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Waveforms MOdels for Machine Type CommuNicationinteGrating 5G Networks

(WONG5)

Document Number D2.2

New waveforms for C-MTC context

Contractual date of delivery: 12/06/2017Project Number and Acronym: ANR-15-CE25-0005, WONG5Editor: Sylvain Traverso (TCS)Authors: Sylvain Traverso (TCS), Yahia Medjahdi

(CNAM), Jean-Baptiste Dore (CEA), DavidDemmer (CEA), Mouna Ben Mabrouk (CS),Rostom Zakaria (CNAM)

Participants: CNAM, TCS, CEA, CSWorkpackage: WP2Security: Public(PU)Nature: ReportVersion: 0.5Total Number of Pages: 42

Abstract:This report is the second one of task WP2 titled ’Waveforms for C-MTC’. The aim of thisdeliverable is to propose new waveforms and to compare with the waveforms kept in D2.1which are adapted to the C-MTC context. The performance assessment and the WF analysisare 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, Filtered-OFDM, FBMC-OQAM, WCP-COQAM, FFT-OFDM, BF-OFDM, Wavelet, WOLA-COQAM,PSD, spectral efficiency, latency, timing offset, CFO, PAPR, complexity, uncoded BER, mul-tipath

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Document Revision HistoryVersion Date Author Summary of main changes0.1 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 firstreview.

0.4 19.07.2017 TCS Minor corrections and update. Ready forlast review.

0.5 21.07.2017 TCS Final version.

WONG5 Deliverable D2.2 2/42

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Executive SummaryThe goals of the WONG5 project are to study and propose the most appropriate post-OFDMwaveforms (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, WOLA-COQAM and Wavelet-OFDM) adapted for the C-MTC context. These waveforms are analyzedin part 4 with the same system model defined in D2.1 (and recalled in part 3) in terms ofpower spectral density, spectral efficiency/latency, asynchronous access, instantaneous averagepower ratio, and complexity. Part 4 is devoted to the multipath performance comparison of thefour 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 51.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Proposal of new waveforms 72.1 FFT-FBMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 BF-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 WOLA-COQAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Wavelet-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.1 Haar-based wavelet-OFDM . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Meyer-based wavelet-OFDM . . . . . . . . . . . . . . . . . . . . . . . 15

3 System Model 173.1 Coexistence scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Waveforms comparison 224.1 PSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Spectral efficiency/Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Asynchronous access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3.1 Timing offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.2 Carrier Frequency Offset . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.4 IAPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Multipath performance comparison 355.1 Impact of delay spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 Impact of realistic multipath channel . . . . . . . . . . . . . . . . . . . . . . 36

6 Conclusion 39

7 References 40


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1. Introduction1.1 Context

The objective the WONG5 project is to study and propose the most appropriate post-OFDMwaveforms (WF) for critical machine type communications (C-MTC). Requirements for C-MTCsystems 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 resistanceto asynchronous users (time and frequency). The aim of deliverable D2.2 is to propose newWF, to analyze them, and to compare them with the restricted set candidates WFs chosen inD2.1 under the requirements of C-MTC systems. In task 3, energy efficiency improvement willbe studied together with their adaptation to analog RF components. During task 4, adaptationof 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 inmind 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 useof already developed PAPR technique

• lower the interference generated by asynchronous users

These WFs are FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM. They arethen 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 modeltakes into account the fact that asynchronous users will be present in a C-MTC system. Theresource blocks (RB) assigned to the user of interest (UOI) are surrounded by RB assigned toother 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,


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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, Wavelet-OFDM) 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 uncodedbit error rate for multipath channels.


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2. Proposal of new waveforms2.1 FFT-FBMC

In order to overcome the FBMC intrinsic interference issue, FFT-FBMC scheme, together witha special data transmission strategy has been proposed in [ZR12, ZLR10]. This scheme pro-ceeds by precoding the data in a subcarrier-wise manner using an IFFT. Thus, the interferencecoming from the same subcarrier is removed by a simple equalization thanks to the subcarrier-wise IFFT/FFT precoding/decoding and cyclic prefix (CP) insertion. Whereas the interferencecoming from the adjacent subcarriers can be avoided by a special data transmission strategyand a good frequency-localized prototype filter.

In FFT-FBMC proposal, blocks of N/2 data complex symbols in each subcarrier k gothrough a N -IFFT operation. The N/2 data symbols are alternately fed to the first and lastN/2 bins of the N -IFFT. When the subcarrier index k is odd (resp. even), the symbols arefed to the first (resp. last) N/2 bins. After that, the N -IFFT outputs are extended with acyclic prefix (CP) of size L, and fed to the FBMC modulator of M carriers in a given subcarrierk. Figure 2-1 depicts the scheme of the FFT-FBMC proposed in [ZLR10]. Let us denote bydk,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 theFBMC modulator can be written as:

ak[n] = ejπn(k+1)√N

N2 −1∑l=0

dk,p[l]ej2πnlN (2.1)

where p is the block index given by p =⌈

nN+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 thissection.

At the output of the FBMC demodulator, the serial symbols zq[n] in each subcarrier q arereshaped into blocks of size N + L to only keep N symbols in each block. This operation isreferred to as "S/P + CP removal" in Figure 2-2. After that, N symbols of each block p′ arefed to a N -FFT whose only N/2 output symbols are kept for detection. Again, the first N/2output symbols are kept when the subcarrier index q is odd, and the last N/2 symbols are keptwhen q is even. Figure 2-2 depicts the overall scheme of FFT-FBMC receiver. Therefore, the

S/P

000

000

000

N IFFT

N IFFT

N IFFT

P/S

P/S

P/S

CP insertion

CP insertion

CP insertion

0

1

M-1

FBMCmodulator

... ... ...

