FBMC/OQAM for the Asynchronous Muti-User MIMO Upin Yao Cheng, Peng Li, and Martin Haardt Communications Research Laboratory, Imenau University of Technoogy P. O. Box 100565, D-98694 Imenau, Germany {y.cheng, peng.i, martin.haardt}@tu-imenau.de http://tu-imenau.de/cr Abstract In this paper, we evauate the performance of fiter ban-based muti-carrier with offset quadrature ampitude moduation (FBMC/OQAM) for the muti-user mutipe-input mutipe-output (MIMO) upin in the presence of timing and frequency misaignments. In such a scenario, mutipe access is achieved by assigning groups of sub-carriers to user nodes. The nodes are equipped with mutipe antennas, and different frequency seective channe modes are considered. In addition, a comparison with orthogona frequency division mutipexing with the cycic prefix insertion (CP-OFDM) as the currenty widey used muti-carrier scheme is presented. The greater robustness of FBMC/OQAM against a ac of synchronization in the time and the frequency domain compared to CP-OFDM is shown via extensive numerica resuts. I. INTRODUCTION Regarded as a promising aternative muti-carrier scheme to orthogona frequency division mutipexing with the cycic prefix insertion (CP-OFDM), fiter ban-based muti-carrier moduation (FB-MC) has recenty received great research attention. By adopting spectray we-contained synthesis and anaysis fiter bans in the transmutipexer configuration [1], [2], FB-MC reduces the sideobes and avoids a high eve of out-of-band radiation which CP-OFDM suffers from. Moreover, the insertion of a CP is not required in systems empoying fiter ban-based muti-carrier with offset quadrature ampitude moduation (FBMC/OQAM), eading to a higher spectra efficiency compared to CP-OFDM-based systems. These advantages of FB-MC gives rise to its potentia appications in, for instance, cognitive radio and professiona mobie radio (PMR) networs, where an effective utiization of the avaiabe fragmented spectrum is needed [3]. In muti-user mutipe-input mutipe-output (MIMO) upin transmissions, perfect synchronization in the time domain and the frequency domain can hardy be guaranteed. It is generay nown that CP-OFDM fais to provide a satisfactory performance in such scenarios, since the timing and frequency misaignments resut in a oss of orthogonaity between the sub-carriers and ead to mutipe access interference as we. To resove these probems, timing offset and frequency offset compensation techniques may be empoyed, and interference canceation agorithms may aso be incorporated to further aeviate the performance degradation. However, these methods unavoidaby induce a heavier computationa burden and may require additiona information exchange which decreases the spectra efficiency. On the other hand, the FB-MC scheme features a we-ocaized spectrum and is more robust against asynchronism compared to CP-OFDM. In [4], it is numericay shown that FBMC/OQAM-based systems are ess sensitive to synchronization errors in upin transmissions than CP- OFDM systems considering singe-antenna user nodes and additive white Gaussian noise (AWGN) channes. Moreover, the authors of [5] arrive at the concusion that FBMC/OQAMbased systems are more robust against carrier frequency offsets compared to CP-OFDM on the upin of mutipe access networs with singe antenna user nodes. In this wor, our focus is aso on FB-MC-based systems that empoy FBMC/OQAM. Here the rea and imaginary parts of each compex-vaued data symbo are staggered by haf of the symbo period [1]. Therefore, the desired signa and the intrinsic interference caused by symbos transmitted on adjacent sub-carriers and time instants are separated in the rea domain and the pure imaginary domain, respectivey [6]. We consider a muti-user upin scenario in the presence of symbo timing offsets or residua carrier frequency offsets, and the user nodes are assigned different groups of sub-carriers to achieve the mutipe access. A nodes are equipped with mutipe antennas, and different frequency seective channe modes are considered. Linear MMSE receiver-based processing is empoyed at the access point (AP) to recover signas from each user node. Comparative performance evauations of FBMC/OQAM and CP-OFDM are carried out. Extensive simuation resuts demonstrate that FBMC/OQAM systems are more robust against timing and frequency misaignments in contrast to CP-OFDM systems. The remainder of the paper is organized as foows. Section II presents an overview of muti-user MIMO upin transmissions, and the data mode is given taing into account the presence of symbo timing offset or the effects of residua carrier frequency offsets. Moreover, the difference between FBMC/OQAM and CP-OFDM is discussed. In Section III, we further describe the receive processing technique that is empoyed in this wor. Numerica experiments and resuts are presented in Section IV, before concusions are drawn in Section V. II. SCENARIO DESCRIPTION AND DATA MODEL We consider a muti-carrier upin mutipe access scenario, where U users each assigned a group of sub-carriers transmit signas to a singe AP simutaneousy. The AP is equipped with Q receive antennas, and the u-th user node has P u transmit antennas, u = 1,2,...,U. The transmitted signas from each user suffer from frequency seective fading characteristics of
