Waveforms MOdels for Machine Type CommuNication inteGrating 5G Networks (WONG5) Document Number D2.2 New waveforms for C-MTC context Contractual date of delivery:

12/06/2017

Project Number and Acronym:

ANR-15-CE25-0005, WONG5

Editor:

Sylvain Traverso (TCS)

Authors:

Sylvain Traverso (TCS), Yahia Medjahdi (CNAM), Jean-Baptiste Dore (CEA), David Demmer (CEA), Mouna Ben Mabrouk (CS), Rostom Zakaria (CNAM)

Participants:

CNAM, TCS, CEA, CS

Workpackage:

WP2

Security:

Public(PU)

Nature:

Report

Version:

0.5

Total Number of Pages:

42

Abstract: This report is the second one of task WP2 titled ’Waveforms for C-MTC’. The aim of this deliverable is to propose new waveforms and to compare with the waveforms kept in D2.1 which are adapted to the C-MTC context. The performance assessment and the WF analysis are performed according to several criteria such as the PSD, spectral efficiency, latency, complexity, time and frequency offset behavior, PAPR, and BER with multipath channels. Keywords: C-MTC, CP-OFDM, post-OFDM, WOLA-OFDM, UFMC, UF-OFDM, FilteredOFDM, FBMC-OQAM, WCP-COQAM, FFT-OFDM, BF-OFDM, Wavelet, WOLA-COQAM, PSD, spectral efficiency, latency, timing offset, CFO, PAPR, complexity, uncoded BER, multipath

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Document Revision History Version

Date

Author

Summary of main changes

0.1

18.05.2017

TCS

Initial structure of the document

0.2

20.06.2017

CNAM / CS

Contributions from CS and CNAM added

0.3

11.07.2017

TCS

Second round of contribution from TCS, CS, CNAM and CEA. Ready for first review.

0.4

19.07.2017

TCS

Minor corrections and update. Ready for last review.

0.5

21.07.2017

TCS

Final version.

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Executive Summary The goals of the WONG5 project are to study and propose the most appropriate post-OFDM waveforms (WF) that could be adapted to critical machine type communications (C-MTC). Deliverable D2.2 proposes in part 2 four new waveforms (FFT-FBMC, BF-OFDM, WOLACOQAM and Wavelet-OFDM) adapted for the C-MTC context. These waveforms are analyzed in part 4 with the same system model defined in D2.1 (and recalled in part 3) in terms of power spectral density, spectral efficiency/latency, asynchronous access, instantaneous average power ratio, and complexity. Part 4 is devoted to the multipath performance comparison of the four proposed new waveforms with the subset waveforms kept in D2.1 (CP-OFDM, f-OFDM, WOLA-OFDM, FBMC-OQAM, UF-OFDM) and adapted to C-MTC context.

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Table of Contents 1 Introduction 1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Proposal of new waveforms 2.1 FFT-FBMC . . . . . . . . . . . . 2.2 BF-OFDM . . . . . . . . . . . . . 2.3 WOLA-COQAM . . . . . . . . . . 2.4 Wavelet-OFDM . . . . . . . . . . 2.4.1 Haar-based wavelet-OFDM 2.4.2 Meyer-based wavelet-OFDM

5 5 5

. . . . . .

7 7 10 11 14 14 15

3 System Model 3.1 Coexistence scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 17 18

4 Waveforms comparison 4.1 PSD . . . . . . . . . . . . . . 4.2 Spectral efficiency/Latency . . 4.3 Asynchronous access . . . . . . 4.3.1 Timing offset . . . . . . 4.3.2 Carrier Frequency Offset 4.4 IAPR . . . . . . . . . . . . . . 4.5 Complexity . . . . . . . . . . .

. . . . . . .

22 22 23 24 26 27 30 31

5 Multipath performance comparison 5.1 Impact of delay spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Impact of realistic multipath channel . . . . . . . . . . . . . . . . . . . . . .

35 35 36

6 Conclusion

39

7 References

40

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1. Introduction 1.1

Context

The objective the WONG5 project is to study and propose the most appropriate post-OFDM waveforms (WF) for critical machine type communications (C-MTC). Requirements for C-MTC systems have been described in D1.1 [DRT16] and can be summarized as follows: low latencies, very high reliability and data integrity, high energy efficiency for mobile systems and resistance to asynchronous users (time and frequency). The aim of deliverable D2.2 is to propose new WF, to analyze them, and to compare them with the restricted set candidates WFs chosen in D2.1 under the requirements of C-MTC systems. In task 3, energy efficiency improvement will be studied together with their adaptation to analog RF components. During task 4, adaptation of candidate WFs to MIMO systems will be developed.

1.2

Objectives

The main objective of deliverable D2.2 is to propose 4 new WFs for C-MTC systems having in mind to: • have a great filtering capability at the transmitter side • ease the use of MIMO techniques • lower as much as possible the Peak to Average Power Ratio (PAPR), or to ease the use of already developed PAPR technique • lower the interference generated by asynchronous users These WFs are FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM. They are then analyzed and compared with the chosen WFs in D2.1: • CP-OFDM as a comparison basis, • filtered OFDM (f-OFDM), • Weighted Overlap and Add-OFDM (WOLA-OFDM), • Universal Filtered OFDM (UF-OFDM), • Filter Bank Multicarrier-Offset QAM (FBMC-OQAM). A common system model has been adopted for all WFs comparisons. This system model takes into account the fact that asynchronous users will be present in a C-MTC system. The resource blocks (RB) assigned to the user of interest (UOI) are surrounded by RB assigned to other users that can have time and frequency offsets related to the UOI. The different comparison criteria are: • Power spectral density, • Spectral efficiency and Latency, • Asynchronous access related to Timing Offset, WONG5 Deliverable D2.2

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• Asynchronous access related to Carrier Frequency Offset (CFO), • Peak to Average Power Ratio, • Complexity. Finally, the 4 proposed waveforms (FFT-FBMC, BF-OFDM, WOLA-COQAM, WaveletOFDM) and the restricted set waveforms kept in D2.1 for C-MTC (CP-OFDM, f-OFDM, WOLA-OFDM, FBMC-OQAM, UF-OFDM) are analyzed and compared in terms of uncoded bit error rate for multipath channels.

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2. Proposal of new waveforms 2.1

FFT-FBMC

In order to overcome the FBMC intrinsic interference issue, FFT-FBMC scheme, together with a special data transmission strategy has been proposed in [ZR12, ZLR10]. This scheme proceeds by precoding the data in a subcarrier-wise manner using an IFFT. Thus, the interference coming from the same subcarrier is removed by a simple equalization thanks to the subcarrierwise IFFT/FFT precoding/decoding and cyclic prefix (CP) insertion. Whereas the interference coming from the adjacent subcarriers can be avoided by a special data transmission strategy and a good frequency-localized prototype filter. In FFT-FBMC proposal, blocks of N/2 data complex symbols in each subcarrier k go through a N -IFFT operation. The N/2 data symbols are alternately fed to the first and last N/2 bins of the N -IFFT. When the subcarrier index k is odd (resp. even), the symbols are fed to the first (resp. last) N/2 bins. After that, the N -IFFT outputs are extended with a cyclic prefix (CP) of size L, and fed to the FBMC modulator of M carriers in a given subcarrier k. Figure 2-1 depicts the scheme of the FFT-FBMC proposed in [ZLR10]. Let us denote by dk,p [l] the l-th complex data symbol in the p-th block to be transmitted in the k-th subcarrier. According to the FFT-FBMC scheme developed in [ZR12], the symbols ak,n at the input of the FBMC modulator can be written as: N

−1 2πnl ejπn(k+1) 2X dk,p [l]ej N ak [n] = √ N l=0

l

(2.1)

m

where p is the block index given by p = N n+L +1. It is worth noticing that the first exponential term in the equation above is related to the alternating rule mentioned in the beginning of this section. At the output of the FBMC demodulator, the serial symbols zq [n] in each subcarrier q are reshaped into blocks of size N + L to only keep N symbols in each block. This operation is referred to as "S/P + CP removal" in Figure 2-2. After that, N symbols of each block p0 are fed to a N -FFT whose only N/2 output symbols are kept for detection. Again, the first N/2 output symbols are kept when the subcarrier index q is odd, and the last N/2 symbols are kept when q is even. Figure 2-2 depicts the overall scheme of FFT-FBMC receiver. Therefore, the 0 0 0

P/S

CP insertion 0

0 0 0

N IFFT

P/S

CP insertion

N IFFT

P/S

...