Figure 2-1: FFT-FBMC transmitter scheme


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Equalization

N FFT

N FFT

N FFT

S/P + CP removal

S/P + CP removal

S/P + CP removal

0

1

M-1

FBMCdem

odulator

... ... ...

Figure 2-2: FFT-FBMC receiver scheme

FFT-FBMC demodulated symbols (just before Equalization block) can be expressed as:

xq,p′ [l′] = 1√N

∑n∈Bp′

e−jπn(q+1)zq[n]e−j 2πnl′N

for l′ ∈{

0, ..., N2 − 1}

(2.2)

where Bp′ ={

(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/2kept symbols for detection in each subcarrier q.

It is shown in [ZR17] that single-tap equalization can be performed. The equivalent channelcoefficients are the MN/2 channel frequency response coefficients weighted by the periodicsquared magnitude of the prototype filter frequency response. Indeed, the FFT-FBMC demod-ulated symbols is expressed as [ZR17]

xq,p′ [l′] = H̃q[l′]dq,p′ [l′] + w̃q,p′ [l′] (2.3)

where w̃q,p′ [l′] is the noise term, and H̃q[l′] is the equivalent channel coefficient given by [ZR17]

H̃q[l′] = H[l′ + q

N

2

]× F [l′] for l′ ∈

{−N4 , ...,

N

4 − 1}

(2.4)

with H[µ] = ∑τ h[τ ]e−j 4π

MNµτ denotes the discrete frequency response of the channel h[τ ] at

tones 2µMN

, and where F [l′] is the discrete Fourier transform (DFT) of the downsampled byM/2 of the prototype filter autocorrelation.

Therefore, one can observe that according to (2.3) the complex orthogonality is restored inFFT-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 qualitativemanner the spectrum of two active adjacent subcarriers in FBMC and FFT-FBMC. The first plotshows 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 Nsmaller subbands where only the N/2 middle ones are active. This corresponds to the N/2nonzero symbols at the input of the N -IFFT in each subcarrier. That is, the N/2 zeros insertedin each N -IFFT serve to isolate the adjacent subbands. It should be noted that normally, inFigure 2-1, the N/2 zeros should be in the middle of each N -IFFT. However, since the "FBMCmodulator" introduces a phase rotation of Φk[n] = ej

π2 (k+n)−jπkn [ZR12], the zero positions

are changed accordingly.


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−3 −2 −1 0 1 2 3 4Subbands

Spe

ctru

m

−3 −2 −1 0 1 2 3 4Subbands

Spe

ctru

m

InterferenceSubband 1Subband 2

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

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


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S/P

Pre-distortion

N/2 subcarriers

Pre-distortion

N/2 subcarriers

Pre-distortion

N/2 subcarriers

N IFFTOFDM

00

N IFFTOFDM

0

0

N IFFTOFDM

00

P/S

P/S

P/S

CP Insertion

CP Insertion

CP Insertion

M IFFT+ PPN

0

1

M-1

•••

•••

•••

OFDM precoding 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 wasfirst proposed in [ZR12] and is detailed in section 2.1. It aims at highly attenuating the filter-bank inherent interferences but leads to a complex receiver structure composed of a synthesisfilter bank concatenated with CP-OFDM demodulators. BF-OFDM can be seen as an improvedversion of FFT-FBMC. The key idea is to prepend a pre-distortion stage to the transmitter chainin 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. Thetransmitter is thus composed of a precoding stage followed by a filter bank. Regarding theprecoding, the pre-distortion stage compensates the distortion induced by filter bank (in bothamplitude and phase) in order to flatten the received signal spectrum inside the carrier bandwidthat the receiver side. Then, the framing maps the N/2 active subcarriers for each carrier. Thesubcarrier allocation depends on the carrier index (its parity) and ensures the perfect complexorthogonality 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 inlegacy CP-OFDM. The filtering is operated by means of a M-point IFFTs and a PolyPhase-Network (PPN). As the symbols are spread in time because of the PPN (with an overlappingfactor equal to K), an overlapping stage is considered at the end of the transmission chain inorder to improve the Spectral Efficiency (SE). However the overlapping generates Inter-SymbolInterferences (ISI) as neighbour symbols in time are captured with the useful one. To come upwith it, the CP length must be greater or equal than 2K − 1 [DGD+17]. This condition onthe CP length leads to a significant loss of SE therefore in practice shorter CP are used at theexpense of a Signal-to-Interference Ratio (SIR) penalty. The common choice is to set the CPlength so that the SE is equivalent to the legacy CP-OFDM.

The receiver is simply composed of a MN2 -point FFT and is therefore highly similar to the

receiver used in conventional OFDM. No filtering stage are required thanks to the predistortionstage that is added at the transmitter side.

BF-OFDM is said to be complex-orthogonal but rigorously it is not. Indeed even if aperfect orthogonality is satisfied at the carrier level by the framing, inter-carrier interferencesare generated by the filter bank. However, the rejection of those interferences are controlled byboth the filter shape and the CP and provides SIR of about 60 dB. Such a SIR level does notdisturb the transmission over the other carriers and that is why the modulation scheme is said


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CP removalS/P

MN2 - pointFFT

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 theSIR. The results of the optimizations for the Gaussian and Frequency-Sampling defined filtersare given in Tab 2-1.

Table 2-1: SIR for various filters.

H0 H1 H2 H3 SIR [dB]

K = 4 PHYDYAS NCP = 4 1 0.972√

2/2 0.235 47.42

K = 2 PHYDYAS NCP = 2 1√

2/2 x x 26.39

K = 4 Optimized NCP = 4 1 0.792 0.375 0.082 70.44

K = 2 Optimized NCP = 2 1 0.485 x x 39.39

Gaussian NCP = 4 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) toobtain WOLA-COQAM [MZSR17]. WOLA was initially introduced in [Qua] by QualcommIncorporated and has been studied in [ZMSR16a] with OFDM in asynchronous 5G scenario.