muti-path channes. A boc-wise fashion of the sub-carrier aocation is adopted. In Fig. 1, we iustrate an exampe for the two-user case. User 1 occupies the sub-carriers with indices = 0,1,...,M 1 1, and User 2 transmits on the sub-carriers with indices = M 1 +G,...,M 1 +M 2 +G 1, where M u denotes the number of sub-carriers aocated to the u-th user, and G represents the number of sub-carriers as the guard band. In case of more than two users, the sub-carrier aocation can be simiary defined except for the fact that mutipe guard bands are empoyed such that adjacent sub-carrier bocs are separated. Ampitude Fig. 1. case user1 guard band user2 subcarrier number(freq.) Iustration of the boc-wise sub-carrier aocation for the two-user In the foowing subsections, the data mode of the mutiuser MIMO upin is given where the symbo timing offsets and residua carrier frequency offsets are taen into account. The difference between an FBMC/OQAM-based system and a CP-OFDM-based system is aso pointed out and refected in the introduction of the data mode. A. Symbo timing offsets In the presence of symbo timing offset, the received signa at the q-th receive antenna of the AP, where q = 1,2,...,Q, can be expressed as r q (t) = U P u h (u) pq (t) s (u) p (t t u )+n q (t), (1) u=1 p=1 where denotes the convoution operation, and h (u) pq (t) means the frequency seective channe impuse response on the in between the p-th transmit antenna of the u-th user and the q-th receive antenna of the AP. At each user node, fu mutipexing is considered, i.e., the number of data streams transmitted by the u-th user equas the number of transmit antennas P u. The muti-carrier signa transmitted at the p-th antenna of the u-th user is denoted by s (u) p (t), and it is obtained by either a CP- OFDM/QAM moduator or an FMBC/OQAM moduator as introduced in Section II-C. Moreover, we use t u to denote the symbo timing offset of the u-th user. The noise term n q (t) is modeed as a circuar symmetric compex Gaussian process with zero mean, and the noise power spectra density is denoted by N 0. Empoying a muti-carrier moduation scheme and aowing users to transmit on different sub-carrier groups contribute to the orthogonaity between the transmissions on different subcarriers and an isoation of different users. Nevertheess, as it is very difficut to ensure that the signas from different users arrive at the AP simutaneousy, the exact symbo-timing is not usuay sufficienty warranted. This may heaviy degrade the performance due to the adjacent channe interference resuting from the oss of the orthogonaity. B. Residua carrier frequency offsets In this paper we define the normaized carrier frequency offset as the ratio of the frequency mismatch and the subcarrier spacing. Thereby, the received signa at the q-th receive antenna of the AP, where q = 1,2,...,Q, in the presence of carrier frequency offsets is written as r q (t) = U u=1 e j 2πηut T P u p=1 h (u) pq (t) s (u) p (t)+n q (t), (2) wheret denotes the symbo duration, andη u is the normaized carrier frequency offset of the u-th user. Here perfect synchronization in the time domain is assumed. Muti-carrier systems carry information data on frequency orthogona sub-carriers for parae transmissions to combat the distortion caused by frequency seective fading channes. However, for practica impementations, the orthogonaity between sub-carriers is not guaranteed due to frequency synchronization errors. Consequenty, the performance might be significanty degraded. Note that carrier frequency offsets can be estimated by using training symbos in both CP-OFDM and FBMC/OQAM-based transmissions. For instance, a maximum ieihood estimator in the frequency domain was investigated in [7], and it heps in compensating carrier frequency offsets caused by phase noise, Dopper frequency shift and physica imitations of osciators. However, a perfect estimation of the carrier frequency offset is sti unavaiabe, and the residua carrier frequency offsets remain. C. Muti-carrier moduation by using FBMC/OQAM and CP- OFDM For simpicity of notation, we ignore the user index u and the data stream index p, and the CP-OFDM moduated symbo is given as s(t) = M 1 =0 S()e j2πf t, (3) where S() denotes the narrowband QAM symbo transmitted on the -th subcarrier, f represents the corresponding carrier frequency, and M is the number of sub-carriers. Each subcarrier component of a CP-OFDM symbo with the effective duration of T sym (incuding the duration of the CP) can be considered as a narrowband signa within a rectanguar samping window of ength T sym. The rectanguar window eads to a sinc function in the frequency domain. In CP-OFDM systems, the power spectrum of a set of these frequency separated sinc functions produces out-of-band power. If the user nodes are not perfecty synchronized, significant interference wi be piced up by adjacent sub-channes. A guard band in the frequency domain can be inserted between the sub-channes to reduce the effect of channe interference at the price of a further oss of spectra efficiency.