1

...

0 0 0

...

S/P

FBMC modulator

N IFFT

CP insertion M-1

Figure 2-1: FFT-FBMC transmitter scheme WONG5 Deliverable D2.2

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FBMC demodulator

S/P + CP removal

N FFT

S/P + CP removal

N FFT

0

Equalization

...

...

...

1

S/P + CP removal

N FFT

M-1

Figure 2-2: FFT-FBMC receiver scheme FFT-FBMC demodulated symbols (just before Equalization block) can be expressed as: 2πnl0 1 X −jπn(q+1) xq,p0 [l0 ] = √ e zq [n]e−j N N n∈Bp0



for l0 ∈ 0, ...,

N −1 2



(

(2.2)

) 0

0

where Bp0 = (p − 1)(N + L) + L/2, ..., p (N + L) − L/2 − 1 . We note again that the first exponential term in the equation above is related to the alternating rule concerning the N/2 kept symbols for detection in each subcarrier q. It is shown in [ZR17] that single-tap equalization can be performed. The equivalent channel coefficients are the M N/2 channel frequency response coefficients weighted by the periodic squared magnitude of the prototype filter frequency response. Indeed, the FFT-FBMC demodulated symbols is expressed as [ZR17] ˜ q [l0 ]dq,p0 [l0 ] + w˜q,p0 [l0 ] xq,p0 [l0 ] = H

(2.3)

˜ q [l0 ] is the equivalent channel coefficient given by [ZR17] where w˜q,p0 [l0 ] is the noise term, and H ˜ q [l0 ] = H l0 + q N × F [l0 ] H 2 



N N for l ∈ − , ..., − 1 4 4 0





(2.4)

4π

with H[µ] = τ h[τ ]e−j M N µτ denotes the discrete frequency response of the channel h[τ ] at tones M2µN , and where F [l0 ] is the discrete Fourier transform (DFT) of the downsampled by M/2 of the prototype filter autocorrelation. Therefore, one can observe that according to (2.3) the complex orthogonality is restored in FFT-FBMC. The intercarrier interference is avoided thanks to the N/2 zeros inserted in the N IFFT in each subband. For the sake of clarity and illustration, Figure 2-3 depicts in a qualitative manner the spectrum of two active adjacent subcarriers in FBMC and FFT-FBMC. The first plot shows that ICI in FBMC is generated due to the overlapping of both filter frequency responses. Whereas, we show for FFT-FBMC in the second plot that each subband is devided into N smaller subbands where only the N/2 middle ones are active. This corresponds to the N/2 nonzero symbols at the input of the N -IFFT in each subcarrier. That is, the N/2 zeros inserted in each N -IFFT serve to isolate the adjacent subbands. It should be noted that normally, in Figure 2-1, the N/2 zeros should be in the middle of each N -IFFT. However, since the "FBMC π modulator" introduces a phase rotation of Φk [n] = ej 2 (k+n)−jπkn [ZR12], the zero positions are changed accordingly. P

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Spectrum

Interference Subband 1 Subband 2

−2

−1

0 1 Subbands

2

−3

3

4

FFT−FBMC subband 1 FFT−FBMC subband 2 FBMC Subband 1 FBMC Subband 2

Spectrum

−3

−2

−1

0 1 Subbands

2

3

4

Figure 2-3: Illustration of the complex orthogonality in FFT-FBMC.

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Pre-distortion

N/2

S / P

subcarriers

0

Pre-distortion

N/2

0 0

subcarriers

0

• • •

N IFFT OFDM • • •

Pre-distortion

N/2

N IFFT OFDM

subcarriers

0 0

N IFFT OFDM

P / S P / S P / S

CP Insertion

0

CP Insertion

1

• • •

CP Insertion OFDM precoding

IFFT + PPN

M

M-1

Filter bank stage

Figure 2-4: BF-OFDM transmitter scheme.

2.2

BF-OFDM

Block-Filtered OFDM (BF-OFDM) is a precoded filter-bank multi-carrier modulation [DGD+ 17] [GDDK17]. The precoding scheme is performed by means of Inverse Fourier Transforms (IFTs) and CP insertion, hence the name of the modulation scheme. The idea of such precoding was first proposed in [ZR12] and is detailed in section 2.1. It aims at highly attenuating the filterbank inherent interferences but leads to a complex receiver structure composed of a synthesis filter bank concatenated with CP-OFDM demodulators. BF-OFDM can be seen as an improved version of FFT-FBMC. The key idea is to prepend a pre-distortion stage to the transmitter chain in order to rely on a low-complex CP-OFDM like receiver. The transmitter and receiver schemes are respectively depicted in figures 2-4 and 2-5. The transmitter is thus composed of a precoding stage followed by a filter bank. Regarding the precoding, the pre-distortion stage compensates the distortion induced by filter bank (in both amplitude and phase) in order to flatten the received signal spectrum inside the carrier bandwidth at the receiver side. Then, the framing maps the N/2 active subcarriers for each carrier. The subcarrier allocation depends on the carrier index (its parity) and ensures the perfect complex orthogonality at the carrier level [DGD+ 17]. Finally, there are the CP-OFDM modulators. Indeed, a CP insertion is required in order to preserve the circularity of the signal, so as in legacy CP-OFDM. The filtering is operated by means of a M-point IFFTs and a PolyPhaseNetwork (PPN). As the symbols are spread in time because of the PPN (with an overlapping factor equal to K), an overlapping stage is considered at the end of the transmission chain in order to improve the Spectral Efficiency (SE). However the overlapping generates Inter-Symbol Interferences (ISI) as neighbour symbols in time are captured with the useful one. To come up with it, the CP length must be greater or equal than 2K − 1 [DGD+ 17]. This condition on the CP length leads to a significant loss of SE therefore in practice shorter CP are used at the expense of a Signal-to-Interference Ratio (SIR) penalty. The common choice is to set the CP length so that the SE is equivalent to the legacy CP-OFDM. The receiver is simply composed of a M2N -point FFT and is therefore highly similar to the receiver used in conventional OFDM. No filtering stage are required thanks to the predistortion stage that is added at the transmitter side. BF-OFDM is said to be complex-orthogonal but rigorously it is not. Indeed even if a perfect orthogonality is satisfied at the carrier level by the framing, inter-carrier interferences are generated by the filter bank. However, the rejection of those interferences are controlled by both the filter shape and the CP and provides SIR of about 60 dB. Such a SIR level does not disturb the transmission over the other carriers and that is why the modulation scheme is said WONG5 Deliverable D2.2

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S CP removal

P

MN 2 - point FFT

/ P

/ S

Figure 2-5: BF-OFDM receiver scheme. to be complex orthogonal. Filter shapes have been optimized with respect to the SIR. Indeed, for filter shape that are defined by a set of parameters, it is possible to find the parameter set values to maximize the SIR. The results of the optimizations for the Gaussian and Frequency-Sampling defined filters are given in Tab 2-1. Table 2-1: SIR for various filters. H0

H1

K = 4 PHYDYAS NCP = 4

1

K = 2 PHYDYAS NCP = 2

1

0.972 √ 2/2

K = 4 Optimized NCP = 4

1

K = 2 Optimized NCP = 2

1

Gaussian NCP = 4

H2 √ 2/2

H3

SIR [dB]

0.235

47.42

x

x

26.39

0.792

0.375

0.082

70.44

0.485

x

x

39.39

BT = 0.33

63.61

It is worth mentioning that thanks to the complex orthogonality, all classical MIMO schemes, as well as PAPR reduction scheme (e.g DFT spread) can be considered.