In the WOLA transmitter process, a time domain windowing operation is performed produc-ing thus soft edges at the beginning and the end of original transmitted block. These soft edgesare added to the cyclic extension of the COQAM symbol of length Ns = K ×N . Indeed, thesmooth transition between the last sample of a given symbol and the first sample of the nextsymbol is provided with point-to-point multiplication of the windowing function and the symbolwith cyclic prefix and cyclic suffix (see Figure 2-7). The samples corresponding to CP (of sizeCP ) from the last part of a given symbol are copied and appended to its beginning. Besides,


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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 WTx 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 toNs + CP +WTx.

After the cyclic extensions insertion, a window of length L = Ns + CP + WTx samples isapplied. In fact, many windowing functions have been studied and compared [BT07] in terms ofenhancing side lobe suppression. Straightforward solution is to define edge of the time domainwindow as a root raised-cosine (RRC) pulse. In this report, we consider the Meyer-RRC pulsecombining 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 confinementof the transmitted signal, the WOLA processing is also applied at the receiver side in orderto enhance asynchronous inter-user interference suppression, as illustrated in Figure 2-8. Notethat the applied receive window is independent of the transmit one and its length is equal toNs + 2WRx. This windowing is followed by Overlap and Add processing which minimizes theeffects of windowing on the useful data. As shown in Figure 2-8, it is worth emphasizing thatthe 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 wavecomponents called wavelets. The Wavelet-OFDM transmitted signal can be defined as:

X(t) =∑n

J−1∑j=J0

2j−1∑k=0

wj,kψj,k(t− nT )

+∑n

2J0−1∑q=0

aJ0,qφJ0,q(t− nT ).

• 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/2ψ(2jt−kT ): the wavelet orthonormal family, ψ is the mother wavelet function;

• φJ0,q = 2J02 φ(2J0t− 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) =

1√T

if 0 ≤ t ≤ T2 ,

− 1√T, if T2 ≤ t ≤ T,

0, else.(2.5)


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

and φhaar(t) =

1√T

if 0 ≤ t ≤ T,

0, else.(2.6)

Figure 2-9: Haar wavelet function for different scales.

Fig. 2-9 describes Haar wavelet functions ψhaarj,k for J0 = 0 and M = 8. As we can notice,

the temporal support of the contracted versions of the mother wavelet function ψhaar are smallerthan 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:

ΨDmey(ω) =

0, if |ω| ≤ 2π

3 ,

2−1/2F h(ω/2), if 2π3 ≤ |ω| ≤

4π3 ,

2−1/2exp(−iω/2)F h(ω/4), if 4π3 ≤ |ω| ≤

8π3 ,

0, if |ω| > 8π3

(2.7)

where F h(ω) = exp(−iω)F b∗(ω + π)

and F b(ω) =

√

2 if |ω| ≤ π3 ,

0, else.

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

and ΦDmey(ω) =

2−1/2F b(ω/2) if |ω| ≤ 4π3 ,

0, else.(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 ModelIn this section, we present the system model which is similar to the one already presentedin deliverable D2.1 [WON16b]. We also present the waveform parameters considered for thecomparisons presented in the following chapters.

3.1 Coexistence scenario

Figure 3-1: Coexistence scenario: two asynchronous users with τ [s] timing offset, ε [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 bandas depicted in Figure 3-1. The blue colored area and the red colored one correspond to thetime/frequency resources allocated to the user of interest and the other one, respectively. Theuseful signal occupies a frequency band of 540 kHz equivalent to 3 LTE resource blocks (LTE-RB bandwidth = 180 kHz) while 1.62 MHz (i.e. 9 LTE-RB) are allocated to the other useron each side of the useful frequency band. A guard-band of δ kHz , illustrated by a graycolored area, is separating the frequency bands of both users. Several cases are considered forguard-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 frequencydomains (i.e. neither timing offset nor frequency offset are considered), and is situated atequal distance from both transmitters1. However, as illustrated in Figure 3-1, a time/frequencysynchronization 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 timingoffset 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

1Note that in this work, we assume the same transmit power per subcarrier for both useful and interferingusers


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Table 3-1: General parameters

General

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 CFOinduces a shift of both red-colored areas of the interfering signal spectrum by ε kHz where theresulting guard bands become δ− ε kHz on one side and δ + ε kHz on the other side. In orderto highlight the impact of this interference, we consider free-distortion channels (perfect andnoiseless channels) between both transmitters on one side and the victim receiver on the otherside.

3.2 Parameters

In this section, we provide the general parameters of the scenario previously described (seeTable 3-1) as well as specific parameters related to the different waveforms considered in thisdocument:

• 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


CP length (NCP) 72

Windowing Raised cosine

WTx,WRx (20, 32)



UF-OFDM


Filter Dolph-Chebyshev with 40 dB stopband attenuation

Filter length 73 (LFIR =ZP+1)

Zero padding length (NZP) 72

Receive windowing Raised cosine



Wavelet-OFDM


Wavelet Type Meyer




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Table 3-3: Waveforms with complex orthogonality (2/2)

f-OFDM


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



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




WOLA-COQAM

CP 72

Transmit windowing Meyer-Raised cosine

WTx,WRx (20, 32)

Prototype Filter PHYDYAS

Overlapping factor (K) 4

FFT size 1024


Sampling Frequency 15.36 MHz


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4. Waveforms comparisonIn this chapter, we analyse the performance of the 4 proposed WFs in terms of PSD, spec-tral efficiency/latency, asynchronous access, IAPR and complexity. CP-OFDM is kept as acomparison basis.

