Prototype Filter Design for FBMC in Massive MIMO Channels

Transcription

1 Prototype Filter Design for FBC in assive IO Channels Air Ainjavaheri, Aran Farhang, Linda E. Doyle, and Behrouz Farhang-Boroujeny ECE Departent, University of Utah, Salt Lake City, Utah, USA, CONNECT, The Telecounications Research Centre, Trinity College Dublin, Ireland. Eail: {ainjav, {farhanga, arxiv: v [cs.it] 1 ar 017 Abstract We perfor an asyptotic study on the perforance of filter bank ulticarrier FBC in the context of assive ulti-input ulti-output IO. We show that the signal-tointerference-plus-noise ratio SINR cannot grow unboundedly by increasing the nuber of base station BS antennas, and is upper bounded by a certain deterinistic value. This is a result of the correlation between the ulti-antenna cobining tap values and the channel ipulse responses between the terinals and the BS antennas. To solve this proble, we introduce a siple FBC prototype filter design ethod that reoves this correlation, enabling us to achieve arbitrarily large SINR values by increasing the nuber of BS antennas. Index Ters assive IO, FBC/OQA, OFD, SINR, channel equalization, asyptotic analysis. I. INTRODUCTION assive ultiple-input ultiple-output IO is one of the key technologies currently considered for the fifth generation 5G of cellular networks. In a assive IO syste, the base station BS is equipped with a large nuber of antennas, in the order of a hundred or a few hundreds, and is siultaneously serving tens of users. By increasing the nuber of BS antennas, the effects of uncorrelated noise and ultiuser interference can be ade arbitrarily sall, [1], [], and hence, unprecedented network capacities can be achieved. Due to its siplicity and robustness to ultipath channels, orthogonal frequency division ultiplexing OFD is the doinant odulation forat that is considered in the assive IO literature, [1], as well as ost of the current wireless standards such as the 4G long ter evolution LTE. However, despite its any advantages, OFD suffers fro a nuber of drawbacks. In particular, due to the high side-lobe levels of the subcarriers, OFD suffers fro a large spectral leakage leading to high out-of-band eissions. Accordingly, stringent synchronization procedures are required in the uplink of ultiuser networks. The users ay experience different Doppler shifts, frequency offsets, tiing offsets, etc., and aintaining the orthogonality between the subcarriers ay not be possible without energy-consuing and resource-deanding procedures. Furtherore, utilization of non-contiguous spectru chunks through carrier aggregation for the future high data rate applications is not possible in the uplink with OFD as a result of high side-lobe levels of its subcarriers, [3]. oreover, This publication has eanated fro research supported in part by a research grant fro Science Foundation Ireland SFI and is co-funded under the European Regional Developent Fund under Grant Nuber 13/RC/077. to avoid interference, large guard bands are required between adjacent frequency channels, which in turn, lowers the spectral efficiency of OFD. It should be ephasized that ore strict requireents in ters of data rate, energy efficiency, and latency are defined for the 5G networks copared to the current ones in LTE, [4]. Therefore, the aforeentioned shortcoings of OFD and the requireents of 5G networks have stirred a great deal of interest in the area of wavefor design aong the research and industrial counities otivating introduction of alternative wavefors capable of keeping the advantages of OFD while addressing its drawbacks, [4] [7]. Filter bank ulticarrier FBC is a 5G candidate wavefor offering a significantly iproved spectral properties over OFD, by shaping the subcarriers using a prototype filter that is well-localized in both tie and frequency, [8]. Therefore, the uplink synchronization requireents can be significantly relaxed, [9], and carrier aggregation becoes a trivial task, [10]. As a result of the above advantages, FBC is currently being considered as an enabling technology in various research and industrial projects; see [10] and the references therein. The application of FBC