2.3

WOLA-COQAM

The weighted overlap and add (WOLA) could be applied to WCP-COFDM (Figure 2-6) to obtain WOLA-COQAM [MZSR17]. WOLA was initially introduced in [Qua] by Qualcomm Incorporated and has been studied in [ZMSR16a] with OFDM in asynchronous 5G scenario. In the WOLA transmitter process, a time domain windowing operation is performed producing thus soft edges at the beginning and the end of original transmitted block. These soft edges are added to the cyclic extension of the COQAM symbol of length Ns = K × N . Indeed, the smooth transition between the last sample of a given symbol and the first sample of the next symbol is provided with point-to-point multiplication of the windowing function and the symbol with cyclic prefix and cyclic suffix (see Figure 2-7). The samples corresponding to CP (of size CP ) from the last part of a given symbol are copied and appended to its beginning. Besides, WONG5 Deliverable D2.2

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Figure 2-6: WCP-COQAM signal construction

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Figure 2-7: WOLA processing: Transmitter side

Figure 2-8: WOLA processing: Receiver side

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the first WT x samples of the symbol are added to the end, corresponding to the cyclic suffix. Thus, the WOLA-COQAM time domain symbols are cyclically extended from Ns samples to Ns + CP + WT x . After the cyclic extensions insertion, a window of length L = Ns + CP + WT x samples is applied. In fact, many windowing functions have been studied and compared [BT07] in terms of enhancing side lobe suppression. Straightforward solution is to define edge of the time domain window as a root raised-cosine (RRC) pulse. In this report, we consider the Meyer-RRC pulse combining the RRC time domain pulse with the Meyer auxiliary function [GMM+ 15]. In addition to the transmit windowing, which is used to improve the spectral confinement of the transmitted signal, the WOLA processing is also applied at the receiver side in order to enhance asynchronous inter-user interference suppression, as illustrated in Figure 2-8. Note that the applied receive window is independent of the transmit one and its length is equal to Ns + 2WRx . This windowing is followed by Overlap and Add processing which minimizes the effects of windowing on the useful data. As shown in Figure 2-8, it is worth emphasizing that the first window part [0, 2WRx − 1] applied at the receiver must be symmetrical w.r.t the point (WRx , 12 ), in order to correctly recover the weighted samples.

2.4

Wavelet-OFDM

The principle of the wavelet transform is to decompose the signal in terms of small wave components called wavelets. The Wavelet-OFDM transmitted signal can be defined as: X(t) =

j −1 X 2X X J−1

wj,k ψj,k (t − nT )

n j=J0 k=0 J

+

0 −1 X 2X

n

aJ0 ,q φJ0 ,q (t − nT ).

q=0

• J − 1: last scale considered, with M = 2J ; • J0 : first scale considered (J0 ≤ j ≤ J − 1); • wj,k : wavelet coefficients located at k-th position from scale j; • aJ0 ,q : approximation coefficients located at q-th position from the first scale J0 ; • ψj,k = 2j/2 ψ(2j t−kT ): the wavelet orthonormal family, ψ is the mother wavelet function; J0

• φJ0 ,q = 2 2 φ(2J0 t − qT ): the scaling orthonormal family at the scale J0 , φ is the mother scaling function. Note that the wavelet functions and the scaling functions have identical energy. 2.4.1

Haar-based wavelet-OFDM

The Haar mother wavelet function ψhaar (t), which belongs to the family of Daubechies wavelets, is expressed as:

ψhaar (t) =

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  √1    T

if 0 ≤ t ≤ T2 ,

− √1 , if

T    0,

T 2

≤ t ≤ T,

(2.5)

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The scaling function φhaar (t) can be described as: and φhaar (t) =

  √1

if 0 ≤ t ≤ T,

0,

else.

T

(2.6)

Figure 2-9: Haar wavelet function for different scales. haar for J0 = 0 and M = 8. As we can notice, Fig. 2-9 describes Haar wavelet functions ψj,k the temporal support of the contracted versions of the mother wavelet function ψ haar are smaller than the symbol period T .

2.4.2

Meyer-based wavelet-OFDM

The Meyer mother wavelet function ψDmey (ω), in the frequency domain is expressed as:   0,     2−1/2 F h (ω/2),

if |ω| ≤ 2π , 3 2π if 3 ≤ |ω| ≤ ΨDmey (ω) = −1/2 h   2 exp(−iω/2)F (ω/4), if 4π ≤ |ω| ≤  3    0, if |ω| > 8π 3

4π , 3 8π , 3

(2.7)

∗

where F h (ω) = exp(−iω)F b (ω + π) and F b (ω) =

√  2 0,

if |ω| ≤ π3 , else.

The scaling function φDmey (ω) can be described as: and ΦDmey (ω) =

 2−1/2 F b (ω/2) 0,

if |ω| ≤ else.

4π , 3

(2.8)

Fig. 2-10 describes Meyer wavelet functions.

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Figure 2-10: Meyer wavelet mother and scale functions

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3. System Model In this section, we present the system model which is similar to the one already presented in deliverable D2.1 [WON16b]. We also present the waveform parameters considered for the comparisons presented in the following chapters.

3.1

Coexistence scenario

Figure 3-1: Coexistence scenario: two asynchronous users with τ [s] timing offset,  [kHz] carrier frequency offset and free guard-bands of δ [kHz]. In this study, we consider a scenario of two users sharing the available frequency band as depicted in Figure 3-1. The blue colored area and the red colored one correspond to the time/frequency resources allocated to the user of interest and the other one, respectively. The useful signal occupies a frequency band of 540 kHz equivalent to 3 LTE resource blocks (LTERB bandwidth = 180 kHz) while 1.62 MHz (i.e. 9 LTE-RB) are allocated to the other user on each side of the useful frequency band. A guard-band of δ kHz , illustrated by a gray colored area, is separating the frequency bands of both users. Several cases are considered for guard-bands: no guard band, 15 kHz, 45 kHz and 75 kHz. The receiver of interest is assumed to be perfectly synchronized, in both time and frequency domains (i.e. neither timing offset nor frequency offset are considered), and is situated at equal distance from both transmitters1 . However, as illustrated in Figure 3-1, a time/frequency synchronization misalignment (τ and ε denote timing and carrier frequency offsets, respectively) can occur between the receiver of interest and the other user. Note that we consider a timing offset distributed between −T /2 and +T /2, where T is the OFDM symbol duration (T = 66.66µs). Due to this synchronization mismatch, the receiver of interest suffers from the 1

Note that in this work, we assume the same transmit power per subcarrier for both useful and interfering users

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RB bandwidth

180 kHz

Useful bandwidth of user of interest (UOI)

540 kHz

Interfering bandwidth

2 × 1.62 MHz

Timing offset (τ )

[-33.33,+33.33]µs

CFO (ε)

[-1.5,+1.5]kHz

Input data

16-QAM

Gaurd-band δ

[0, 15, 45, 75] kHz

interference inducing thus performance degradation. It is worth mentioning that the CFO induces a shift of both red-colored areas of the interfering signal spectrum by ε kHz where the resulting guard bands become δ − ε kHz on one side and δ + ε kHz on the other side. In order to highlight the impact of this interference, we consider free-distortion channels (perfect and noiseless channels) between both transmitters on one side and the victim receiver on the other side.

3.2

Parameters

In this section, we provide the general parameters of the scenario previously described (see Table 3-1) as well as specific parameters related to the different waveforms considered in this document: • Waveforms with complex orthogonality: Tables 3-2 and 3-3, • Waveforms with real orthogonality: Table 3-4,

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Table 3-2: WFs with complex orthogonality (1/2) CP-OFDM FFT size (NFFT )

1024

CP length (NCP )

72

Subcarrier spacing

15 kHz

Sampling Frequency (Fs )

15.36 MHz WOLA-OFDM

FFT size (NFFT )

1024

CP length (NCP )

72

Windowing

Raised cosine

WTx ,WRx

(20, 32)

Subcarrier spacing

15 kHz

Sampling Frequency (Fs )

15.36 MHz UF-OFDM

FFT size (NFFT )

1024

Filter

Dolph-Chebyshev with 40 dB stop band attenuation

Filter length

73 (LFIR =ZP+1)

Zero padding length (NZP )

72

Receive windowing

Raised cosine

Subcarrier spacing

15 kHz

Sampling Frequency (Fs )

15.36 MHz Wavelet-OFDM

FFT size (NFFT )

1024

Wavelet Type

Meyer

Subcarrier spacing

15 kHz

Sampling Frequency (Fs )

15.36 MHz

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Table 3-3: Waveforms with complex orthogonality (2/2) f-OFDM FFT size (NFFT )

1024

Filter

the same at both Tx and Rx, see D2.1 [WON16b] for exact definition

Filter length

512

CP length (NCP )

72

Transition band

2.5 × 15 kHz

Burst truncation

NCP /2 on each side

Subcarrier spacing

15 kHz

Sampling Frequency (Fs )

15.36 MHz

BF-OFDM / FFT-FBMC M

64

N

64

K

4

BF-OFDM Rx FFT size

2048

CP size

4

Carrier bandwidth

180 kHz

Sampling Frequency

11.52 MHz

Prototype Filter

Gaussian (BT=0.33)

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Table 3-4: Waveforms with real orthogonality FBMC-OQAM Prototype Filter

PHYDYAS

Overlapping factor (K)

4

FFT size (NFFT )

1024

Subcarrier spacing

15 kHz

Sampling Frequency (Fs )

15.36 MHz WOLA-COQAM

CP

72

Transmit windowing

Meyer-Raised cosine

WTx ,WRx

(20, 32)

Prototype Filter

PHYDYAS

Overlapping factor (K)

4

FFT size

1024

Subcarrier spacing

15 kHz

Sampling Frequency

15.36 MHz

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4. Waveforms comparison In this chapter, we analyse the performance of the 4 proposed WFs in terms of PSD, spectral efficiency/latency, asynchronous access, IAPR and complexity. CP-OFDM is kept as a comparison basis.