4.1 PSD

It is well established that traditional CP-OFDM has poor frequency domain localization. Forinstance, LTE system requires the use of 10% of the system bandwidth as guard bands. Theselarge guard bands located at both edges of the spectrum are necessary in order to reach enoughattenuation to meet LTE spectrum mask requirement. It is expected that future 5G systemsuse more efficiently the allocated bandwidth and large guard bands can be seen as a waste ofspectral efficiency. Thus, good or excellent spectral containment will be a key parameter forfuture 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 proposedwaveforms. We choose to plot only the contribution of the interference users so that we canobserve at the same time the level of out-of band emission and the level of emission withina spectral hole. As expected, the worst PSD performance is given by the traditional CP-OFDM waveform. Wavelet-OFDM provides only very slight far-end PSD improvement withrespect to OFDM. A major drawback of Wavelet-OFDM is its incapacity of creating a notchin-between bands due to the Meyer wavelet. WOLA-COQAM improves by about 25 dB thePSD performance thanks to the WOLA processing at the transmitter side which smoothes thetransitions between successive blocks. The far-end PSD is dominated by the FFT-FBMC andBF-OFDM waveforms which combine OFDM precoding with filterbank.

0 5 10 15−140

−120

−100

−80

−60

−40

−20

0

Frequency [MHz]

PS

D [d

B]

CP−OFDMWaveletWOLA−COQAMFFT−FBMCBF−OFDM

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 Date: 21/7/2017

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

−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 16−60

−50

−40

−30

−20

−10

0

Subcarrier Index

PS

D [d

B]


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 sinceit gives a clear idea of achievable data rates for a given bandwidth. In Table 4-1, we present theSE according to the number of transmitted parallel vector symbols S, and also its asymptoticversion called Asymptotic Spectral Efficiency (ASE) where S tends toward infinity. Note thatwe do not include the impact of the constellation dimension since it is supposed to be identicalfor all WFs. The required number of parallel vectors is different for each WF and depends onthe number of complex QAM symbols NQAM to be transmitted, but also on the way a blocksymbol is built. S is given by:

S =

dNQAMNAe for OFDM

dNQAMNAe for Wavelet-OFDM

dNQAMK×NA

e for WOLA-COQAM

d NQAMMA×N2

e for FFT-FBMC and BF-OFDM

1LTE subcarrier spacing is 15 kHz


WONG5 Date: 21/7/2017

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 NFFTNFFT+NCP

NFFTNFFT+NCP S × NFFT+NCP

Fs

Wavelet-OFDM NFFTNFFT+NCP

NFFTNFFT+NCP S × NFFT+NCP

Fs

FFT-FBMC S×N2K+ 1

2 [S×(N+NCP )−1]N

N+NCPM×N2 ×S+M×NCP2 ×(S−1)+[(NCP−3)×M4 +K×M2 ]

Fs

BF-OFDM S×N2K+ 1

2 [S×(N+NCP )−1]N

N+NCP

M2

[S×N+NCP (S−1)+NCP−3

2 +K]

Fs

WOLA-COQAM S×K×NFFTS×(K×NFFT+NCP )+WTx

K×NFFTK×NFFT+NCP

S×(K×NFFT+NCP )+WTxFs

where d.e refers to the ceiling operation, and NA and MA are respectively the number ofused subcarriers and the number of active carriers (for FFT-OFDM and BF-OFDM). We canobserve that none of the considered waveforms can achieve full spectral efficiency (i.e. =1) dueto the use of a guard interval (CP).

The latency of a WF is also another key parameter, especially when considering very lowresponse systems such as in tactile Internet scenarios. In this deliverable, we use the End-to-EndPhysical layer latency criterion (E2E) defined as the time delay from which the FEC (ForwardError 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 FECat the transmitter side, and the beginning of the channel decoding at the receiver side. Thus, itis important to note that E2E does not take into account the processing time required by channelcoding and decoding or equalization because it is implementation and design dependent. Thepotential delay introduced by the channel is also not considered. E2E comparison is providedby Table 4-1 and is also graphically presented in figure 4-3 according to NQAM and for a userwhich uses 3 RBs corresponding to 3 × N

2 = 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 ofmagnitude. In order to better assess the performance of the other WFs, we present in figure4-4 the E2E with respect to traditional CP-OFDM scheme. We can also observe that for smallNQAM values, the latencies are in general (much) greater than traditional OFDM, and thereexist 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 forWOLA-OFDM which has slightly better performance than OFDM due to the use of a singleCP for the transmission of several (K) blocks.

4.3 Asynchronous access

In this section, as mentioned previously, we discuss the performance of the considered waveformsin multi-user asynchronous access. In order to focus on the asynchronous interference impacton the performance of various waveform schemes, we propose to measure the normalized mean


WONG5 Date: 21/7/2017

500 1000 1500 2000 2500 30000

1

2

3

4

5

6

Transmitted Complex Symbols

End

−T

o−E

nd P

HY

late

ncy

[ms]

CP−OFDM and Wavelet−OFDMWOLA−COQAMFFT−FBMCBF−OFDM

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

500 1000 1500 2000 2500 30000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Transmitted Complex Symbols

End

−T

o−E

nd P

HY

late

ncy

ratio

with

res

pect

to O

FD

M

WaveletWOLA−COQAMFFT−FBMCBF−OFDM

Figure 4-4: End-to-End Physical layer latency ratio with respect to traditional CP-OFDMscheme for a user which used 3 RBs

squared error (MSE)2 on decoding the useful symbols of the user of interest in ideal noiseless2The normalized MSE is computed by dividing the MSE by the average power of the signal constellation


WONG5 Date: 21/7/2017

carrier index

dela

y er

ror

[µs]

δ =0 kHz

20 40 60 80

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =15 kHz

20 40 60 80

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =45 kHz

20 40 60 80

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =75 kHz

20 40 60 80

−30

−20

−10

0

10

20

30−40

−35

−30

−25

−20

−15

−10

carrier index

dela

y er

ror

[µs]

