IEEE ICC 2017 Wireless Communications Symposium

A Complex Orthogonal WCP Circular Filtered Multi-Carrier (COW-CFMC) Scheme Rostom Zakaria, Didier Le Ruyet

Carlos Aur´elio Faria da Rocha, Bartolomeu F. Uchˆoa Filho

CEDRIC Conservatoire National des Arts et M´etiers Paris, France Emails: [email protected]; [email protected]

GPqCom/LCS/EEL Universidade Federal de Santa Catarina Florianopolis, Brazil Emails: [email protected]; [email protected]

Abstract—In this paper, we propose a scheme that preserves the advantages of Windowed Cyclic Prefix FBMC/Circular Offset Quadrature Amplitude Modulation (WCP-COQAM) while guaranteeing the complex orthogonality. Indeed, WCP-COQAM is based on block processing and uses circular filtering in order to remove time overheads. However, like FBMC/OQAM scheme, WCP-COQAM suffers from the presence of intrinsic interference that prevents the combination with some Multiple Input Multiple Output (MIMO) techniques such as Alamouti Coding. This intrinsic interference results from the non-complex orthogonal property of WCP-COQAM and Filter Bank MultiCarrier (FBMC). In this work, we show that circular filtering makes the transmultiplexer impulse response circulant. Our proposed scheme, called COW-CFMC, exploits this circularity to restore the complex orthogonality by precoding the data symbols in each subcarrier. Thus, we show by simulation that our proposed scheme can enable Alamouti coding in a straightforward manner.1

I. I NTRODUCTION Internet of Things (IoT) applications, Device-to-Device (D2D) communications and the increase of Machine-Type Communications (MTC) mark the transition from the cell centric network model to distributed modes. In this context, high tolerance to interference and robustness to frequencytime synchronization errors are necessary attributes for the modulation waveform. In view of these requirements, Filter Bank Multi-Carrier (FBMC) modulation [1] has recently attracted a lot of attention and is considered as one of the potential candidate for 5G cellular networks [2]. The main property of FBMC is that each subcarrier is filtered and consequently, the sidelobes are suppressed. Hence, FBMC achieves a higher spectral efficiency and a good resilience against time and frequency misalignment that may enable asynchronous multiple access. However, these features are obtained to the detriment of the complex orthogonality. Each demodulated data symbol is accompanied by the so-called intrinsic interference coming from the neighboring transmitted symbols. To cope with the intrinsic interference the quadrature amplitude modulation (QAM) must be replaced by offset QAM (OQAM) symbol. 1 This work was partially funded through the French ANR projects WONG5 (ANR-15-CE25-0005-02) and ACCENT5 (ANR-14-CE28-0026-02) and by the CNPq, Brazil under grants 306145/2013-8 and 400703/2014-9.

978-1-4673-8999-0/17/$31.00 ©2017 IEEE

One of the drawbacks of FBMC is the signal ramp-up and ramp-down at the beginning and the end of each data burst due to linear filtering. Such transition intervals are not negligible overheads if the data burst is very short. Moreover, FBMC incurs an overhead due to the T /2 time offset between the OQAM symbols, where T is the symbol duration [3]. A new concept of multi-carrier modulation has recently appeared in the literature where the linear filtering is replaced by a circular filtering for pulse shaping [3], [4]. A periodic filter is used to realize the circular convolution at the transmitter, which is equivalent to the tail-biting process. This idea was originally proposed with the introduction of Generalized Frequency Division Multiplexing (GFDM) [5]. Thanks to the use of a circular filtering, the overall multicarrier modulation system can be seen as a block transform processing and a Cyclic Prefix (CP) is inserted to enhance the orthogonality under multi-path channel. In [4], the authors have also adopted the circular filtering to FBMC. In order to cope with the multipath interference and to prevent the degradation of the Power Spectrum Density (PSD) due to the block processing, a CP and a windowing are added. This scheme is called Windowed Cyclic Prefix FBMC/circular OQAM (WCP-COQAM). However, for both FBMC and WCP-COQAM, the presence of the intrinsic interference prevents the combination with some MIMO techniques such as space-time block coding and spatial multiplexing (SM) with maximum likelihood (ML) detection [6], [7]. Another FBMC scheme (named FFT-FBMC) was proposed in [8], [9]. This scheme performs Inverse Fast Fourier Transform (IFFT) precoding and FFT decoding with CP insertion on each subcarrier in order to suppress the FBMC intrinsic interference. It was shown that MIMO techniques such as Space-Time Block Coding (STBC) and SM-ML can be performed straightforwardly in FFT-FBMC [9]. However, like the FBMC scheme, FFT-FBMC still suffers from the time overhead when short data bursts are considered due to the signal ramp-up/ramp-down and the half symbol offset overhead. In this paper, we propose a new scheme that combines the advantages of both WCP-COQAM and FFT-FBMC. That is, we aim to remove the edge time transitions as well as the half symbol offset overhead while guaranteeing the complex orthogonality. Indeed, we propose to replace the classical