4.1

PSD

It is well established that traditional CP-OFDM has poor frequency domain localization. For instance, LTE system requires the use of 10% of the system bandwidth as guard bands. These large guard bands located at both edges of the spectrum are necessary in order to reach enough attenuation to meet LTE spectrum mask requirement. It is expected that future 5G systems use more efficiently the allocated bandwidth and large guard bands can be seen as a waste of spectral efficiency. Thus, good or excellent spectral containment will be a key parameter for future 5G waveform in order to support neighboring and non orthogonal signals. We present in figure 4-1 the PSD (Power Spectral Density) comparison of the proposed waveforms. We choose to plot only the contribution of the interference users so that we can observe at the same time the level of out-of band emission and the level of emission within a spectral hole. As expected, the worst PSD performance is given by the traditional CPOFDM waveform. Wavelet-OFDM provides only very slight far-end PSD improvement with respect to OFDM. A major drawback of Wavelet-OFDM is its incapacity of creating a notch in-between bands due to the Meyer wavelet. WOLA-COQAM improves by about 25 dB the PSD performance thanks to the WOLA processing at the transmitter side which smoothes the transitions between successive blocks. The far-end PSD is dominated by the FFT-FBMC and BF-OFDM waveforms which combine OFDM precoding with filterbank.

0

−20

PSD [dB]

−40

−60

−80

−100

CP−OFDM Wavelet WOLA−COQAM FFT−FBMC BF−OFDM

−120

−140

0

5

10

15

Frequency [MHz]

Figure 4-1: Interference users PSD comparison In figure 4-2, we present a zoom of the PSD at the right edge of the spectrum according to WONG5 Deliverable D2.2

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the LTE subcarrier index 1 . We can observe the poor decaying of the Wavelet-OFDM PSD due to the Meyer wavelet which experiences a very slow ramp down in the frequency domain. On the other hand, WOLA processing provides an interesting PSD improvement of about 10 dB with respect to OFDM even for the first unused subcarrier. Finally, FFT-FBMC and BF-OFDM have very fast PSD decaying. It is interesting to observe the impact of the prototype filter over one resource block on the PSD of FFT-FBMC, but also the impact of the pre-distortion used for BF-OFDM in order to flatten the transmitted PSD.

0

−10

PSD [dB]

−20

−30

−40

−50

CP−OFDM Wavelet WOLA−COQAM FFT−FBMC BF−OFDM

−60 −16−15−14−13−12−11−10−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Subcarrier Index

Figure 4-2: Comparison of the interference users PSD edge according to the subcarrier index

4.2

Spectral efficiency/Latency

Spectral efficiency (SE) given in bits/s/Hz is a key parameter for high data rate systems since it gives a clear idea of achievable data rates for a given bandwidth. In Table 4-1, we present the SE according to the number of transmitted parallel vector symbols S, and also its asymptotic version called Asymptotic Spectral Efficiency (ASE) where S tends toward infinity. Note that we do not include the impact of the constellation dimension since it is supposed to be identical for all WFs. The required number of parallel vectors is different for each WF and depends on the number of complex QAM symbols NQAM to be transmitted, but also on the way a block symbol is built. S is given by:          

S=        

1

NQAM e NA NQAM d N e A NQAM d K×N e A N d MQAM N e A× 2

d

for OFDM for Wavelet-OFDM for WOLA-COQAM for FFT-FBMC and BF-OFDM

LTE subcarrier spacing is 15 kHz

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Table 4-1: Spectral efficiency and End-to-End Physical layer latency comparisons WF

Spectral

Asymptotic

End-to-End

Efficiency

Spectral Efficiency

Physical layer latency

OFDM

NFFT NFFT +NCP

NFFT NFFT +NCP

S×

Wavelet-OFDM

NFFT NFFT +NCP S× N 2 1 K+ 2 [S×(N +NCP )−1]

NFFT NFFT +NCP

S×

FFT-FBMC

N N +NCP

BF-OFDM

S× N 2 1 K+ 2 [S×(N +NCP )−1]

N N +NCP

WOLA-COQAM

S×K×NFFT S×(K×NFFT +NCP )+WTx

K×NFFT K×NFFT +NCP

M× N ×S+M × 2 M 2

NCP 2

NFFT +NCP Fs

NFFT +NCP Fs ×(S−1)+[(NCP −3)× M +K× M 4 2 ] Fs

h

S×N +NCP (S−1)+

NCP −3 +K 2

Fs S×(K×NFFT +NCP )+WTx Fs

where d.e refers to the ceiling operation, and NA and MA are respectively the number of used subcarriers and the number of active carriers (for FFT-OFDM and BF-OFDM). We can observe that none of the considered waveforms can achieve full spectral efficiency (i.e. =1) due to the use of a guard interval (CP). The latency of a WF is also another key parameter, especially when considering very low response systems such as in tactile Internet scenarios. In this deliverable, we use the End-to-End Physical layer latency criterion (E2E) defined as the time delay from which the FEC (Forward Error Correction) is capable to decode the bits corresponding to the NQAM transmitted symbols. In other words, it refers to the time between the availability of the bits at the output of the FEC at the transmitter side, and the beginning of the channel decoding at the receiver side. Thus, it is important to note that E2E does not take into account the processing time required by channel coding and decoding or equalization because it is implementation and design dependent. The potential delay introduced by the channel is also not considered. E2E comparison is provided by Table 4-1 and is also graphically presented in figure 4-3 according to NQAM and for a user which uses 3 RBs corresponding to 3 × N2 = 96 subcarriers for FFT-FBMC and BF-OFDM, and NA = 3 × 12 = 36 subcarriers for all other considered WFs. We can observe that the latencies of the considered waveforms are in the same order of magnitude. In order to better assess the performance of the other WFs, we present in figure 4-4 the E2E with respect to traditional CP-OFDM scheme. We can also observe that for small NQAM values, the latencies are in general (much) greater than traditional OFDM, and there exist only few WFs and few settings which provide better performance. When NQAM increases, the E2E latency of the considered waveforms tends to have similar performance, except for WOLA-OFDM which has slightly better performance than OFDM due to the use of a single CP for the transmission of several (K) blocks.