in assive IO channels has been recently studied in [11], where its so-called selfequalization property leading to a channel flattening effect was reported through siulations. According to this property, the effects of channel distortions i.e., intersybol interference and intercarrier interference will diinish by increasing the nuber of BS antennas. In [1], ulti-tap equalization is proposed for FBC-based assive IO to iprove the equalization accuracy copared to the single-tap equalization per subcarrier at the expense of a higher coputational coplexity. The authors in [13] show that the pilot containation proble in ulti-cellular assive IO networks, [1], can be resolved in a straightforward anner with FBC signaling due to its special structure. These studies prove that FBC is an appropriate atch for assive IO and vice versa as they can both bring pivotal properties into the picture of 5G systes. Specifically, this cobination is of a great iportance as not only the sae spectru is being utilized by all the users but it is also used in a ore efficient anner. Since the literature on FBC-based assive IO is not ature yet, these systes need to go through eticulous analysis and investigation. Hence, in this paper, we perfor an in-depth analysis on the perforance of FBC in assive IO. We show that the self-equalization property shown

2 through siulations and claied in [11] and [1] is not very accurate. ore specifically, by increasing the nuber of BS antennas, the channel distortions average out only up to a certain extent, but not copletely. Thus, the SINR saturates at a certain deterinistic level. This deterines an upper bound for the SINR perforance of the syste. We derive an analytical expression for this saturation level, and propose a prototype filter design ethod to resolve the proble. With the proposed prototype filter in place, SINR grows without a bound by increasing the BS array size, and arbitrarily large SINR values are achievable. It is worth entioning that although the theories developed in this paper are applicable to all types of FBC systes, the forulations are based on the ost coon type in the literature that was developed by Saltzberg, [14], and is known by different naes including OFD with offset quadrature aplitude odulation OFD/OQA, FBC/OQA, and staggered ultitone ST, [8]. Throughout this paper, we refer to it as FBC for siplicity. The rest of the paper is organized as follows. To pave the way for the derivations presented in the paper, we review the FBC principles in Section II. In Section III, we present the asyptotic equivalent channel odel between the obile terinals and the BS in an FBC assive IO setup. This analysis will lead to an upper bound for the SINR perforance of the syste. Our proposed prototype filter design ethod is introduced in Section IV. The atheatical analysis of the paper as well as the efficacy of the proposed filter design technique are nuerically evaluated in Section V. Finally, we conclude the paper in Section VI. Notations: atrices, vectors and scalar quantities are denoted by boldface uppercase, boldface lowercase and noral letters, respectively. [A] n represents the eleent in the th row and n th colun of A and A 1 signifies the inverse of A. I is the identity atrix of size. The superscripts T, H and indicate transpose, conjugate transpose, and conjugate operations, respectively. Also, represents the linear convolution, E{ } denotes the expected value of a rando variable, and R{ } signifies the real part of a coplex nuber. The notation CN0,σ represents the circularly-syetric coplex noral distribution with zero ean and variance σ. Finally, δ ij represents the Kronecker delta function. II. FBC PRINCIPLES We present the theory of FBC in discrete tie. Let d,n denote the real-valued data sybol transitted over the th subcarrier and n th sybol tie index. The total nuber of subcarriers is assued to be. To avoid the interference between the sybols and aintain the orthogonality, the data sybol d,n should be phase adjusted using the phase ter e jθ,n, where θ,n = π +n. Accordingly, each sybol has a ± π phase difference with its adjacent neighbors in tie and frequency. The sybols