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linear filtering by a circular one in the previously proposed FFT-FBMC scheme. Or alternatively, it can also be seen as proposing to introduce IFFT precoding and FFT decoding in each subcarrier to the WCP-COQAM scheme. We call our proposed scheme Complex Orthogonal Windowed CP Circular Filtered Multi-Carrier (COW-CFMC). As we have mentioned above, a CP insertion in each subcarrier was proposed for FFT-FBMC to make the transmultiplexer impulse response circulant. However, we will show that thanks to the use of circular filtering, the transmultiplexer impulse response is already circulant in WCP-COQAM. Therefore, for our proposed COW-CFMC scheme, there is no need to insert a CP in each subcarrier. Thus, the proposed system has a good spectral efficiency and guarantees the complex orthogonality. Thanks to this last property, the scheme can be easily coupled with MIMO techniques such as STBC and SM-ML. The rest of the paper is organized as follows: in Section II, we give a brief review of WCP-COQAM waveform and focus on its property of circularity. After that, we introduce our proposed scheme in Section III. Simulation results comparing the performance of the proposed scheme with other existing ones are given in Section IV. Finally, we provide some conclusions and remarks in Section V. II.

REVIEW AND PROPERTIES OF

WCP-COQAM

A. Review on WCP-COQAM

M −1  

ak,n g[m − nM/2]ej

2πk M (m−D)

ejφk,n , (1)

k=0 n∈Z

where M is the number of subcarriers, ak,n are the real-valued transmitted symbols at time index n and subcarrier k, and D is the delay term to insure the causality. This delay depends on the length Lg of the prototype filter response g[m], Lg = KM where K is the overlapping factor. The phase term φk,n is given by [10]: π φk,n = (n + k) − πkn (2) 2 In [4], the authors have proposed to replace the linear convolution used in FBMC with a circular convolution similar to the GFDM and CB-FMT. The main advantage of the socalled circular OQAM (COQAM) scheme is removing the time overheads caused by the linear filtering and the OQAM structure itself. Circular filtering implies block-wise processing. Assuming that N is the number of real symbol slots per block and M is the number of subcarriers, the transmitted signal block has a length of M N/2. The discrete-time COQAM signal s[m], with m ∈ {0, ..., M N/2 − 1}, is expressed as [4]: s[m] =

M −1 N −1   k=0 n=0

ak,n g˜[m − nM/2]ej

2

where |m|N stands for the modulo-N operation. It is worth noting that the authors in [4] set the overlapping factor K = N/2. That is, the initial prototype filter g[m] has the same length Lg = KM = M N/2 as the transmitted signal block. In order to keep the orthogonality after the transmission over a frequency selective channel, a cyclic prefix (CP) is added to the transmitted signal block s[m], m ∈ {0, ..., M N/2 − 1}. Furthermore, due to the degradation of the PSD resulting from the block processing, a windowing before the transmission also has to be applied. The overall scheme is called WCPCOQAM [4]. The CP of length LCP is composed of two parts : the guard interval of length LGI to fight the interference due to multi-path channel effect and the part dedicated to the windowing transitions LRI . At the receiver side, the overall CP is first removed and then the demodulated received symbol yq,l in subcarrier q ∈ {0, ..., M − 1} and time index l ∈ {0, ..., N − 1} can be obtained as follows: M N/2−1

yq,l =



s[m]˜ g [m − lM/2]e−j

2πq M (m−D)

e−jφq,l

(5)

m=0

First of all, we recall the baseband discrete time model of the classical FBMC. The transmitted signal s[m] in FBMC can be written as follows [10]: s[m] =

where the prototype filter response g˜[m] is obtained by performing the periodic repetition of the initial prototype filter g[m] as follows:   g˜[m] = g |m| M N (4)