4.3

Asynchronous access

In this section, as mentioned previously, we discuss the performance of the considered waveforms in multi-user asynchronous access. In order to focus on the asynchronous interference impact on the performance of various waveform schemes, we propose to measure the normalized mean WONG5 Deliverable D2.2

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6

End−To−End PHY latency [ms]

5

4

3

2

CP−OFDM and Wavelet−OFDM WOLA−COQAM FFT−FBMC BF−OFDM

1

0

500

1000 1500 2000 Transmitted Complex Symbols

2500

3000

Figure 4-3: End-to-End Physical Layer latency (in ms) according to the number of transmitted NQAM symbols for a user using 3 RBs

End−To−End PHY latency ratio with respect to OFDM

1.8 Wavelet WOLA−COQAM FFT−FBMC BF−OFDM

1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8

500

1000 1500 2000 Transmitted Complex Symbols

2500

3000

Figure 4-4: End-to-End Physical layer latency ratio with respect to traditional CP-OFDM scheme for a user which used 3 RBs squared error (MSE)2 on decoding the useful symbols of the user of interest in ideal noiseless 2

The normalized MSE is computed by dividing the MSE by the average power of the signal constellation

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δ =15 kHz

−10

−20

−20

−20

−15

−10

−20

0

−25

10

−30 −35

−10 0 10

−10 0 10

delay error [µs]

−20

delay error [µs]

−30

−10 0 10

20

20

20

20

30

30

30

30

40 60 carrier index

80

20

δ =0 kHz

40 60 carrier index

80

20

δ =15 kHz

40 60 carrier index

80

20

δ =45 kHz

40 60 carrier index

80

−40

δ =75 kHz −10

−30

−30

−20

−20

−20

−20

−15

−10

−20

0

−25

10

−30 −35

−10 0 10

−10 0 10

delay error [µs]

−30 delay error [µs]

−30 delay error [µs]

−10 0 10

20

20

20

20

30

30

30

30

20

40 60 carrier index

80

20

δ =0 kHz

40 60 carrier index

80

20

δ =15 kHz

40 60 carrier index

80

20

δ =45 kHz

40 60 carrier index

80

−40

δ =75 kHz −10

−30

−30

−20

−20

−20

−20

−15

−10

−20

0

−25

10

−30 −35

−10 0 10

delay error [µs]

−30 delay error [µs]

−30

−10 0 10

delay error [µs]

delay error [µs]

δ =75 kHz

−30

20

delay error [µs]

δ =45 kHz

−30 delay error [µs]

delay error [µs]

δ =0 kHz −30

−10 0 10

20

20

20

20

30

30

30

30

10

20 carrier index

30

10

20 carrier index

30

10

20 carrier index

30

10

20 carrier index

30

−40

Figure 4-5: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: per-subcarrier NMSE against TO, δ = 0, 15, 45 and 75kHz (73.125kHz for FFT-FBMC and BF-OFDM) channel. Note that normalized MSE is adopted since it remains the same for all constellation schemes. Both per-subcarrier MSE and average MSE are assessed vs. timing offset or carrier frequency offset. Indeed, per-subcarrier MSE can provide a meaningful information about the distribution of asynchronous interference across useful subcarriers. Several values of guardbands are examined: δ = 0, 15, 45 and 75 kHz. Note that pseudo-3D-MSE (per-subcarrier MSE), we use a color map indicating the MSE levels: from dark blue color when the MSE is less than or equal to −40dB to dark red color when the MSE is greater than or equal to −10dB. 4.3.1

Timing offset

In order to distinguish the degradation induced by timing synchronization errors from the one caused by CFO, we consider in this section that there is no CFO (ε = 0 Hz) between the interfering signal and the useful one. The timing misalignment τ varies from −33.33µs to +33.33µs. The per-subcarrier MSEs of the proposed WFs are depicted in Figure 4-5. Regarding FFT-FBMC case, one can observe that the MSE is almost between −30 dB and −38 dB except two regions: WONG5 Deliverable D2.2

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• Inner subcarrier located at the edges of the useful RBs frequency bands, where the MSE is about −28 dB. Such a result can be explained by the fact the subcarrier gain at the RB edges is slightly lower than the gain of subcarriers located at the middle of the RB. In order to avoid this phenomenon and ensure a uniform gain for all RB subcarriers, a pre-distortion could be performed, as in BF-OFDM. • Edge subcarriers (in the vicinity of interfering subcarriers), where the MSE varies from more than −10 dB when δ = 0 Hz to −30 dB when δ = 75 kHz. As in filter-bank WFs the edge subcarriers are highly impacted by interference but this distortion is spread over more than one subcarrier because of the non-uniform gain over RB subcarriers (i.e. the gain at the edge is weaker than the average gain). Although the fact that BF-OFDM transmitter is similar to FFT-FBMC one, the performance are not the same. Indeed, BF-OFDM MSE is higher than FFT-FBMC one when the timing errors are outside the CP region. This is a direct consequence of the BF-OFDM receiver which is no more than the classical CP-OFDM receiver (i.e a simple FFT). In fact, the BF-OFDM rectangular receive filter brings an important amount of interference from the asynchronous user. However, the FFT-FBMC receiver is more efficient in asynchronous case thanks to the filtering performed by the analysis filter-bank. Note that, there is no asynchronous interference when the synchronization error does not exceed the CP (i.e. MSE about −65 dB corresponding to the intrinsic interference of the optimized BF-OFDM filter). In Wavelet-OFDM case, when δ = 0 the MSE is above −25 dB for all the subcarriers. This means that the effect of the adjacent user is the same for all the subcarriers. This can be explained by the redistribution of the frequency allocation for each symbol. Indeed, we are no more sure after wavelet transform which are the border subcarriers. In addition, when a timing offset occurs, one carrier from a decomposition level j impacts at the same time 2 carriers from the decomposition level j + 1. This makes the interference level higher than OFDM especially at delay error = 0s. When using a guard band, the performance of Wavelet-OFDM are better. The MSE level is between −33 dB and −28 dB. The average MSEs of FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM, obtained over all subcarriers, are plotted versus the TO for guard-bands δ = 0, 15, 45 and 75kHz, in Figure 4-6. Looking at the average MSEs of FFT-FBMC and BF-OFDM, the results confirm the remarks previously noted when analyzing the per-subcarrier MSEs. Also, the best performance of FFTFBMC is almost achieved when δ = 73.125kHz while larger guard-bands can offer better performance in the BF-OFDM case. Such a result can be explained by the fact that the receive filtering of FFT-FBMC significantly reduces the asynchronous interference while the rectangular receive filter of BF-OFDM brings an important amount of interference from the coexisting asynchronous user. It is worth noticing that BF-OFDM performs better than FFTFBMC in the CP-region since the prototype filter is designed to ensure the lowest degradation in negligible TO case. 4.3.2

Carrier Frequency Offset

In this section, we assume that both users are perfectly synchronized in time domain but there is an offset between their respective carrier frequencies. The objective here is to examine the impact of CFO-induced inter-user interference on the performances of the various considered WONG5 Deliverable D2.2

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δ =0kHz

-10

δ=11.25kHz

-10

FFT-FBMC BF-OFDM WOLA-COQAM, δ =15 kHz Wavelet-OFDM, δ=15kHz

-15 -20 -20 -25 -30 MSE [dB]

MSE [dB]

-30 -35

-40

-40 -50 -45 FFT-FBMC BF-OFDM WOLA-COQAM Wavelet-OFDM

-50 -55

-60

-60

-70 -30

-20

-10

0 delay error [µs]

10

20

30

-30

δ=45kHz

-10

-10

0 delay error [µs]

10

20

30

10

20

30

δ=73.125kHz

-10

FFT-FBMC BF-OFDM WOLA-COQAM Wavelet-OFDM

-20

-20

FFT-FBMC BF-OFDM WOLA-COQAM,δ=75kHz Wavelet-OFDM, δ=75kHz

-15 -20 -25

-30 MSE [dB]

MSE [dB]

-30 -40

-35 -40

-50 -45 -50 -60 -55 -70

-60 -30

-20

-10

0 delay error [µs]

10

20

30

-30

-20

-10

0 delay error [µs]

Figure 4-6: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: average MSE against TO, δ = 0, 15, 45 and 75kHz (73.125kHz for FFT-FBMC and BF-OFDM)

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δ =0 kHz

δ =15 kHz

−10

δ =45 kHz

−10

δ =75 kHz

−10

−10

−10

5

−5 0 5

CFO [x0.15KHz]

0

CFO [x0.15KHz]

CFO [x0.15KHz]

CFO [x0.15KHz]

−15 −5

−5 0 5

−5 −20 0

−25 −30

5 −35

10

10 20

40 60 carrier index

80

10 20

δ =0 kHz

40 60 carrier index

80

10 20

δ =15 kHz

40 60 carrier index

80

20

δ =45 kHz

40 60 carrier index

80

−40

δ =75 kHz

−10

−10

−10

−10

−5

−5

−5

−5

−10

5

0 5

CFO [x0.15KHz]

0

CFO [x0.15KHz]

CFO [x0.15KHz]

CFO [x0.15KHz]

−15

0 5

−20 0

−25 −30

5 −35

10

20

40 60 carrier index

10

80

20

δ =0 kHz

40 60 carrier index

10

80

20

δ =15 kHz

−10

40 60 carrier index

10

80

20

δ =45 kHz

−10

40 60 carrier index

80

−40

δ =75 kHz

−10

−10

−10

5

−5 0 5

CFO [x0.15KHz]