are then pulse-shaped using the prototype filter pl, which has been designed such that ql = pl p l is a Nyquist pulse with zero crossings at saple intervals. To express the above procedure in a atheatical for, the discrete-tie FBC wavefor can be written as, [15], where xl = + 1 n= =0 d,n a,n l, 1 a,n l = p l n/e jθ,n, and p l = ple j πl is the prototype filter odulated to the center frequency of subcarrier. The functions a,n l can be thought as a set of basis functions that are used to odulate the data sybols. Note that the spacing between successive sybols in the tie doain is / saples. In the frequency doain, the spacing between successive subcarriers is1/ in noralized frequency. It can be shown that the basis functions a,n l are orthogonal in the real doain, [15], i.e., { a,n l,a,n l + R = R l= a,n la,n l } = δ δ nn. Hence, the data sybols can be extracted fro the synthesized signal, xl, according to d,n = xl,a,n l R. 3 Fig. 1 shows the block diagra of the FBC transceiver. Note that considering the transitter prototype filter pl, and the receiver prototype filter p l, the overall effective pulse shape ql = pl p l is a Nyquist pulse by design. Also, in practice, in order to ipleent the synthesis transitter side and analysis receiver side filter banks efficiently, one can incorporate the polyphase ipleentation of filter banks to reduce the coputational coplexity, [15]. The presence of a frequency-selective channel incurs soe interference on the received sybols, and thus, one ay adopt soe sort of equalization to retrieve the transitted sybols at the receiver side. Let hl denote the ipulse response of the channel. In this paper, we liit our study to a case where the channel ipulse response reains tie invariant over the interval of interest. Hence, the received signal at the receiver can be expressed as L 1 yl = hl xl+νl = hlxl l+νl, 4 where L is the length of the channel ipulse response, and νl is the additive noise. At the receiver side, after atched filtering and phase copensation, and before taking the real part see Fig. 1, the deodulated signal y,n can be expressed as y,n = + 1 H,nn d,n +ν,n, 5

3 e jθ 0,n Synthesis filter bank Analysis filter bank e jθ 0,n d 0,n p 0 l p 0 l y 0,n R{ } ˆd 0,n e jθ 1,n e jθ 1,n d 1,n p 1 l Σ xl Ideal Channel yl p 1 l y 1,n R{ } ˆd 1,n e jθ 1,n e jθ 1,n d 1,n p 1 l p 1 l y 1,n R{ } ˆd 1,n Fig. 1. Block diagra of the FBC transceiver in discrete tie. where ν,n is the noise contribution, and the interference coefficient H,nn can be calculated according to H,nn = h n n e jθ,n θ,n, 6a h l = p l hl p l. 6b The sybol denotes deciation with the rate of. In 6, h l is the equivalent channel ipulse response between the transitted sybols at subcarrier and the received ones at subcarrier. This includes the effects of the transitter pulse-shaping, the ultipath channel, and the receiver pulse-shaping; see Fig. 1. According to 5, the deodulated sybol y,n undergoes interference originating fro other tie-frequency sybols. In practice, the prototype filter pl is designed to be well localized in tie and frequency. As a result, the interference is liited to a sall nuber of neighboring sybols around the desired tie-frequency point,n. In order to devise a siple equalizer to cobat the frequency-selective effect of the channel, it is usually assued that the sybol period, /, is relatively large copared to the channel length, L. With this assuption, the deodulated signal y,n can be expressed as, [16], y,n H d,n +u,n +ν,n, 7 where H L 1 πl hle j is the channel frequency response at the center of the th subcarrier. The ter u,n is called the intrinsic interference and is purely iaginary. This ter represents the contribution of the intersybol interference ISI and intercarrier interference ICI fro the adjacent tiefrequency sybols around the desired point, n. Based on 7, the effect of channel distortions can be copensated using a single-tap equalizer per subcarrier. After equalization, what reains is the real-valued data sybol d,n, the iaginary ter u,n, and the noise contribution. Finally, by taking the real part fro the equalized sybol, one can reove the intrinsic interference and obtain an estiate