2πk M (m−D)

ejφk,n , (3)

B. Properties of Circular OQAM In this subsection, we will demonstrate that the transmultiplexer impulse response in WCP-COQAM is circulant. By plugging the expression of s[m] given by (3) into (5) we obtain the expression of the demodulated received symbols yq,l written as: yq,l =

−1 M −1 N  

M N/2−1



ak,n

k=0 n=0

× ej

g˜[m − nM/2]˜ g [m − lM/2]

m=0

2π(k−q) (m−D) M

ejφk,n −jφq,l

(6)

Let us define Γq,k (l, n) as: M N/2−1

Γq,k (l, n) =



g˜[m − nM/2]˜ g [m − lM/2]

m=0

× ej

2π(k−q) (m−D) M

ejφk,n −jφq,l

(7)

Therefore, according to (6) and (7), we can write: yq,l =

−1 M −1 N  

Γq,k (l, n)ak,n

(8)

k=0 n=0

The function Γq,k (l, n) given in (7) is proportional to the M/2downsampled correlation function between the frequency shifted versions of g˜[m], shifted by 2πkm and 2πqm M M . On the other hand, the prototype filter g[m] is assumed to be frequency well localized such that the spectrum of the signal in a given subcarrier is only spread over both immediate adjacent subcarriers [6]. Therefore, the function Γq,k (l, n) is negligible

IEEE ICC 2017 Wireless Communications Symposium

if |q − k| > 1. Hence, the summation in (8) with respect to k can be simplified to be only over the set {q − 1, q, q + 1}. In a matrix form, the vector yq = [yq,0 , ..., yq,N −1 ]T of size N × 1 containing the N demodulated symbols in a given subcarrier q can be hence expressed as: yq =

Subtituting m + M N/2 by m in the first summation term, we obtain: MN 

2 −1  MN M Γq,k (l, n) = − g[m]˜ g m − (n − l) 2 2 MN M m=

=×e

q+1 

Γq,k ak

(9)

j

where Γq,k is a N × N matrix whose entries are Γq,k (l, n) in the l-th row and n-th column, and ak = [ak,0 , ..., ak,N −1 ]T is the vector of size N ×1 containing the N transmitted symbols in subcarrier k. In the following, we shall demonstrate that the matrix Γq,k is circulant ∀(q, k) ∈ {0, ..., M − 1}2 . To begin with, we substitute m − lM/2 by m in (7). Hence, we obtain:

2

π

ej 2 (k−q+n−l) ejπ(l−n)k

M N/2−lM/2−1



+

k=q−1

−l

2

2π(k−q) (m−D) M

g[m]˜ g [m − (n − l)M/2]

m=0

= × ej

2π(k−q) (m−D) M

π

ej 2 (k−q+n−l) ejπ(l−n)k (14)

According to the periodicity of g˜[m] (that is g˜[m − M N/2] = g˜[m]), we can recombine both summation terms in the equation above and write: MN 2

Γq,k (l, n) =

−1

g[m]˜ g [m − (n − l)M/2]

m=0 M N/2−lM/2−1



Γq,k (l, n) =

= × ej

g˜[m]˜ g [m − (n − l)M/2]

m=−l M 2

× ej

2π(k−q) (m−D) M

ejπl(k−q) ejφk,n −jφq,l

(10)

After that, since l ≥ 0, we can split the sum over m as Γq,k (l, n) =

−1 

g˜[m]˜ g [m − (n − l)M/2]