0

CFO [x0.15KHz]

CFO [x0.15KHz]

CFO [x0.15KHz]

−15 −5

−5 0 5

−5 −20 0

−25 −30

5 −35

10

10 10

20 carrier index

30

10 10

20 carrier index

30

10 10

20 carrier index

30

10

20 carrier index

30

−40

Figure 4-7: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: per-subcarrier NMSE against CFO, δ = 0, 15, 45 and 75kHz (73.125kHz for FFT-FBMC and BF-OFDM)

WFs. The CFO ε considered here varies from −1.5kHz to +1.5kHz. Several cases of guardbands are examined: δ = 0, 15, 45 and 75 kHz. As mentioned in Section 3, the CFO shifts both interfering spectrum subbands in the same direction. This is why one of the guard-bands is reduced to δ − εkHz and the other is increased to δ + εkHz. In Figure 4-7, we have the per-subcarrier MSE of FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM, respectively. As in timing offset, FFT-FBMC exhibits almost the same MSE. Indeed, the MSE at the edges of each RB is about −30 dB, whereas it is less than −35 dB in the other subcarriers. As we have previously explained, this phenomenon is due to the filter shape in frequency domain. It is also worth noticing that except in both subcarrier edges the MSE is almost invariant with respect to CFO. In BF-OFDM case, the MSE is below −30 dB in a larger region around the CP. Unlike the TO case where the MSE is very low only in the CP region. In Wavelet-OFDM case, although the waveform is orthogonal, the MSE is not zero when the CFO is equal to zero. Indeed, as the wavelet transform re-allocates the sub-carriers in time and frequency, with the scenario proposed for this section, the symbols can be on the same carrier at the same time creating a high level of interference regardless the CFO level. In other words, the coexistence WONG5 Deliverable D2.2

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δ=11.25kHz -10

-20

FFT-FBMC BF-OFDM WOLA-COQAM, δ =15 kHz Wavelet-OFDM, δ=15kHz

-25 -20 -30 -30 MSE [dB]

MSE [dB]

-35 -40 -45

-50

-50 -55

FFT-FBMC BF-OFDM WOLA-COQAM Wavelet-OFDM

-60 -65 -0.1

-40

-0.08

-0.06

-0.04

-60

-0.02 0 0.02 CFO [x15kHz]

0.04

0.06

0.08

-70 -0.1

0.1

-0.08

-0.06

-0.04

δ=45kHz

0.06

0.08

0.1

0.04

0.06

0.08

0.1

-10 FFT-FBMC BF-OFDM WOLA-COQAM Wavelet-OFDM

-20

FFT-FBMC BF-OFDM WOLA-COQAM, δ =75 kHz Wavelet-OFDM, δ=75kHz

-20

-30 MSE [dB]

-30 MSE [dB]

0.04

δ=73.125kHz

-10

-40

-40

-50

-50

-60

-60

-70 -0.1

-0.02 0 0.02 CFO [×15kHz]

-0.08

-0.06

-0.04

-0.02 0 0.02 CFO [×15kHz]

0.04

0.06

0.08

0.1

-70 -0.1

-0.08

-0.06

-0.04

-0.02 0 0.02 CFO [×15kHz]

Figure 4-8: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: average MSE against CFO, δ = 0, 15, 45 and 75kHz (73.125kHz for FFT-FBMC and BF-OFDM) of two users sharing the same band and using the Wavelet-OFDM results in a high level of interference even if the system is synchronous. The average MSEs of FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM, computed over all subcarriers, are plotted, in Figure 4-8, as function of CFO for guard-bands δ = 0, 15, 45 and 75kHz, respectively.

4.4

IAPR

All multicarrier schemes have in common the major problem of very high fluctuation of the instantaneous power of the signal to be transmitted. More specifically, the probability of having an instantaneous power 8 to 12 dB greater than the mean power is non negligible. These instantaneous power peaks produce signal excursions into the nonlinear region of operation of the power amplifier (PA) at the RF front-end, causing signal distortions and spectral regrowth. Thus, it is important to assess and compare the performance in terms of power fluctuation of the considered waveform. Therefore, it is interesting to analyze the CCDF of the instantaneous power (IAPR, Instantaneous to Average Power Ratio) given by [CBS06]: 







|s(n)|2 |s(n)|2    h i h i > P0  = Prob CCDF E |s(n)|2 E |s(n)|2

(4.1)

where n refers to the time index of the whole signal to be transmitted. WONG5 Deliverable D2.2

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The WFs IAPR CCDFs are presented in figure 4-9. We can observe that all proposed waveforms have almost similar IAPR performance, except Wavelet-OFDM which provides slightly better performance of about 0.5 dB for a probability of 10−4 . −1

10

−2

Prob(Pmax > Po)

10

−3

10

−4

10

CP−OFDM Wavelet WOLA−COQAM FFT−FBMC BF−OFDM

−5

10

4

5

6

7

8

9

10

11

Po [dB]

Figure 4-9: IAPR CCDF-based comparison between the considered WFs.

4.5

Complexity

This section aims at estimating the complexity of the transmitter and receiver schemes for the considered WFs. The complexity will be assessed by counting the number of real multiplications per unit of time to perform both the modulation and demodulation process (equalization and (de)coding stages will not be taken into account in this evaluation). It has been preferred to assess the number of multiplications per unit of time in order to compare as fairly as possible the schemes that do not share the same sampling frequency. To do so, a burst of S symbol vectors is considered. For the schemes that exhibit symbol overlapping, the complexity will be benchmarked when S tends to infinity. From now, it will be assumed that one complex multiplication can be carried out with three real multiplications [Kra99]. Fs will denote the sampling frequency and Ts the sampling period. Moreover, the Cooley-Tukey implementation will be considered for the Fast Fourier Transforms (FFT). CP-OFDM The complexity of the transmitter (resp. the receiver) is reduced to a N-points IFFT (resp. N-points IFFT), which leads to: COFDM,Tx/Rx = WONG5 Deliverable D2.2

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The number of multiplications per unit of time is then: COFDM,Tx/Rx S S(NFFT + NCP )Ts COFDM,Tx/Rx Fs = (NFFT + NCP )

COFDM,Tx/Rx =

(4.3)

FFT-FBMC As for UF-OFDM, FFT-FBMC processes the data at the RB level. For each active RB (B out of M ) there is the N-point IFFT and then there is the filter bank. The complexity of the receiver is the same. N N = 3B 1 + log2 2 2 M log2 (M ) + 2KM N + 3N 2 



CFFT−FBMC,Tx/Rx



(4.4)

The number of multiplications per unit of time is then: CFFT−FBMC,Tx/Rx S [KM + M2 (S(N + NCP ) − 1)]Ts S→∞ CFFT−FBMC,Tx/Rx Fs −−−→ M (N + NCP ) 2

CFFT−FBMC,Tx/Rx =

(4.5)

BF-OFDM When it comes to BF-OFDM, at the transmitter side, there is an additional stage with respect to the FFT-FBMC scheme: the predistortion stage. Moreover, the receiver is reduced to a MN -point FFT. 2 N N N + 3B 1 + log2 2 2 2 M log2 (M ) + 2KM N + 3N 2 





CBFOFDM,Tx = 3B

MN MN log2 ( ) 4 2 The number of multiplications per unit of time is then: CBFOFDM,Rx = 3

CBF−OFDM,Tx/Rx S [KM + M2 (S(N + NCP ) − 1)]Ts S→∞ CBF−OFDM,Tx/Rx −−−→ M Fs (N + NCP ) 2

(4.6) (4.7)

CBF−OFDM,Tx/Rx =

(4.8)

WOLA-COQAM For the WOLA-COQAM, the data is processed by block of length K. For each block, the NFFT -point IFFT (with 3 × NFFT log2 (NFFT ) real multiplications) and the filtering performed 2 WONG5 Deliverable D2.2

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by the PolyPhase-Network (2NFFT K real multiplications) run therefore K times. After than the Cyclic Prefix is appended (no extra multiplications) and the overall block is windowed (4WTx real multiplications) For the receiver, the incoming block is first windowed (4WRx real multiplications), the CP is then discarded (no arithmetic operations) and a KNFFT -point FFT captures the entire block. The block is then processed by the real prototype filter (2NFFT K real multiplications). Finally the block is divided into NFFT sub-blocks of size K which go trough K-point IFFT (3NFFT K log2 (2K) real multiplications in total). NFFT log2 (NFFT ) + 2NFFT K + 4WTx =K 3 2 



