% of the users attained the adequate SINR for error free channel estimation (see Fig. 4(a)). It can be also seen from the same figure that in the case of Data Reuse 3, the SINR improves only for users close to the BS but the improvement remains marginal for low SINR users. According to the same figure, the SINR gain obtained from the data reuse decreases for a larger cell size, since it is a noise limited scenario. Finally it should be noted that the SINR gain obtained by data reuse is similar to the regular and Costas array pilot patterns (compare Fig. 4(a) to Fig. 4(b)).

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Fig. 5. The cdf of the SINR for Regular and Costas Array pilot design for varios pilot power boosting and a cell radius of 500m.

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(b) Costas. Fig. 4. The cdf of the SINR for Regular and Costas array pilot design for data reuse of 1 and 3; and cell radii of 500 and 1500m.

B. Impact of Pilot power boosting It can be seen from Fig. 5 that the power boosting factor has a substantial impact on the pilot SINR. For the regular pilot pattern, a power pilot boosting of 9dB yields 8 to 12 dB SINR gain compared to the case with no power pilot boosting. Moreover the Costas array yields better performance than the regular pilot pattern when the power boosting factor increases. For instance the SINR gain of Costas array relative to the regular pilot pattern is 3dB for a pilot power boosting of 9dB. The SINR loss of regular pattern is not a surprise. In fact, the allocated power per sub-carrier pilot for a specific OFDM symbol is inversely proportional to the pilot boost factor, since there is a power constraint per OFDM symbol (see Eq. 5). VI. C ONCLUSION In an OFDM, multi-cell multi-antenna system, the pilot overhead that allows to support different variants of the advanced antenna schemes, various requirements such as synchronization, radio node identifications, may turn to be prohibitive in terms of spectral efficiency. Hence it is crucial to design these pilots in such a way to balance between accuracy and reliability in terms of channel estimation on one hand; and power and spectral efficiency on the other hand.

In this paper, we investigated the link and system performance of regular and irregular pilot designs. From the link results, while Costas array and regular pilot patterns yielded similar performance, both required the pilot signals to be boosted by 9 dB in order to achieve an adequate SNR. The pilot boosting implies a much lower peak power rate for the Costas array compared to the regular pilot pattern. Further we explored an alternative method to reduce the interference perceived by the pilot signals by introducing a data frequency reuse at interfering BSs. The data frequency reuse yields minor SINR improvement for the pilot signals and can not be seen as viable alternative to power boosting. Finally, beside providing excellent synchronization signals in an OFDM system and accommodating substantially higher number of unique patterns, we have shown that the Costas array yields 3 to 6 dB higher SINR compared to the regular pilot pattern for a power pilot boosting of 9 dB. R EFERENCES [1] IST-2003-507581-WINNER, “D2.1, identification of radio-link technologies,” Framework Programme 6, Tech. Rep., June 2004. [2] ——, “D2.3, assessment of radio-link technologies,” Framework Programme 6, Tech. Rep., Feb. 2005. [3] ETSI, “Digital video broadcasting (dvb); framing structure, channel coding and modulation for digital terrestrial television,” ETSI, Tech. Rep. EN 300 744 V1.5.1, June 2004. [4] J.-C. Guey, “Synchronization Signal Design for OFDM Based On TimeFrequency Hopping Patterns,” Communications, 2007. ICC ’07. IEEE International Conference on, pp. 4329–4334, June 2007. [5] R. Nilsson, O. Edfors, M. Sandell, and P. Borjesson, “An analysis of two-dimensional pilot-symbol assisted modulation for OFDM,” Personal Wireless Communications, 1997 IEEE International Conference on, pp. 71–74, Dec. 1997. [6] J. Costas, “Medium constraints on sonar design and performance,” General Electric Company, Tech. Rep. Class 1 Rep. R65EMH33, November 1965, a synopsis of this report appeared in the Eascon. Conv. Rec., 1975, pp. 68A–68L. [7] S. W. Golomb and H. Taylor, “Constructions and properties of costas arrays,” Proc. IEEE, vol. 72, no. 9, pp. 1143–1163, Sept. 1984. [8] J. Meinil¨a, Ed., IST-2003-507581 WINNER I, D5.4, Final report on link level and system level channel models, 2005, no. v1, https://www.istwinner.org/Documents/Deliverables/D5-4-V1.pdf. [9] 3GPP, “Spatial channel model for multiple input multiple output (mimo) simulations, Tech. Rep. 3GPP TR 25.996 V6.1.0, Sept. 2003, http://www.3gpp.org/ftp/Specs/html-info/25996.htm.