δ =0 kHz

20 40 60 80

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =15 kHz

20 40 60 80

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =45 kHz

20 40 60 80

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =75 kHz

20 40 60 80

−30

−20

−10

0

10

20

30−40

−35

−30

−25

−20

−15

−10

carrier index

dela

y er

ror

[µs]

δ =0 kHz

10 20 30

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =15 kHz

10 20 30

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =45 kHz

10 20 30

−30

−20

−10

0

10

20

30

carrier index

dela

y er

ror

[µs]

δ =75 kHz

10 20 30

−30

−20

−10

0

10

20

30−40

−35

−30

−25

−20

−15

−10

Figure 4-5: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: per-subcarrierNMSE 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 constellationschemes. Both per-subcarrier MSE and average MSE are assessed vs. timing offset or carrierfrequency offset. Indeed, per-subcarrier MSE can provide a meaningful information about thedistribution of asynchronous interference across useful subcarriers. Several values of guard-bands are examined: δ = 0, 15, 45 and 75 kHz. Note that pseudo-3D-MSE (per-subcarrierMSE), we use a color map indicating the MSE levels: from dark blue color when the MSE is lessthan 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 onecaused by CFO, we consider in this section that there is no CFO (ε = 0 Hz) between theinterfering 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 Date: 21/7/2017

• Inner subcarrier located at the edges of the useful RBs frequency bands, where the MSEis about −28 dB. Such a result can be explained by the fact the subcarrier gain at theRB 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, apre-distortion could be performed, as in BF-OFDM.

• Edge subcarriers (in the vicinity of interfering subcarriers), where the MSE varies frommore than −10 dB when δ = 0 Hz to −30 dB when δ = 75 kHz. As in filter-bank WFsthe edge subcarriers are highly impacted by interference but this distortion is spread overmore than one subcarrier because of the non-uniform gain over RB subcarriers (i.e. thegain at the edge is weaker than the average gain).

Although the fact that BF-OFDM transmitter is similar to FFT-FBMC one, the performanceare not the same. Indeed, BF-OFDM MSE is higher than FFT-FBMC one when the timingerrors are outside the CP region. This is a direct consequence of the BF-OFDM receiver whichis no more than the classical CP-OFDM receiver (i.e a simple FFT). In fact, the BF-OFDMrectangular receive filter brings an important amount of interference from the asynchronoususer. However, the FFT-FBMC receiver is more efficient in asynchronous case thanks to thefiltering performed by the analysis filter-bank. Note that, there is no asynchronous interferencewhen the synchronization error does not exceed the CP (i.e. MSE about −65 dB correspondingto the intrinsic interference of the optimized BF-OFDM filter). In Wavelet-OFDM case, whenδ = 0 the MSE is above −25 dB for all the subcarriers. This means that the effect of theadjacent user is the same for all the subcarriers. This can be explained by the redistribution ofthe frequency allocation for each symbol. Indeed, we are no more sure after wavelet transformwhich are the border subcarriers. In addition, when a timing offset occurs, one carrier from adecomposition 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. Whenusing 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, ob-tained 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 remarkspreviously noted when analyzing the per-subcarrier MSEs. Also, the best performance of FFT-FBMC is almost achieved when δ = 73.125kHz while larger guard-bands can offer betterperformance in the BF-OFDM case. Such a result can be explained by the fact that thereceive filtering of FFT-FBMC significantly reduces the asynchronous interference while therectangular receive filter of BF-OFDM brings an important amount of interference from thecoexisting asynchronous user. It is worth noticing that BF-OFDM performs better than FFT-FBMC in the CP-region since the prototype filter is designed to ensure the lowest degradationin negligible TO case.

4.3.2 Carrier Frequency Offset

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


WONG5 Date: 21/7/2017

delay error [µs]-30 -20 -10 0 10 20 30

MS

E [d

B]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10δ =0kHz

FFT-FBMCBF-OFDMWOLA-COQAMWavelet-OFDM

delay error [µs]-30 -20 -10 0 10 20 30

MS

E [d

B]

-70

-60

-50

-40

-30

-20

-10δ=11.25kHz

FFT-FBMCBF-OFDMWOLA-COQAM, δ =15 kHzWavelet-OFDM, δ=15kHz

delay error [µs]-30 -20 -10 0 10 20 30

MS

E [d

B]

-70

-60

-50

-40

-30

-20

-10δ=45kHz


delay error [µs]-30 -20 -10 0 10 20 30

MS

E [d

B]

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10δ=73.125kHz

FFT-FBMCBF-OFDMWOLA-COQAM,δ=75kHzWavelet-OFDM, δ=75kHz

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


WONG5 Date: 21/7/2017

carrier index

CF

O [x

0.15

KH

z]δ =0 kHz

20 40 60 80

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =15 kHz

20 40 60 80

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =45 kHz

20 40 60 80

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =75 kHz

20 40 60 80

−10

−5

0

5

10 −40

−35

−30

−25

−20

−15

−10

carrier index

CF

O [x

0.15

KH

z]

δ =0 kHz

20 40 60 80

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]δ =15 kHz

20 40 60 80

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =45 kHz

20 40 60 80

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =75 kHz

20 40 60 80

−10

−5

0

5

10 −40

−35

−30

−25

−20

−15

−10

carrier index

CF

O [x

0.15

KH

z]

δ =0 kHz

10 20 30

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =15 kHz

10 20 30

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =45 kHz

10 20 30

−10

−5

0

5

10

carrier index

CF

O [x

0.15

KH

z]

δ =75 kHz

10 20 30

−10

−5

0

5

10 −40

−35

−30

−25

−20

−15

−10

Figure 4-7: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: per-subcarrierNMSE 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 guard-bands are examined: δ = 0, 15, 45 and 75 kHz. As mentioned in Section 3, the CFO shiftsboth interfering spectrum subbands in the same direction. This is why one of the guard-bandsis 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-COQAMand Wavelet-OFDM, respectively.