CWOLA−COQAM,Tx

NFFT K log2 (KNFFT ) 2 + 3NFFT K log2 (2K) + 2NFFT K

(4.9)

CWOLA−COQAM,Rx = 4WRx + 3

(4.10)

The number of multiplications per unit of time is then: 2CWOLA−COQAM,Tx/Rx S ((KNFFT + NCP )2S + WTx )Ts S→∞ CWOLA−COQAM,Tx/Rx −−−→ Fs (KNFFT + NCP ))

CWOLA−COQAM,Tx/Rx =

(4.11)

Wavelet-OFDM The wavelet transform is based on two filters: a low-pass filter and a high-pass filter of length K. The number of carriers is M = NF F T = 2J . The number of additions and multiplications is J X

j=J0 +1

2j K ≤

J X

2j K = 2M K

j=1

Therefore, the complexity of the wavelet transform is O(M K). The complexity of the FFT and the IFFT is O(M log2 (M )). The additional complexity caused by wavelet is O( log K(M ) ) which 2 is not considerable as K is bounded and M is large. In this deliverable, we consider Meyer wavelet where K = 47. Analysis According to the aforementioned closed-form expressions and the configurations given in Tables 3-2, 3-3 and 3-4, it is possible to numerically assess the complexity of the different transmission and reception schemes as given in Tab. 4-2. The proposed waveforms embeds filtering stages and are therefore more complex than the CP-OFDM. FFT-FBMC and BF-OFDM transmitter schemes are the most efficient among the four proposed thanks to their reduced number of PPN carriers (M instead of NFFT ). WOLACOQAM has an inherent higher complexity induced by its block processing and the transposition in the wavelet domain requires a lot of multiplications which accounts for the high complexity of the Wavelet-OFDM. The absence of a fast algorithm to compute the wavelet transform is the reason behind the high complexity level for Wavelet-OFDM. Regarding the receiver schemes, aforementioned observations still hold. BF-OFDM provides the most efficient receiver scheme as it is reduced to a simple FFT and does not embed any filtering stage. WONG5 Deliverable D2.2

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Table 4-2: Tx/Rx complexity normalized with respect to OFDM WFs

Tx

Rx

5RBs

25RBs

50RBs

CP-OFDM

1.00

1.00

1.00

1.00

FFT-FBMC

1.81

2.10

2.46

2.46

BF-OFDM

1.82

2.16

2.58

0.84

WOLA-COQAM

6.46

6.46

6.46

2.46

WAVELET-OFDM

6.71

6.71

6.71

6.71

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5. Multipath performance comparison In this section, we present the multipath performance of the waveforms in terms of uncoded bit error rate (BER). We first consider the impact of the channel delay spread, and then we present the performance in front of a standardized multipath channel. In this chapter, we consider that the transmitted signal occupied a useful bandwidth of 9 MHz corresponding to 50 resource blocks for the LTE configuration. We define the signal-to-noise ratio (SNR) as the ratio between the signal power and the noise power inside the allocated bandwidth, i.e. 9 MHz.

5.1

Impact of delay spread

In this subsection, we discuss the robustness of the studied waveforms against channel delay spread [ZMSR16b]. The considered channel impulse response (CIR) of the Lc-path fading channel is defined as

h(t) =

LX c −1

hl δ(t − ∆l )

(5.1)

l=0

where: • hl is the complex amplitude, which is assumed to be Gaussian i.i.d. random variable distributed. • ∆l is the propagation delay of the l-th path. The BER performance comparison according to ∆l is depicted in Figure 5-1 for the particular case of a two taps channel (Lc =2) which respectively have a mean power of 0 and -0.6 dB. Note that an ideal frequency domain ZF-single tap equalization is considered for all schemes. These results have been obtained by averaging 1000 channel realizations with an SNR of 27.6 dB. Indeed, the choice of a high SNR is done in order to highlight the channel impact on the waveform performance. These results are compared with the performance of CP-OFDM based LTE standard with a guard interval of 4.6875 µs. UF-OFDM has the worst BER performance because the guard interval (ZP) is completely used for resource band filtering at the transmitter and windowing at the receiver. The interblock interferences become greater as the delay spread increases. WOLA-OFDM and WOLA-COQAM have both little resistance to delay spread due to the fact that most of the CP is used for windowing at the transmitter and receiver sides. The PPN version of FBMC and FFT-FBMC have similar BER performance. The BER slowly decrease as the delay spread inscreases due to the one-tap equalizer which is no more efficient for large delay spread. The Frequency Spread (FS) version of FBMC has slightly better BER performance thanks to a better frequency granularity in the equalization. OFDM, f-OFDM and Wavelet-OFDM have a similar behavior which is an almost stable performance when the delay spread is below the CP length, and a large degradation when the delay spread is greater than the CP length due to the fact that these waveforms are highly sensitive to the orthogonality. Finally, BF-OFDM has the best resistance to delay spread thanks to a longer cyclic prefix (but with the same spectral efficiency) as well as a smaller inter-carrier-spacing. WONG5 Deliverable D2.2

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0

10

OFDM f−OFDM WOLA WOLA−COQAM FBMC (Rx PPN) FBMC (Rx FS) UF−OFDM Wavelet FFT−FBMC BF−OFDM (64) BF−OFDM (128)

−1

BER

10

−2

10

−3

10

−4

10

1

2

3 4 Delay spread [µs]

5

6

7

Figure 5-1: BER performance vs channel delay spread

5.2

Impact of realistic multipath channel

In this subsection, we discuss the robustness of the studied waveforms against the Hiperlan2 Bran channel E, as defined in [WON16a]. We consider two mobility values of 5 and 150 km/h corresponding to a quasi-static drone and to a full speed celerity. In order not to overload the presentation of the results, we present only the performance for the QPSK modulation but similar performance (taking into account an x and y-axis shifts) are obtained for greater constellation orders. As for the previous BER comparison, we consider for all waveforms an ideal frequency domain ZF-single tap equalization. Figures 5-2 and 5-3 present the comparison of the uncoded BER for 5 km/H. We can observe that all waveforms provide the same performance, except Wavelet-OFDM which has a slightly steeper slope corresponding to a better use of the frequency diversity provided by the multipath channel. Figures 5-4 and 5-5 present the comparison of the uncoded BER for 150 km/H. We can observe that all waveforms experience an error floor due to the time-varying channel implied by a greater mobility. The worst performance are those obtained by the WOLA-COQAM because the same outdated equalization coefficients are used for K consecutive blocks. FFT-FBMC and the 128 version of the BF-OFDM have almost the same BER performance. The large error floor is due to a larger symbol duration compared to OFDM. For BF-OFDM the duration of the symbol is 2.6 times greater than the duration of an OFDM symbol. If the prototype filter is shortened, as for instance for the 64 version of the BF-OFDM, then the error floor could be lowered to a threshold very close to the Wavelet-OFDM one. Finally, f-OFDM, WOLA-OFDM, UF-OFDM and FBMC (Both PPN and FS versions) have similar performance to the CP-OFDM case.