In case of FBMC/OQAM systems, OQAM is empoyed and the transmitter buids the signa as [1] s(t) = M/2 1 =0 n ( R{S(2)}g(t nt)+ ji{s(2)}g(t nt T )e 2 ) j2π(2)f2t + ( R{S(2 +1)}g(t nt T 2 )+ ) ji{s(2 +1)}g(t nt) e j2π(2+1)f2+1t, where n is the tap index of the puse shaping fiter g(t). The items R{S()} and I{S()} denote the rea and imaginary parts of the QAM compex-vaued symbos, respectivey. The in-phase and quadrature components of the QAM signa have a time offset of haf a symbo period. A set of spectray we contained synthesis and anaysis fiter bans is considered in the FBMC/OQAM transmission systems. One of the common approaches is to use moduated uniform poyphase fiter bans based on prototype fiter design, and the system spectra characteristics are determined by the prototype fiter. By empoying FBMC/OQAM, the side obes of the muti-carrier components can be significanty reduced [8], and the insertion of a CP is not required. III. RECEIVE PROCESSING At the AP, assuming that the signas from the U users are perfecty separated, receive processing techniques for pointto-point MIMO FBMC/OQAM systems can be empoyed. Considering that the channe on each sub-carrier can be treated as fat fading, the received signa on the -th sub-carrier and at the n-th time instant from the u-th user is written as foows y (u) [n] =H(u) [n]d(u) [n]+ n+3 +1 i=n 3= 1 H (u) [i]c i d (u) [i] (4) +n (u) [n], (,i) (,n), (5) where d (u) [n] RPu is the desired signa from the u-th user on the -th sub-carrier and at the n-th time instant when (+ n) is even 1. The terms c i d (u) [i] contribute to the intrinsic interference and are pure imaginary, where = 1,,+1, i = n 3,...,n + 3, and (,i) (,n). The coefficients c i represent the system impuse response determined by the synthesis and anaysis fiters. The PHYDYAS prototype fiter [8] is used, and the overapping factor is chosen to be K = 4. For more detais about FBMC/OQAM systems, the reader is referred to [9]. Here H (u) [n] CQ Pu contains the frequency responses of the channes between each transmit antenna of the u-th user and each receive antenna of the AP, and n (u) [n] denotes the additive white Gaussian noise vector with variance σ 2 n. In severa pubications on MIMO FBMC/OQAM systems, such as [10] and [11], it is assumed that the channes on 1 For the case where (+n) is odd, the desired signa on the -th sub-carrier and at the n-th time instant is pure imaginary, whie intrinsic interference is rea. As the two cases are essentiay equivaent to each other, we ony tae the case where ( +n) is even to describe the receive processing empoyed in this paper. adjacent sub-carriers are amost the same. The received signa on the -th sub-carrier and at the n-th time instant from the u-th user can be accordingy written as d (u) y (u) (u) [n] =H(u) [n] d [n]+n(u) [n], (6) where [n] contains the rea-vaued desired signa and the pure imaginary interference d (u) [n] = d(u) [n]+ n+3 (u) d +1 i=n 3= 1 c i d (u) [i], (,i) (,n). Considering [n] as an equivaent transmitted signa, (6) resembes the data mode of a MIMO CP-OFDM system. Consequenty, transmission strategies that have been deveoped for MIMO CP-OFDM systems can be straightforwardy extended to MIMO FBMC/OQAM systems where ony one additiona step is required, i.e., taing the rea part of the resuting signa. In this wor, a inear MMSE receiver is empoyed, and the recovered desired signa from the u-th user is then obtained as where W [n] C Q Pu. (7) ˆd (u) [n] = R { W H [n]y (u) [n] }, (8) It is worth noting that the two-step receiver proposed in [11] can aso be appied to further enhance the performance. By combining inear processing and widey inear processing, the two-step receiver expoits the non-circuarity of the