As in timing offset, FFT-FBMC exhibits almost the same MSE. Indeed, the MSE at theedges of each RB is about −30 dB, whereas it is less than −35 dB in the other subcarriers. Aswe 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 withrespect to CFO. In BF-OFDM case, the MSE is below −30 dB in a larger region around theCP. Unlike the TO case where the MSE is very low only in the CP region. In Wavelet-OFDMcase, 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 thescenario proposed for this section, the symbols can be on the same carrier at the same timecreating a high level of interference regardless the CFO level. In other words, the coexistence


WONG5 Date: 21/7/2017

CFO [x15kHz]-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

MS

E [d

B]

-65

-60

-55

-50

-45

-40

-35

-30

-25

-20


CFO [×15kHz]-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

MS

E [d

B]

-70

-60

-50

-40

-30

-20

-10δ=11.25kHz


CFO [×15kHz]-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

MS

E [d

B]

-70

-60

-50

-40

-30

-20

-10δ=45kHz


CFO [×15kHz]-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

MS

E [d

B]

-70

-60

-50

-40

-30

-20

-10δ=73.125kHz


Figure 4-8: FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM: average MSEagainst 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 ofinterference even if the system is synchronous.

The average MSEs of FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM, com-puted over all subcarriers, are plotted, in Figure 4-8, as function of CFO for guard-bandsδ = 0, 15, 45 and 75kHz, respectively.

4.4 IAPR

All multicarrier schemes have in common the major problem of very high fluctuation of theinstantaneous power of the signal to be transmitted. More specifically, the probability of havingan instantaneous power 8 to 12 dB greater than the mean power is non negligible. Theseinstantaneous power peaks produce signal excursions into the nonlinear region of operation ofthe 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 ofthe considered waveform. Therefore, it is interesting to analyze the CCDF of the instantaneouspower (IAPR, Instantaneous to Average Power Ratio) given by [CBS06]:

CCDF |s(n)|2

E[|s(n)|2

] = Prob

|s(n)|2

E[|s(n)|2

] > P0

(4.1)

where n refers to the time index of the whole signal to be transmitted.


WONG5 Date: 21/7/2017

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

4 5 6 7 8 9 10 1110

−5

10−4

10−3

10−2

10−1

Po [dB]

Pro

b(P

max

> P

o)


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 theconsidered WFs. The complexity will be assessed by counting the number of real multiplicationsper 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 toassess the number of multiplications per unit of time in order to compare as fairly as possiblethe schemes that do not share the same sampling frequency. To do so, a burst of S symbolvectors is considered. For the schemes that exhibit symbol overlapping, the complexity will bebenchmarked when S tends to infinity.

From now, it will be assumed that one complex multiplication can be carried out with threereal 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 = 3NFFT

2 log2(NFFT) (4.2)


WONG5 Date: 21/7/2017

The number of multiplications per unit of time is then:

COFDM,Tx/Rx = COFDM,Tx/RxS

S(NFFT +NCP )Ts

= COFDM,Tx/Rx

(NFFT +NCP )Fs (4.3)

FFT-FBMC

As for UF-OFDM, FFT-FBMC processes the data at the RB level. For each active RB (Bout of M) there is the N-point IFFT and then there is the filter bank. The complexity of thereceiver is the same.

CFFT−FBMC,Tx/Rx = 3BN2

(1 + log2

(N

2

))+ 2KMN + 3NM

2 log2(M) (4.4)


CFFT−FBMC,Tx/Rx = CFFT−FBMC,Tx/RxS

[KM + M2 (S(N +NCP )− 1)]Ts

S→∞−−−→CFFT−FBMC,Tx/RxM2 (N +NCP )

Fs (4.5)

BF-OFDM

When it comes to BF-OFDM, at the transmitter side, there is an additional stage with respectto the FFT-FBMC scheme: the predistortion stage. Moreover, the receiver is reduced to aMN

2 -point FFT.

CBFOFDM,Tx = 3BN2 + 3BN2

(1 + log2

(N

2

))+ 2KMN + 3NM

2 log2(M) (4.6)

CBFOFDM,Rx = 3MN

4 log2(MN

2 ) (4.7)


CBF−OFDM,Tx/Rx = CBF−OFDM,Tx/RxS

[KM + M2 (S(N +NCP )− 1)]Ts

S→∞−−−→CBF−OFDM,Tx/RxM2 (N +NCP )

Fs (4.8)

WOLA-COQAM

For the WOLA-COQAM, the data is processed by block of length K. For each block, theNFFT-point IFFT (with 3 × NFFT

2 log2(NFFT) real multiplications) and the filtering performed


WONG5 Date: 21/7/2017

by the PolyPhase-Network (2NFFTK real multiplications) run therefore K times. After thanthe 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 realmultiplications), the CP is then discarded (no arithmetic operations) and a KNFFT-point FFTcaptures the entire block. The block is then processed by the real prototype filter (2NFFTKreal multiplications). Finally the block is divided into NFFT sub-blocks of size K which gotrough K-point IFFT (3NFFTK log2(2K) real multiplications in total).

CWOLA−COQAM,Tx = K(

3NFFT

2 log2(NFFT) + 2NFFTK)

+ 4WTx (4.9)

CWOLA−COQAM,Rx = 4WRx + 3NFFTK

2 log2(KNFFT)

+ 3NFFTK log2(2K) + 2NFFTK (4.10)


CWOLA−COQAM,Tx/Rx = 2CWOLA−COQAM,Tx/RxS

((KNFFT +NCP )2S +WTx)TsS→∞−−−→

CWOLA−COQAM,Tx/Rx

(KNFFT +NCP )) Fs (4.11)

Wavelet-OFDM

The wavelet transform is based on two filters: a low-pass filter and a high-pass filter of lengthK. The number of carriers is M = NFFT = 2J . The number of additions and multiplicationsis

J∑j=J0+1

2jK ≤J∑j=1

2jK = 2MK

Therefore, the complexity of the wavelet transform is O(MK). The complexity of the FFT andthe IFFT is O(M log2(M)). The additional complexity caused by wavelet is O( K

log2(M)) whichis not considerable as K is bounded and M is large. In this deliverable, we consider Meyerwavelet where K = 47.