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QPSK, BRAN−Channel, 5km/H −1

10

−2

BER

10

−3

10

OFDM f−OFDM WOLA WOLA−COQAM Wavelet FFT−FBMC

−4

10

5

10

15 SNR[dB]

20

25

Figure 5-2: BER performance vs SNR for CP-OFDM, f-OFDM, WOLA-OFDM, WOLACOQAM, Wavelet-OFDM and FFT-FBMC, mobility is set to 5 km/H and a QPSK modulation is considered QPSK, BRAN−Channel, 5km/H −1

10

−2

BER

10

−3

10

OFDM BF−OFDM (64) BF−OFDM (128) FBMC−PPN FBMC−FS UF−OFDM

−4

10

5

10

15 SNR[dB]

20

25

Figure 5-3: BER performance vs SNR for CP-OFDM, BF-OFDM with 64 and 128 carriers, FBMC and UF-OFDM, mobility is set to 5 km/H and a QPSK modulation is considered

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QPSK, BRAN−Channel, 150km/H −1

10

−2

BER

10

−3

10

OFDM f−OFDM WOLA WOLA−COQAM Wavelet FFT−FBMC

−4

10

5

10

15 SNR[dB]

20

25

Figure 5-4: BER performance vs SNR for CP-OFDM, f-OFDM, WOLA-OFDM, WOLACOQAM, Wavelet-OFDM and FFT-FBMC, mobility is set to 150 km/H and a QPSK modulation is considered QPSK, BRAN−Channel, 150km/H −1

10

−2

BER

10

−3

10

OFDM BF−OFDM (64) BF−OFDM (128) FBMC−PPN FBMC−FS UF−OFDM

−4

10

5

10

15 SNR[dB]

20

25

Figure 5-5: BER performance vs SNR for CP-OFDM, BF-OFDM with 64 and 128 carriers, FBMC and UF-OFDM, mobility is set to 150 km/H and a QPSK modulation is considered

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6. Conclusion In this deliverable, four new waveforms have been introduced (FFT-FBMC, BF-OFDM, WOLACOQAM and Wavelet-OFDM) for the C-MTC context. In the framework of the same system model defined in D2.1 (power spectral density, spectral efficiency/latency, asynchronous access, instantaneous average power ratio, and complexity comparison), these new proposals have been evaluated and analyzed. It appears that the proposed waveforms drastically improve the PSD with respect to OFDM, except the Wavelet-OFDM which is not capable to create spectrum notch due to the Meyer wavelet. The spectral efficiencies of the proposed waveforms are excellent and in the same order of magnitude of the CP-OFDM. For short packet transmission, the wavelet-OFDM has the advantage of being capable to have similar (excellent) latency than CP-OFDM, whereas the 3 others waveforms slightly increase the latency in most of the case. For large packet transmission, all waveforms have similar latencies, except the WOLA-COQAM which has slightly better performance. Regarding the asynchronous performance, the proposed waveforms appear to be particularly adapted to time/frequency asynchronicities, which is particularly important for C-MTC communications. Since all the proposed waveforms are multicarrier schemes, they all have the same PAPR issue. Of course, PAPR reduction algorithms could be used in order to solve this problem; this problematic is currently under investigation in the work package 3. A complexity assessment of the proposed waveforms has been conducted for different number of activeRBs, and it appears that there is no large complexity explosion with respect to CPOFDM. Nevertheless, we can note that FFT-FBMC and BF-OFDM schemes are about 3 times less complex than WOLA-COQAM and Wavelet-OFDM. There is also a benefit in the use of BF-OFDM since the receiver is less complex than an equivalent CP-OFDM receiver. Finally, we have compared the four proposed new waveforms with the subset waveforms kept in D2.1 (CP-OFDM, f-OFDM, WOLA-OFDM, FBMC-OQAM, UF-OFDM) for multipath channels. First, we have evaluated the performance according to the channel delay spread, and then in front of realistic multipath channel taking into account the mobility. It appears that UF-OFDM is very sensitive to delay spread, whereas all other waveforms are much more robust. BF-OFDM has a greater capability when the delay spreads exceed the predefined guard interval. For the low mobility case (5 km/H), all waveforms have the same performance. At 150 km/H, WOLA-COQAM, FFT-FBMC and BF-OFDM experience an error floor ten times greater than the one obtained with the other schemes. BF-OFDM and FFT-FBMC error floor can be managed and lowered if the number of transmitted carriers decreases, or equivalently if the intercarrier spacing is increased.

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7. References [BT07]

Norman C Beaulieu and Peng Tan. On the effects of receiver windowing on OFDM performance in the presence of carrier frequency offset. IEEE Transactions on Wireless Communications, 6(1):202–209, 2007.

[CBS06]

C. Ciochina, F. Buda, and H. Sari. An analysis of ofdm peak power reduction techniques for wimax systems. In 2006 IEEE International Conference on Communications, volume 10, pages 4676–4681, June 2006.

[DGD+ 17] David Demmer, Robin Gerzaguet, Jean-Baptiste Doré, Didier Le Ruyet, and Dimitri Kténas. Block-Filtered OFDM: an exhaustive waveform to overcome the stakes of future wireless technologies. In submitted to IEEE ICC (ICC), Paris, France, May 2017. [DRT16]

J-B Dore, Daniel Rovira, and Sylvain Traverso. Wong5 project, deliverable 1.1: Scenario description of critical - machine type communications. ANR, Tech. Rep, 2016.

[GDDK17] Robin Gerzaguet, David Demmer, Jean-Baptiste Doré, and Dimitri Kténas. BlockFiltered OFDM: a new promising waveform for multi-service scenarios. In submitted to IEEE ICC 2017 (ICC), Paris, France, May 2017. [GMM+ 15] I. Gaspar, M. Matthe, N. Michailow, L. Leonel Mendes, D. Zhang, and G. Fettweis. Frequency-shift Offset-QAM for GFDM. IEEE Communications Letters, 19(8):1454–1457, Aug 2015. [Kra99]

Steven G Krantz. Handbook of Complex Variables. Birkhäuser Basel, 1999.

[MZSR17] Y. Medjahdi, R. Zayani, H. Shaïek, and D. Roviras. Wola processing: A useful tool for windowed waveforms in 5g with relaxed synchronicity. In 2017 IEEE International Conference on Communications Workshops (ICC Workshops), pages 393–398, May 2017. [Qua]

Qualcomm, Incorporated. R1-162199 - Waveform candidates.

[WON16a] WONG5. Wong5 project, deliverable 1.2: System specifications and kpi’s for critical machine type communications scenario. ANR, Tech. Rep, 2016. [WON16b] WONG5. Wong5 project, deliverable 2.1: Critical and comparative study of waveforms in c-mtc context. ANR, Tech. Rep, 2016. [ZLR10]

R. Zakaria and D. Le Ruyet. A novel FBMC scheme for Spatial Multiplexing with Maximum Likelihood detection. In Wireless Communication Systems (ISWCS), 2010 7th International Symposium on, pages 461 –465, sept. 2010.

[ZMSR16a] R. Zayani, Y. Medjahdi, H. Shaiek, and D. Roviras. WOLA-OFDM: a potential candidate for asynchronous 5G. In IEEE Global Communications Conference (GLOBECOM), 2016. [ZMSR16b] R. Zayani, Y. Medjahdi, H. Shaiek, and D. Roviras. Wola-ofdm: A potential candidate for asynchronous 5g. In 2016 IEEE Globecom Workshops (GC Wkshps), pages 1–5, Dec 2016. WONG5 Deliverable D2.2

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[ZR12]

R. Zakaria and D. Le Ruyet. A Novel Filter-Bank Multicarrier Scheme to Mitigate the Intrinsic Interference: Application to MIMO Systems. IEEE Transactions on Wireless Communications, 11(3):1112–1123, March 2012.

[ZR17]

R. Zakaria and D. Le Ruyet. Analysis of the FFT-FBMC Equalization in Selective Channels. IEEE Signal Processing Letters, 24(6):897–901, June 2017.

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Glossary and Definitions Acronym

Meaning

BF-OFDM

Block-Filtered OFDM

C-MTC

Critical-Machine Type Communications

CCDF

Complementary Cumulative Distribution Function

COQAM

Circular Offset QAM

CFO

Carrier Frequency Offset

CP

Cyclic Prefix

FBMC

Filter Bank Multi-Carrier

FFT

Fast Fourier Transform

FFT-FBMC

Fast Fourier Transform - Filter Bank Multi-Carrier

f-OFDM

filtered-OFDM

FS

Frequency Spreading

IAPR

Instantaneous-to-Average Power Ratio

LTE

Long Term Evolution

MIMO

Multi-Input Multi-Output

MSE

Mean Square Error

OFDM

Orthogonal Frequency Division Multiplexing

OLA

Overlap and Add

OLS

Overlap and Save

PAPR

Peak-to-Average Power Ratio

PPN

Poly-Phase Network

PSD

Power Spectral Density

RB

Resource Block

RRC

Root Raised-Cosine

Rx-W-OFDM

CP-OFDM with receive windowing

Tx-W-OFDM

CP-OFDM with transmit windowing

UFMC (i.e. UF-OFDM)

Universal-Filtered Multi-Carrier (i.e. Universal-Filtered OFDM)

UOI

User Of Interest

WF

WaveForm

WOLA

Weighted Overlap and Add

WOLA-COQAM

Weighted Overlap and Add - Circular Offset QAM

ZP

Zero Padding

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