of d,n. It should be noted that the perforance of the above single-tap equalization priarily depends on the validity of the assuption that the sybol duration is uch larger than the channel length. However, in highly frequency-selective channels, where the above assuption is not accurate, ore advanced equalization ethods should be deployed to counteract the channel distortions, [10]. III. ASSIVE IO FBC: ASYPTOTIC ANALYSIS In this section, we extend the forulation of the previous section to assive IO channels to be used in our subsequent asyptotic analysis. Then, we show that linear cobining of the signals received at the BS antennas, using the channel frequency coefficients, leads to a residual interference even with an infinite nuber of BS antennas. Hence, the SINR is upper bounded by a certain deterinistic value, and arbitrarily large SINR perforances cannot be achieved as the nuber of BS antennas grows large. In the subsequent section, we show that this proble can be resolved through a siple prototype filter design ethod. We consider a single-cell assive IO setup [1], with K single-antenna obile terinals Ts that are siultaneously counicating with a BS equipped with an array of N antenna eleents. As entioned earlier, in this paper, we consider the uplink transission while the results and our proposed technique are trivially applicable to the downlink transission as well. Let x k l represent the transit signal of the terinal k. The received signal at the i th BS antenna can be obtained as y i l = K 1 k=0 x k l h i,k l+ν i l, 8 where h i,k l is the channel ipulse response between the k th terinal and the i th BS antenna, and ν i l is the additive noise at the input of the i th BS antenna. We assue that the saples of the noise signal ν i l are a set of independent and identically distributed i.i.d. CN0,σν rando variables and the channel tap h i,k l, l {0,...,L 1}, follows a CN0, ρl distribution. oreover, we assue that the channels corresponding to different terinals and different BS antennas are independent. Here, ρl,l = 0,...,L 1, is the channel power delay profile PDP. Throughout this

4 paper, we assue that the channel PDP is noralized such that L 1 ρl = 1. oreover, we assue that for each terinal, the average transitted power is equal to one, i.e., E{ x k l } = 1. As a result, considering the above channel odel, the signal-to-noise ratio SNR at the input of the BS antennas can be calculated as SNR = 1/σν. To siplify the analysis throughout the paper, we assue that the BS has a perfect knowledge of the channel state inforation CSI. Using 8 and extending 5 to the IO case, we have y,n = + 1 H,nn d,n +ν,n, 9 where the N 1 vector y,n contains the deodulated sybols across different BS antennas and corresponding to the,n tie-frequency point. The vector ν,n contains the noise contributions across different BS antennas. d,n contains the data sybols of all the Ts transitted at the point,n. H,nn is an N K atrix with its eleent ik, denoted by H i,k,nn, representing the interference coefficient corresponding to the channel h i,k l. The interference coefficient H i,k,nn can be calculated siilar to 6 as H i,k,nn = hi,k n n e jθ,n θ,n, 10a h i,k l = p l h i,k l p l. 10b We assue that the BS utilizes a single-tap equalizer per subcarrier. Cobining the eleents ofy,n through an N K cobining atrixw and taking the real part of the resulting signal, the estiate of the transitted data sybols for all the Ts can be obtained as } ˆd,n = R {W H y,n { + = R { + = R 1 1 W H H,nn d,n +WH ν,n } G,nn d,n +ν,n, 11 where G,nn WH H,nn, and ν,n WH ν,n. In this paper, we consider three linear cobiners, naely, axiu-ratio cobining RC, zero-forcing ZF, and iniu ean-square error SE. These cobiners can be obtained as, [], H D 1, for RC, W = H H H 1, H for ZF, 1 H H H 1, H +σνi K for SE, whereh is the atrix of channel coefficients at the center of th subcarrier, i.e., [H ] ik = H i,k L 1 h πl j i,kle. In the RC case, the K K noralization atrix D is a diagonal atrix that contains the squared nor of the k th colun of H on its k th diagonal eleent, i.e., [D ] kk = N 1 i=0 Hi,k. Note that according to the law of large nubers, D tends to NI K