Analysis

According to the aforementioned closed-form expressions and the configurations given in Tables3-2, 3-3 and 3-4, it is possible to numerically assess the complexity of the different transmissionand reception schemes as given in Tab. 4-2.

The proposed waveforms embeds filtering stages and are therefore more complex than theCP-OFDM. FFT-FBMC and BF-OFDM transmitter schemes are the most efficient among thefour proposed thanks to their reduced number of PPN carriers (M instead of NFFT). WOLA-COQAM has an inherent higher complexity induced by its block processing and the transpositionin the wavelet domain requires a lot of multiplications which accounts for the high complexity ofthe Wavelet-OFDM. The absence of a fast algorithm to compute the wavelet transform is thereason behind the high complexity level for Wavelet-OFDM. Regarding the receiver schemes,aforementioned observations still hold. BF-OFDM provides the most efficient receiver schemeas it is reduced to a simple FFT and does not embed any filtering stage.


WONG5 Date: 21/7/2017

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


WONG5 Date: 21/7/2017

5. Multipath performance comparisonIn this section, we present the multipath performance of the waveforms in terms of uncodedbit error rate (BER). We first consider the impact of the channel delay spread, and then wepresent the performance in front of a standardized multipath channel. In this chapter, weconsider that the transmitted signal occupied a useful bandwidth of 9 MHz corresponding to50 resource blocks for the LTE configuration. We define the signal-to-noise ratio (SNR) as theratio 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 delayspread [ZMSR16b]. The considered channel impulse response (CIR) of the Lc-path fadingchannel is defined as

h(t) =Lc−1∑l=0

hlδ(t−∆l) (5.1)

where:

• hl is the complex amplitude, which is assumed to be Gaussian i.i.d. random variabledistributed.

• ∆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 particularcase 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 27.6dB. Indeed, the choice of a high SNR is done in order to highlight the channel impact on thewaveform performance. These results are compared with the performance of CP-OFDM basedLTE standard with a guard interval of 4.6875 µs.

UF-OFDM has the worst BER performance because the guard interval (ZP) is completelyused for resource band filtering at the transmitter and windowing at the receiver. The interblockinterferences become greater as the delay spread increases. WOLA-OFDM and WOLA-COQAMhave both little resistance to delay spread due to the fact that most of the CP is used forwindowing at the transmitter and receiver sides. The PPN version of FBMC and FFT-FBMChave similar BER performance. The BER slowly decrease as the delay spread inscreases dueto the one-tap equalizer which is no more efficient for large delay spread. The FrequencySpread (FS) version of FBMC has slightly better BER performance thanks to a better frequencygranularity in the equalization. OFDM, f-OFDM and Wavelet-OFDM have a similar behaviorwhich is an almost stable performance when the delay spread is below the CP length, and alarge degradation when the delay spread is greater than the CP length due to the fact that thesewaveforms are highly sensitive to the orthogonality. Finally, BF-OFDM has the best resistanceto delay spread thanks to a longer cyclic prefix (but with the same spectral efficiency) as wellas a smaller inter-carrier-spacing.


WONG5 Date: 21/7/2017

1 2 3 4 5 6 710

−4

10−3

10−2

10−1

100

BE

R

Delay spread [µs]

OFDMf−OFDMWOLAWOLA−COQAMFBMC (Rx PPN)FBMC (Rx FS)UF−OFDMWaveletFFT−FBMCBF−OFDM (64)BF−OFDM (128)

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 Hiperlan2Bran channel E, as defined in [WON16a]. We consider two mobility values of 5 and 150 km/hcorresponding to a quasi-static drone and to a full speed celerity. In order not to overloadthe presentation of the results, we present only the performance for the QPSK modulationbut similar performance (taking into account an x and y-axis shifts) are obtained for greaterconstellation orders. As for the previous BER comparison, we consider for all waveforms anideal frequency domain ZF-single tap equalization.

Figures 5-2 and 5-3 present the comparison of the uncoded BER for 5 km/H. We canobserve that all waveforms provide the same performance, except Wavelet-OFDM which has aslightly steeper slope corresponding to a better use of the frequency diversity provided by themultipath channel.

Figures 5-4 and 5-5 present the comparison of the uncoded BER for 150 km/H. We canobserve that all waveforms experience an error floor due to the time-varying channel implied bya greater mobility. The worst performance are those obtained by the WOLA-COQAM becausethe same outdated equalization coefficients are used for K consecutive blocks. FFT-FBMCand the 128 version of the BF-OFDM have almost the same BER performance. The large errorfloor is due to a larger symbol duration compared to OFDM. For BF-OFDM the duration ofthe symbol is 2.6 times greater than the duration of an OFDM symbol. If the prototype filteris shortened, as for instance for the 64 version of the BF-OFDM, then the error floor could belowered 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-OFDMcase.