signas of an FBMC/OQAM system. IV. SIMULATION RESULTS In this section, we present numerica resuts with respect to the comparison between CP-OFDM and FBMC/OQAM in asynchronous muti-user MIMO upin settings. The muticarrier scheme-reated parameters are set according to those for LTE 5 MHz transmissions. The sub-carrier spacing is 15 Hz, and the FFT size is 512. Here the CP ength for CP- OFDM is set tot/8. In case of FBMC/OQAM, the PHYDYAS prototype fiter [8] is used, and the overapping factor is chosen as K = 4. In a exampes, we empoy the inear MMSE-based receive processing that is described in detai in Section III. A. Upin transmissions with symbo timing offsets First, we consider a 2-user scenario where the two users and the base station are each equipped with two antennas. A boc-wise sub-carrier aocation scheme as iustrated in Fig. 1 is adopted. The ITU Pedestrian-A channe mode [12] is used in the simuations. Assuming perfect synchronization in the time domain and in the frequency domain, we present the bit error rate () performances of CP-OFDM and FBMC/OQAM in Fig. 2. Note that the SNR here represents E b /N 0. It can be observed that when no guard band is empoyed, the performance of FBMC/OQAM becomes worse than that of CP-OFDM in the high SNR regime. The reason is that without a guard band the ast sub-carrier of the first user is interfered by the transmission of its adjacent sub-carrier which beongs to the second user and experiences a different channe, whie in the receive processing presented in Section III the channe is treated as the same for the desired symbo on
FBMC CP OFDM FBMC, GB = 1 10 4 Fig. 2. Comparison between FBMC/OQAM and CP-OFDM for a 2-user upin scenario considering perfect synchronization in the time domain and in the frequency domain (GB - guard band in the number of sub-carriers) each sub-carrier and the intrinsic interference. It aso appies to the detection of the signa on the first sub-carrier of the second user. This fact resuts in the performance degradation of FBMC/OQAM. On the other hand, when empoying one subcarrier as guard band, the aforementioned probem is soved, and the transmissions of the two users are we separated. The corresponding resuts shown in Fig. 2 compy with this argument. We now continue to examine an unsynchronized scenario as described in Section II-A where the symbo timing offset with respect to each user is assumed to be in the range of (T/8,T/4). The other parameters and settings are the same as introduced in previous text. Fig. 3 shows the performances of CP-OFDM and FBMC/OQAM in the presence of symbo timing offsets. The impacts of different sizes of the guard band on CP-OFDM and FBMC/OQAM are iustrated, respectivey. It can be seen that when there is no guard CP OFDM, ITU Ped A, GB = 0 CP OFDM, ITU Ped A, GB = 1 CP OFDM, ITU Ped A, GB = 10 FBMC, ITU Ped A, GB = 0 FBMC, ITU Ped A, GB = 1 FBMC, ITU Ped A, GB = 10 improvement is observed in case of FBMC/OQAM, whie for CP-OFDM the gain compared to the zero-guard-band case is negigibe. As the size of the guard band is increased to 10 sub-carriers, we can ony see a very sight improvement for CP-OFDM, and it sti suffers from an error foor. On the other hand, it can be observed that for FBMC/OQAM when one sub-carrier is used as the guard band, the performance is as good as that in the case of 10 sub-carriers. These resuts corroborate the theory that as FBMC/OQAM systems are endowed with an agie spectrum, guard bands with very sma sizes suffice to isoate groups of sub-carriers for different users or services. In addition, by comparing the resuts in Fig. 3 to those in Fig. 2, it can be noticed that for the case of FBMC/OQAM the performance degradation compared to the