2π(k−q) (m−D) M

∀(q, k) ∈ {0, ..., M − 1}2 , ∀(l, n) ∈ {0, ..., N − 1}2 , ∀δ ∈ Z : (16) Γq,k (|l + δ|N , |n + δ|N ) = Γq,k (l, n) First of all, we recall some properties about modulo operation: ∀(l, n, N, M ) ∈ Z4 , we have



g˜[m]˜ g [m − (n − l)M/2]

m=0

=×e

j

2π(k−q) (m−D) M

π

ej 2 (k−q+n−l) ejπ(l−n)k (11)

where the phase terms φ are replaced by their terms given by (2). According to the definition of g˜[m] given by (4) and the fact that l ∈ {0, ..., N − 1}, we have: 

 g˜[m] = g m + g˜[m] = g[m]

MN 2



 , ..., −1 if m ∈ −l M 2  if m ∈ 0, ..., M2N − l M 2 −1 (12)

Therefore, we can rewrite (11) as: Γq,k (l, n) =

−1 

|n + l|N = ||n|N + |l|N |N |M n|M N = M |n|N

π

ej 2 (k−q+n−l) ejπ(l−n)k

M N/2−lM/2−1

+

g[m + M N/2]˜ g [m − (n − l)M/2]

2π(k−q) (m−D) M

π

ej 2 (k−q+n−l) ejπ(l−n)k

M N/2−lM/2−1

+



g[m]˜ g [m − (n − l)M/2]

m=0

= × ej

2π(k−q) (m−D) M

π

ej 2 (k−q+n−l) ejπ(l−n)k (13)

(17) (18)

Therefore, according to (4), we can rewrite the term g˜[m − (n − l)M/2] in (15) as 





M M = g

m − (n − l)

g˜ m − (n − l) 2 2 MN 2

M (19) = g˜ m − |n − l|N 2 where the second equality holds because |m| M N = m since 2 in (15) the summation on m is over {0, ..., M N/2 − 1}. On the other hand, we can calculate Γq,k (|l + δ|N , |n + δ|N ) as Γq,k (|l + δ|N , |n + δ|N ) = MN

 2 −1  M g[m]˜ g m − (|n + δ|N − |l + δ|N ) 2 m=0 = × ej

2π(k−q) (m−D) M

m=−l M 2

= × ej

π

ej 2 (k−q+n−l) ejπ(l−n)k (15)

To prove that the matrices Γq,k (∀(q, k) ∈ {0, ..., M − 1}2 ) are circulant, we can proceed by demonstrating that:

m=−l M 2

= × ej

2π(k−q) (m−D) M

π

π

ej 2 (k−q) Φk (|l + δ|N , |n + δ|N ) (20)

where Φk (l, n) = ej 2 (n−l) ejπ(l−n)k . Using the definition of g˜[m] given in (4) and taking into account the properties given in (17)-(18), we can show that



 M M g˜ m − (|n + δ|N − |l + δ|N ) = g˜ m − |n − l|N 2 2

IEEE ICC 2017 Wireless Communications Symposium

Hence, using equations (19), we can deduce that for m ∈ {0, ..., M N/2 − 1} we have: 



M M = g˜ m − (n − l) g˜ m − (|n + δ|N − |l + δ|N ) 2 2 (21) Moreover, we can develope the phase term Φk (., .) in (20) as: Φk (|l + δ|N , |n + δ|N ) π

= ej 2 (|n+δ|N −|l+δ|N ) ejπk(|l+δ|N −|n+δ|N ) (22) We can easily show that: = ej

2π c |n|pc

(23)

Therefore, assuming that N is multiple of 4, we can deduce that: π

Φk (|l + δ|N , |n + δ|N ) = ej 2 (n−l) ejπk(l−n)

(24)

Finally, according to (24) and (21), we rewrite (20) as

=×e

j

2π(k−q) (m−D) M

e

0 0 0

yq =

e

WH Dq,k Wak

(26)

where Dq,k is the diagonal matrix obtained by diagonalizing Γq,k by the unitary matrix W. Therefore, the diagonal elements in Dq,k are given by: Dq,k (l, l) =