WONG5 Date: 21/7/2017

5 10 15 20 2510

−4

10−3

10−2

10−1

QPSK, BRAN−Channel, 5km/H

BE

R

SNR[dB]

OFDMf−OFDMWOLAWOLA−COQAMWaveletFFT−FBMC

Figure 5-2: BER performance vs SNR for CP-OFDM, f-OFDM, WOLA-OFDM, WOLA-COQAM, Wavelet-OFDM and FFT-FBMC, mobility is set to 5 km/H and a QPSK modulationis considered

5 10 15 20 2510

−4

10−3

10−2

10−1


BE

R

SNR[dB]

OFDMBF−OFDM (64)BF−OFDM (128)FBMC−PPNFBMC−FSUF−OFDM

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


WONG5 Date: 21/7/2017

5 10 15 20 2510

−4

10−3

10−2

10−1


BE

R

SNR[dB]

OFDMf−OFDMWOLAWOLA−COQAMWaveletFFT−FBMC

Figure 5-4: BER performance vs SNR for CP-OFDM, f-OFDM, WOLA-OFDM, WOLA-COQAM, Wavelet-OFDM and FFT-FBMC, mobility is set to 150 km/H and a QPSK modula-tion is considered

5 10 15 20 2510

−4

10−3

10−2

10−1


BE

R

SNR[dB]

OFDMBF−OFDM (64)BF−OFDM (128)FBMC−PPNFBMC−FSUF−OFDM

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


WONG5 Date: 21/7/2017

6. ConclusionIn this deliverable, four new waveforms have been introduced (FFT-FBMC, BF-OFDM, WOLA-COQAM and Wavelet-OFDM) for the C-MTC context. In the framework of the same systemmodel defined in D2.1 (power spectral density, spectral efficiency/latency, asynchronous access,instantaneous average power ratio, and complexity comparison), these new proposals have beenevaluated 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 Meyerwavelet. The spectral efficiencies of the proposed waveforms are excellent and in the sameorder of magnitude of the CP-OFDM. For short packet transmission, the wavelet-OFDM hasthe advantage of being capable to have similar (excellent) latency than CP-OFDM, whereasthe 3 others waveforms slightly increase the latency in most of the case. For large packet trans-mission, all waveforms have similar latencies, except the WOLA-COQAM which has slightlybetter performance. Regarding the asynchronous performance, the proposed waveforms appearto be particularly adapted to time/frequency asynchronicities, which is particularly importantfor C-MTC communications. Since all the proposed waveforms are multicarrier schemes, theyall have the same PAPR issue. Of course, PAPR reduction algorithms could be used in orderto 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 numberof activeRBs, and it appears that there is no large complexity explosion with respect to CP-OFDM. Nevertheless, we can note that FFT-FBMC and BF-OFDM schemes are about 3 timesless complex than WOLA-COQAM and Wavelet-OFDM. There is also a benefit in the use ofBF-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 waveformskept in D2.1 (CP-OFDM, f-OFDM, WOLA-OFDM, FBMC-OQAM, UF-OFDM) for multipathchannels. 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 appearsthat UF-OFDM is very sensitive to delay spread, whereas all other waveforms are much morerobust. BF-OFDM has a greater capability when the delay spreads exceed the predefined guardinterval. For the low mobility case (5 km/H), all waveforms have the same performance. At150 km/H, WOLA-COQAM, FFT-FBMC and BF-OFDM experience an error floor ten timesgreater than the one obtained with the other schemes. BF-OFDM and FFT-FBMC error floorcan be managed and lowered if the number of transmitted carriers decreases, or equivalently ifthe intercarrier spacing is increased.


WONG5 Date: 21/7/2017

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 onWireless Communications, 6(1):202–209, 2007.

[CBS06] C. Ciochina, F. Buda, and H. Sari. An analysis of ofdm peak power reductiontechniques for wimax systems. In 2006 IEEE International Conference on Commu-nications, volume 10, pages 4676–4681, June 2006.

[DGD+17] David Demmer, Robin Gerzaguet, Jean-Baptiste Doré, Didier Le Ruyet, and DimitriKténas. Block-Filtered OFDM: an exhaustive waveform to overcome the stakes offuture wireless technologies. In submitted to IEEE ICC (ICC), Paris, France, May2017.

[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. Block-Filtered OFDM: a new promising waveform for multi-service scenarios. In submittedto IEEE ICC 2017 (ICC), Paris, France, May 2017.

[GMM+15] I. Gaspar, M. Matthe, N. Michailow, L. Leonel Mendes, D. Zhang, and G. Fet-tweis. 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. ShaÃ¯ek, and D. Roviras. Wola processing: A use-ful tool for windowed waveforms in 5g with relaxed synchronicity. In 2017 IEEEInternational Conference on Communications Workshops (ICC Workshops), pages393–398, May 2017.

[Qua] Qualcomm, Incorporated. R1-162199 - Waveform candidates.

[WON16a] WONG5. Wong5 project, deliverable 1.2: System specifications and kpi’s for criticalmachine type communications scenario. ANR, Tech. Rep, 2016.

[WON16b] WONG5. Wong5 project, deliverable 2.1: Critical and comparative study of wave-forms in c-mtc context. ANR, Tech. Rep, 2016.

[ZLR10] R. Zakaria and D. Le Ruyet. A novel FBMC scheme for Spatial Multiplexing withMaximum 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 poten-tial candidate for asynchronous 5G. In IEEE Global Communications Conference(GLOBECOM), 2016.

[ZMSR16b] R. Zayani, Y. Medjahdi, H. Shaiek, and D. Roviras. Wola-ofdm: A potentialcandidate for asynchronous 5g. In 2016 IEEE Globecom Workshops (GC Wkshps),pages 1–5, Dec 2016.


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[ZR12] R. Zakaria and D. Le Ruyet. A Novel Filter-Bank Multicarrier Scheme to Mitigatethe Intrinsic Interference: Application to MIMO Systems. IEEE Transactions onWireless Communications, 11(3):1112–1123, March 2012.

[ZR17] R. Zakaria and D. Le Ruyet. Analysis of the FFT-FBMC Equalization in SelectiveChannels. IEEE Signal Processing Letters, 24(6):897–901, June 2017.


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Glossary and DefinitionsAcronym MeaningBF-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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