as the nuber of BS antennas increases. In the following and to siplify the } forulations, we only consider the case of RC. We then show that the results are also applicable to the cases of ZF and SE as the nuber of BS antennas grows large. Before we proceed, we review soe results fro probability theory. Let a = [a 1,...,a n ] T and b = [b 1,...,b n ] T be two rando vectors each containing i.i.d. eleents. oreover, assue thati th eleents ofaandbare correlated according to E { a i b i} = Cab, i = 1,...,n. Consequently, according to the law of large nubers, the rando variable 1 n ah b converges alost surely to C ab as n tends to infinity. In the asyptotic regie, i.e., as N tends to infinity, the eleents of G,nn = WH H,nn can be calculated using the law of large nubers. Let G kk,nn denote the eleent kk of G,nn. In the case of RC, as N grows large, G kk,nn converges alost surely to G kk,nn E { H i,k H i,k,nn }. 13 To calculate the right hand side of 13, we use 10 to find the equivalent channel ipulse response between the transitted data sybols and the received ones after cobining the signals across different BS antennas. To this end, as N grows large, the equivalent channel ipulse response between the transitted sybols at subcarrier of Tk and the received ones at subcarrier of T k tends to 1 g kk l E { H i,k = p l E } p l h i,k l p l { H i,k hi,k l} p l. 14 The above expression includes a correlation between the channel frequency coefficient H i,k and the channel ipulse response h i,k l. This correlation can be calculated as { H L 1 i,k hi,k E l} = E { h i,klh i,k l } e j πl where ρ l ρle j πl. = ρle j πl δkk = ρ lδ kk, 15 Proposition 1. In an FBC-based assive IO syste, as the nuber of BS antennas tends to infinity, the effects of ultiuser interference and noise vanish. However, soe residual ISI and ICI fro the sae user reain. In particular, for a given user k, the equivalent channel ipulse response between the transitted data sybols at subcarrier and the received ones at subcarrier tends to g kk l p l ρ l p l. 16 As a result, the SINR saturates to R { } G kk,nn SINR k,n + 1,n,n R { G kk,nn }, 17 1 Note that in 13 and 14, we have used the letters G and g, respectively, to denote the equivalent channel coefficients after cobining. On the other hand, letters H and h have been used in 10, to refer to the respective channel coefficients before cobining.

5 where G kk,nn = gkk n n e jθ,n θ,n. Proof. As suggested by 15, when k k, the channel response tends to zero. Hence, ultiuser interference fades away. A siilar arguent can be developed for the noise contribution. However, when k = k, which iplies the interference fro the sae user on itself, the channel response tends to 16. Notice that due to the presence of ρ l, the orthogonality condition of does not hold anyore even with an infinite nuber of BS antennas. Hence, soe residual ISI and ICI will reain and will cause the SINR to saturate at the level in 17. Although the above discussions and analysis was ade for RC, we note that Proposition 1 is valid for the ZF and SE cobiners as well. In particular, for the ZF and SE cobiners, one ay use the fact that due to the law of large 1 nubers, when N grows large, N HH H tends to I K, and hence the ZF and SE atrices in 1 tend to that of the RC, []. Thus, the sae asyptotic SINR value and channel ipulse response as for the RC can be obtained for the ZF and SE cobiners. IV. PROPOSED PROTOTYPE FILTER DESIGN ETHOD As discussed in the previous section, even with an infinite nuber of BS antennas, soe residual ICI and ISI reain due to the correlation between the cobining tap values and the channel ipulse responses between the Ts and the BS antennas. As a solution to this proble, in this section, we propose a prototype filter design ethod to reove the above correlation. In 16, the probleatic ter that leads to the saturation issue is the odulated channel PDP,ρ l. In the absence of this ter, the channel response g kk l = p l p l does not incur any interference and the orthogonality condition is copletely satisfied, provided that ql = pl p l is a Nyquist pulse. This observation suggests that we can odify the prototype filter used