Γq,k (l , 0)e−j

2π  N ll

(27)

Γq,k (l , 0) =

g[m]˜ g [m + l M/2]

2π(k−q) (m−D) M

CP insertion

N IFFT

P/S

CP insertion M-1

Fig. 1. FFT-FBMC transmitter scheme

Therefore, similarly as in [9], let us consider that the transmitted symbol block ak in subcarrier k is the IDFT output of a data symbol block dk (i.e. ak = WH dk ). Hence, taking the DFT of the received block yq in subcarrier q, we obtain from (26) the following: rq = W H y q =

q+1 

Dq,k Wak

k=q−1

= Dq,q dq + Dq,q−1 dq−1 + Dq,q+1 dq+1

m=0

= × ej

P/S

1

0 0 0

where, according to (15), −1

N IFFT

0 0 0

S/P

l =0

MN 2

CP insertion

(25)

k=q−1

N −1 

P/S

0

jπ 2 (k−q+n−l) jπk(l−n)

which is the same expression as that of Γq,k (l, n) given in (15). This shows that condition (16) is satisfied, which proves that the matrices Γq,k , (q, k) ∈ {0, ..., M − 1}2 are circulant. Therefore, the matrices Γq,k are diagonalizable by the discrete Fourier transform (DFT) matrix W and their eigenvalues are the DFT coefficients of the sequences {Γq,k (l, 0), l ∈ {0, ..., N − 1}}. Hence, we can rewrite (9) as: q+1 

N IFFT

FBMC modulator

Γq,k (|l + δ|N , |n + δ|N ) = MN 

2 −1  M g[m]˜ g m − (n − l) 2 m=0

...

2π c n

...

ej

...

∀(p, c) ∈ Z2∗ , :

symbols in each subcarrier by performing a IDFT. Before being fed to the FBMC modulator, the IDFT outputs are appended with a CP to make the transmultiplexer impulse response circulant. At the receiver side, the CPs are removed after the FBMC demodulator, and then the DFT is performed in each subcarrier to recover the data symbols. To guarantee the complex orthogonality, half of each precoding IDFT inputs are set to zero, while the remaining inputs are fed with complex data symbols. Fig. 1 depicts the basic scheme of the FFT-FBMC transmitter. It is worth noticing that FFTFBMC can be seen as several contiguous blocks of CP-OFDM transmissions where each CP-OFDM transmission block is filtered by the FBMC prototype filter. This results in a multicarrier transmission where contiguous blocks of subcarriers are filtered individually with the same filter. We note that this transmission scheme was also used later in [11] to introduce the so-called Resource-Block Filtered OFDM (RB-F-OFDM) which is very similar to FFT-FBMC. In the following, we apply the same principle above to the WCP-COQAM scheme and explain the processing in more details.

π





ej 2 (k−q−l ) ejπl k

(28)

The two last terms represent the interference coming from the immediate adjacent subcarriers q ± 1. According to (27), the coefficients in the diagonal matrix Dq,q are the N -DFT of Γq,q (l , 0) which is, according to (28), given by:

III. COW-CFMC PROPOSAL Equation (26) shows that WCP-COQAM does not guarantee the complex orthogonality and then the received demodulated symbols are affected by the intrinsic interference. This interference is also present in the classical FBMC. In order to enable the complex orthogonality for FBMC, the authors in [8] proposed the FFT-FBMC scheme which precodes the data

(29)



MN 2

−1

Γq,q (l , 0) =

m=0



π 



g[m]˜ g [m + l M/2] e−j 2 l ejπl q 

Rg˜ [l M 2 ]

(30)



M We note that Rg˜ [l M 2 ] is the 2 -downsampled autocorrelation function of the periodic filter g˜[m] (please also note that

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In order to avoid interference terms in (29), we propose, as in [9], to only transmit useful complex data symbols in the first half N -block when the subcarrier index q is even, and in the second half N -block when the subcarrier index q is odd (please see Fig. 3). That is, we can write:   ¯ T , 0T T if q is even d q (32) d q =  T T T ¯ if q is odd 0 ,d q