perfect synchronization scenario is quite sma. By contrast, such a performance gap for the CP-OFDM-based system is much more significant. We further show resuts for a 4-user scenario in Fig. 4. The other simuation parameters are same as described in CP OFDM, ITU Ped A, GB = 0 CP OFDM, ITU Ped A, GB = 1 CP OFDM, ITU Ped A, GB = 10 FBMC, ITU Ped A, GB = 0 FBMC, ITU Ped A, GB = 1 FBMC, ITU Ped A, GB = 10 Fig. 4. Comparison between FBMC/OQAM and CP-OFDM for a 4-user upin scenario in the presence of symbo timing offsets in the range of (T/8,T/4) (GB - guard band in the number of sub-carriers) the first experiment. Simiar observations can be made that FBMC/OQAM is more robust against symbo timing offsets compared to CP-OFDM. Moreover, the size of the guard band required to separated different groups of sub-carriers is substantiay smaer than that for CP-OFDM. 10 4 Fig. 3. Comparison between FBMC/OQAM and CP-OFDM for a 2-user upin scenario in the presence of symbo timing offsets in the range of (T/8,T/4) (GB - guard band in the number of sub-carriers) band, FBMC/OQAM significanty outperforms CP-OFDM. With a singe sub-carrier as the guard band, a performance B. Upin transmissions with residua carrier frequency offsets Next we compare CP-OFDM with FBMC/OQAM in an upin scenario where the residua carrier frequency offset is present by means of numerica simuations. In the first exampe, a 2-user scenario is considered. The two users and the base station are each equipped with two antennas, and the boc-wise sub-carrier aocation scheme is adopted. The ITU Vehicuar-A channe mode [12] is used in the simuations. Moreover, the users are assumed to be perfecty synchronized in the time domain. Fig. 5 shows the performances of CP-OFDM and FBMC/OQAM in the presence of the residua carrier frequency offset. As the maximum possibe vaue of the
residua carrier frequency offset is increased to 0.15, we observe a significant performance degradation for CP-OFDM due to inter-carrier interference. By comparison, FBMC/OQAM shows a greater robustness against frequency misaignments, as the performance oss is much smaer compared to that of CP- OFDM when the residua carrier frequency offset increases. Meanwhie, FBMC/OQAM outperforms CP-OFDM in both cases. FBMC, residua CFO ( 0.1 0.1), ITU Veh A CP OFDM, residua CFO ( 0.1, 0.1), ITU Veh A FBMC, residua CFO ( 0.15 0.15), ITU Veh A CP OFDM, residua CFO ( 0.15 0.15), ITU Veh A FBMC, residua CFO ( 0.1 0.1), ITU Veh A CP OFDM, residua CFO ( 0.1 0.1), ITU Veh A FBMC, residua CFO ( 0.15 0.15), ITU Veh A CP OFDM, residua CFO ( 0.15 0.15), ITU Veh A Fig. 6. Comparison between FBMC/OQAM and CP-OFDM for a 4-user upin scenario in the presence of residua carrier frequency offsets Fig. 5. Comparison between FBMC/OQAM and CP-OFDM for a 2-user upin scenario in the presence of residua carrier frequency offsets Second, a 4-user scenario is investigated. The other simuation parameters are the same as in the first exampe. The corresponding resuts are iustrated in Fig. 6. Simiary, it can be seen that CP-OFDM is more sensitive to the residua carrier frequency offset compared to FBMC/OQAM. When the residua carrier frequency offset is increased, the gap of performances between FBMC/OQAM and CP-OFDM is arger. It shoud be noted that in addition to the frequency misaignment, another factor that affects the performance of FBMC/OQAM is the muti-path channe considered in this exampe. If the channe deay spread is greater than the muti-carrier symbo period, the transmission suffers from inter symbo interference. Nevertheess, the receive processing technique empoyed in this wor as described in Section III (actuay a one-tap equaizer) is a straightforward extension of the inear