at the BS such that ql = pl ρl p l, 18 is still a Nyquist pulse. In 18, pl denotes the odified prototype filter. Applying a discrete-tie Fourier transfor DTFT to 18, we have Qω = Pω ρω P ω, 19 where ρω denotes the DTFT of ρl. We note that since ql = pl p l, we ay write Qω = Pω. Thus, Pω = Pω ρ ω. 0 Finally, applying an inverse-dtft to Pω will give us the ipulse response of the odified prototype filter, pl. The following proposition suarizes the above results. Proposition. The SINR saturation proble can be resolved by incorporating the odified prototype filter Pω = Pω ρ ω at the BS. Consequently, as N grows large, ISI and ICI in addition to the effects of ultiuser interference and noise tend to zero, and arbitrarily large SINR values can be achieved. Proof. Following 0, the equivalent channel ipulse response in 16 tends to that of an ideal channel. Hence, the effects of ICI and ISI will vanish asyptotically. Note that since the channels of different users are independent see 15, the effect of ultiuser interference still tends to zero with the odified prototype filter in place. A siilar arguent applies for the noise contribution. It is worth to ention a nuber of points here. First, we note that in the above approach, only the prototype filter used at the BS is odified and other parts of the FBC transceiver, including the cobining taps, will reain unchanged. Also, it should be noted that according to 0, the odified prototype filter depends on the channel PDP. Hence, the BS needs to estiate the channel PDP to be able to construct pl. Fortunately, in assive IO scenarios, the proble of channel PDP estiation is relatively easy and feasible. In particular, the channel PDP can be deterined by calculating the variance of channel ipulse responses across different BS antennas. As the nuber of BS antennas increases, according to the law of large nubers, this estiate becoes closer to the exact channel PDP. Last but not least, we note that in the above analysis, we did not ake any assuption about the flatness of the channel response over the bandwidth of the subcarriers. Thus, the result obtained in Proposition is valid for any frequency-selective channel. V. NUERICAL RESULTS In this section, we evaluate the analysis of the previous sections as well as the efficacy of our proposed prototype filter design ethod using coputer siulations. We let = 56 and assue there are K = 10 terinals in the network. The terinals use the PHYDYAS prototype filter, [17], with overlapping factor of 4, to synthesize their FBC signals. A noralized exponentially decaying channel PDP, ρl = e αl / L 1 e αl,l = 0...,L 1, with α = 0.1 and L = 40 is assued. At the BS side, a odified prototype filter designed according to 0 is used to analyze the received FBC signals across different antennas. Figs. and 3 present the tie and frequency responses, respectively, of the odified prototype filter and copare the against the original PHYDYAS filter. oreover, the sinc pulse, as the pulse-shape of the subcarriers in OFD, is shown in Fig. 3 as a reference. As shown, both prototype filters provide a significantly lower spectral leakage copared to the sinc pulse. It should be entioned that although the original and odified filters do not differ significantly in shape, they lead to copletely different SINR behaviors, as it is shown in the following. We next copare the SINR perforance of the FBC transission with and without prototype filter odification. Fig. 4 shows the average SINR with averaging over different channel realizations versus the nuber of BS antennas. The noise level is selected such that the SNR at the input of the BS