*>O@





¯ q is a ( N × 1)-vector of complex data symbols, and where d 2 0 is a zero vector of size N2 × 1. Let us also set the following:   (0) (0) ¯ 0 Dq,k rq (33) rq = (1) , and Dq,k = (1) , ¯ rq 0 Dq,k





í









,QGH[O

(i)

Fig. 2. Spectrum of the M -downsampled autocorrelation function of the 2 periodic Mirabbasi-Martin filter g˜[m] with overlapping factor K = 8.

g[m] = g˜[m] for 0 ≤ m < M N/2). Since we consider, as we have previously mentionned, that the filter g[m] is 1 1 at least spectrally confined in [− M ,M ], downsampling the  autocorrelation function Rg˜ [l ] by M/2 does not cause aliasing and hence the spectrum shape of Rg˜ [l ] is preserved. Fig. 2 illustrates an example, using Mirabbasi-Martin [12] filter with K = 8, of the spectrum G[l] of Rg˜ [l M 2 ] obtained by N −1  M −j 2π ll N G[l] = l =0 Rg˜ [l 2 ]e . Therefore, equation (30) shows that Γq,q (l , 0) is the phase π  shifted by e− 2 l ejπql version of Rg˜ [l M 2 ]. Thus, according to (27), the coefficients Dq,k (l, l) are the circularly shifted version of G[l] by N2 q − N4 to the right. Hence, we can write:



N N Dq,q (l, l) = G

l − q +

2 4 N

(31)

Therefore, the coefficients in the diagonal matrix Dq,q (l, l) depend on the parity of q. Fig. 3 illustrates the coefficients Dq,q (l, l) for q even and odd.



&RHIILFLHQWVRIWKHGLDJRQDOPDWUL['TT

2GGVXEFDUULHULQGH[T (YHQVXEFDUULHULQGH[T 









í









,QGH[O

Fig. 3. Coefficients of the diagonal matrix Dq,q for even and odd subcarrier index q using Mirabbasi-Martin filter with overlapping factor K = 8.

(i)

where rq , i ∈ {0, 1} is a ( N2 ×1)-vector, and Dq,k , i ∈ {0, 1} ¯ are square matrices of size N × N . Therefore, we can and 0 2 2 show that equation (29) becomes: (i) ¯ r(i) q = Dq,q dq ,

for i = |q|2

(34)

This last expression shows that the transmitted complex data ¯ q (p), p ∈ {0, ..., N/2 − 1} are received free symbols d¯q,p = d (i) of interference because Dq,q is a diagonal matrix. Therefore, our proposed scheme satisfies the complex orthogonality and enables any transmission technique that requires complex orthogonality such as STBC and SM-ML. It is important to notice that compared to the FFT-FBMC, there is no need to add a cyclic prefix after the IFFT operation in each subcarrier thanks to the circular convolution. IV. S IMULATION RESULTS In this section we will first evaluate the PSD of the proposed COW-CFMC scheme with respect to other existing schemes. Following [4] for the evaluation, we have considered M = 64 with M/2 active subcarriers. We have compared the PSD of the proposed COW-CFMC scheme with the ones of the CPOFDM, FFT-FBMC and WCP-COQAM schemes in Fig. 4. We have chosen N = 16 and LGI = LRI = 16 using Hamming window for the WCP-COQAM and COW-CFMC schemes. As for the prototype filter, we used the MirabbasiMartin filter with overlapping factor K = N2 = 8. Fig. 4 shows that FFT-FBMC exhibits the best PSD. We can also observe that the proposed COW-CFMC scheme achieves the same PSD than the WCP-COQAM scheme. The relatively high PSD leakage of COW-CFMC and WCP-COQAM compared to the one of FFT-FBMC is due to the block processing. However, compared to CP-OFDM, COW-CFMC and WCP-COQAM schemes present lower spectrum leakage. In addition, we have also considered in Fig. 5 the case where 10 subcarriers are switched off using the same parameter settings as previously. The results show again that COW-CFMC and WCP-COQAM schemes have the same low radiation level in the empty band. In order to illustrate the complex orthogonality property of the COW-CFMC scheme, we have also evaluated the COWCFMC scheme with the Alamouti diversity code for two