MMSE receiver in CP-OFDM systems. It does not suffice to provide a satisfactory performance. When a mutitap equaizer [13] is used for FBMC/OQAM, a performance improvement can be expected. V. CONCLUSION Our focus in this contribution is on the performance evauation of FBMC/OQAM in muti-user MIMO upin scenarios suffering from a ac of perfect synchronization in the time domain and the frequency domain. Without imiting our investigations to the case of singe-antenna nodes or the AWGN channe as in [4], we present a thorough overview of muti-carrier muti-user MIMO upin transmissions taing into consideration the effects of timing and frequency misaignments. Through extensive simuation resuts, it is shown that FBMC/OQAM systems are more robust against symbo timing offsets compared to CP-OFDM. For FBMC/OQAM, one-sub-carrier guard bands are sufficient to achieve a good isoation of sub-carrier groups beonging to different users, which corroborates the theoretica anaysis. On the other hand, CP-OFDM-based systems sti suffer from performance degradation, though substantiay arger guard bands are empoyed. In addition, it is aso demonstrated that FBMC/OQAM is more immune to residua carrier frequency offsets than CP- OFDM that may require additiona efforts in combating the mutipe access interference due to frequency misaignments. For the purpose of comparison, CP-OFDM is aso discussed and considered in the numerica experiments. ACKNOWLEDGMENT The authors gratefuy acnowedge the financia support by the European Union FP7-ICT project EM- PhAtiC (http://www.ict-emphatic.eu) under grant agreement no. 318362 and fruitfu discussions with the project partners. REFERENCES [1] P. Siohan, C. Sicet, and N. Lacaie, Anaysis and design of OFDM/OQAM systems based on fiterban theory, IEEE Transactions on Signa Processing, vo. 50, no. 5, pp. 1170 1183, May 2002. [2] M. G. Beanger, Specification and design of a prototype fiter for fiter ban based muticarrier transmission, in Proc. IEEE Int. Conf Acoustics, Speech, and Signa Processing, Sat Lae City, USA, May 2001. [3] M. Renfors, F. Bader, L. Batar, D. Le Ruyet, D. Roviras, P. Mege, and M. Haardt, On the use of fiter ban based muticarrier moduation for professiona mobie radio, in Proc. 77th IEEE Vehicuar Technoogy Conf. (VTC 2013 Spring), June 2013. [4] T. Fusco, A. Petrea, and M. Tanda, Sensitivity of muti-user fiterban muticarrier systems to synchronization errors, in Proc. ISCCSP, Mar. 2008. [5] H. Saeedi-Sourc, Y. Wu, J. W. M. Bergmans, S. Sadri, and B. Farhang- Boroujeny, Compexity and performance comparison of fiter ban muticarrier and OFDM in upin of muticarrier mutipe access networs, IEEE Transactions on Signa Processing, vo. 59, no. 4, pp. 1907 1912, Apr. 2011. [6] M. Beanger, FBMC physica ayer: A primer, Jun. 2010.
[7] P. H. Moose, A technique for orthogona frequency division mutipexing frequency offset correction, IEEE Transactions on Communications, vo. 42, pp. 2908 2914, 1994. [8] FP7-ICT Project PHYDYAS - Physica Layer for Dynamic Spectrum Access and Cognitive Radio. http://www.ict-phydyas.org.,,. [9] M. G. Beanger, FBMC physica ayer: a primer, June 2010. [10] R. Zaaria, D. e Ruyet, and M. Beanger, Maximum Lieihood Detection in spatia mutipexing with FBMC, in Proc. 2010 European Wireess, June 2010. [11] Y. Cheng and M. Haardt, Widey Linear Processing in MIMO FBMC/OQAM Systems, in Proc. ISWCS 2013, Aug. 2013. [12] ITU-R Recommendation M.1225, Guideines for evauation of radio transmission technoogies for IMT-2000, 1997. [13] D. S. Wadhauser, L. G. Batar, and J. A. Nosse, MMSE subcarrier equaization for fiter ban based muticarrier systems, in Proc. IEEE 9th Worshop Signa Processing Advances in Wireess Communications (SPAWC), Juy 2008.