6 Fig.. Ipulse responses of the PHYDYAS and odified PHYDYAS filters Fig. 3. Frequency responses of the PHYDYAS and odified PHYDYAS filters and coparison with the sinc pulse Fig. 4. SINR perforance coparison. antennas is equal to 10 db. Fro Fig. 4 we can see that when the prototype filter is not odified, the SINR perforance of all three detectors, i.e., RC, ZF, and SE, tends to the saturation level predicted by 17 as N grows large. However, when we incorporate the odified prototype filter, the SINR grows without a liit by increasing N. Here, only the case of ZF detector is shown. Also, the SINR perforance of OFD with cyclic prefix CP-OFD and with ZF detector is shown as a benchark. There is a sall difference around 1.5 db between the SINR of CP-OFD and FBC with our proposed odified prototype filter. This is due to the fact that the presence of CP in OFD leads to a coplete reoval of all various interference coponents. In contrast, the FBC wavefor is designed to increase the bandwidth efficiency, by not including any CP overhead and providing uch lower out-of-band eission. VI. CONCLUSION In this paper, we studied the perforance of FBC transission in the context of assive IO. We considered single-tap equalization per subcarrier using the conventional linear cobiners, i.e., RC, ZF, and SE. One of our findings in this paper was that the correlation between the cobining tap values and the channel ipulse responses leads to an interference which does not fade away as the BS array size increases. Therefore, the SINR is upper-bounded by a certain deterinistic value and arbitrarily large SINR values cannot be achieved. We derived an analytical expression for this upper bound, identified the source of SINR saturation, and proposed a prototype filter design ethod to reove the above correlation and resolve the proble. REFERENCES [1] T. L. arzetta, Noncooperative cellular wireless with unliited nubers of base station antennas, IEEE Transactions on Wireless Counications, vol. 9, no. 11, pp , 010. [] H. Q. Ngo, E. G. Larsson, and T. L. arzetta, Energy and spectral efficiency of very large ultiuser IO systes, IEEE Transactions on Counications, vol. 61, no. 4, pp , 013. [3]. Iwaura, K. Etead,.-H. Fong, R. Nory, and R. Love, Carrier aggregation fraework in 3GPP LTE-advanced [WiAX/LTE update], IEEE Counications agazine, vol. 48, no. 8, pp , 010. [4] P. Banelli, S. Buzzi, G. Colavolpe, A. odenini, F. Rusek, and A. Ugolini, odulation forats and wavefors for 5G networks: Who will be the heir of OFD?: An overview of alternative odulation schees for iproved spectral efficiency, IEEE Signal Processing agazine, vol. 31, no. 6, pp , 014. [5] B. Farhang-Boroujeny and H. oradi, OFD inspired wavefors for 5G, IEEE Counications Surveys & Tutorials, 016. [6] F. Schaich and T. Wild, Wavefor contenders for 5G - OFD vs. FBC vs. UFC, in IEEE ISCCSP 014. [7] A. Farhang, N. archetti, F. Figueiredo, and J. P. iranda, assive IO and wavefor design for 5th generation wireless counication systes, in IEEE 5GU, 014. [8] B. Farhang-Boroujeny, OFD versus filter bank ulticarrier, IEEE Signal Processing agazine, vol. 8, no. 3, pp. 9 11, 011. [9] A. Ainjavaheri, A. Farhang, A. RezazadehReyhani, and B. Farhang- Boroujeny, Ipact of tiing and frequency offsets on ulticarrier wavefor candidates for 5G, in IEEE SP/SPE 015. [10] A. I. Pérez-Neira,. Caus, R. Zakaria, D. Le Ruyet, E. Kofidis,. Haardt, X. estre, and Y. Cheng, IO signal processing in offset-qa based filter bank ulticarrier systes, IEEE Transactions on Signal Processing, vol. 64, no. 1, pp , 015. [11] A. Farhang, N. archetti, L. E. Doyle, and B. Farhang-Boroujeny, Filter bank ulticarrier for assive IO, in 014 IEEE 80th Vehicular Technology Conference VTC014-Fall, 014, pp [1] A. Ainjavaheri, A. Farhang, N. archetti, L. E. Doyle, and B. Farhang- Boroujeny, Frequency spreading equalization in ulticarrier assive IO, in IEEE ICC, 015. [13] A. Farhang, A. Ainjavaheri, N. archetti, L. E. Doyle, and B. Farhang- Boroujeny, Pilot decontaination in CT-based assive IO networks, in IEEE ISWCS, 014. [14] B. Saltzberg, Perforance of an efficient parallel data transission syste, IEEE Transactions on Counication Technology, vol. 15, no. 6, pp , [15] B. Farhang-Boroujeny, Filter bank ulticarrier odulation: A wavefor candidate for 5G and beyond, Advances in Electrical Engineering, 014. [16] C. Lélé, J.-P. Javaudin, R. Legouable, A. Skrzypczak, and P. Siohan, Channel estiation ethods for preable-based OFD/OQA odulations, European Transactions on Telecounications, 008. [17]. Bellanger, D. Le Ruyet, D. Roviras,. Terré, J. Nossek, L. Baltar, Q. Bai, D. Waldhauser,. Renfors, T. Ihalainen et al., FBC physical layer: a prier, PHYDYAS, January, 010.