IEEE ICC 2017 Wireless Communications Symposium







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transmit and one receive antennas. The system parameters are as follows : M = 64 subcarriers, subcarrier spacing of Δf = 15kHz, N = 16, TGI = TRI = 16 and uncoded QPSK modulation. We have assumed Perfect channel estimation and that the channels follow the ITU Pedestrean-A channel model. The BER performance is given in Fig 6. As expected, the COW-CFMC based Alamouti transmission achieves the same performance as the CP-OFDM scheme thanks to the complex orthogonality. The same conclusion can be drawn when considering open loop MIMO systems using spatial multiplexing with ML detection. V. C ONCLUSION We have proposed in this paper a new filtered multicarrier scheme that restores the complex orthogonality in WCPCOQAM. Alternatively, the proposed scheme (COW-CFMC) can be also seen as a modified version of FFT-FBMC by replacing the linear filtering by circular filtering. We have shown that COW-CFMC also preserves the advantage of WCP-COQAM as it removes the time overheads of linear filtering. Simulation results show that COW-CFMC and WCP-





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Fig. 6. Alamouti BER performance comparaison between CP-OFDM and COW-CFMC schemes

COQAM schemes have the same PSD. Moreover, we have also shown by simulation that Alamouti coding can be performed straightforwardly with COW-CFMC scheme without any BER performance degradation. R EFERENCES [1] M. Bellanger and PHYDYAS team. FBMC physical layer: a primer. website: www.ict-phydyas.org, 2010 June. [2] P. Banelli, S. Buzzi, G. Colavolpe, A. Modenini, F. Rusek, and A. Ugolini. Modulation Formats and Waveforms for 5G Networks: Who Will Be the Heir of OFDM?: An overview of alternative modulation schemes for improved spectral efficiency. Signal Processing Magazine, IEEE, 31(6):80–93, Nov 2014. [3] M. J. Abdoli, M. Jia, and J. Ma. Weighted circularly convolved filtering in OFDM/OQAM. In 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), pages 657–661, Sept 2013. [4] H. Lin and P. Siohan. Multi-carrier modulation analysis and WCPCOQAM proposal. EURASIP Journal on Advances in Signal Processing, 2014(1):79, 2014. [5] G. Fettweis, M. Krondorf, and S. Bittner. GFDM - Generalized Frequency Division Multiplexing. In Vehicular Technology Conference, 2009. VTC Spring 2009. IEEE 69th, pages 1–4, April 2009. [6] A. I. P´erez-Neira, M. Caus, R. Zakaria, D. Le Ruyet, E. Kofidis, M. Haardt, X. Mestre, and Y. Cheng. MIMO Signal Processing in OffsetQAM Based Filter Bank Multicarrier Systems. IEEE Transactions on Signal Processing, 64(21):5733–5762, Nov 2016. [7] R. Zakaria and D. Le Ruyet. Intrinsic interference reduction in a filter bank-based multicarrier using QAM modulation . Physical Communication, 11:15 – 24, 2014. Radio Access Beyond OFDM(A). [8] 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. [9] R. Zakaria and D. Le Ruyet. A Novel Filter-Bank Multicarrier Scheme to Mitigate the Intrinsic Interference: Application to MIMO Systems. Wireless Communications, IEEE Transactions on, 11(3):1112 –1123, march 2012. [10] P. Siohan, C. Siclet, and N. Lacaille. Analysis and design of OFDM/OQAM systems based on filterbank theory . Signal Processing, IEEE Transactions on, 50(5):1170 –1183, may 2002. [11] J Li, E. Bala, and R. Yang. Resource block Filtered-OFDM for future spectrally agile and power efficient systems . Physical Communication, 11:36 – 55, 2014. Radio Access Beyond OFDM(A). [12] S. Mirabbasi and K. Martin. Design of prototype filter for near-perfectreconstruction overlapped complex-modulated transmultiplexers. In Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on, volume 1, pages I–821–I–824 vol.1, 2002.