1 A New Data-Aided Synchronization Scheme for FBMC-OQAM Systems Xiadong Liu, Daiming Qu, Tao Jiang Wuhan National Laboratory for Optoelectronics, School of Electronics Information and Communications, Huazhong University of Science and Technology, Wuhan, China. E-mail: xiadongliu@hust.edu.cn, qudaiming@hust.edu.cn, tao.jiang@ieee.org Abstract—Although the Filter bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) systems are robust against double selective fading channels, it unfortunately is still sensitive to timing offset and carrier frequency offset (CFO) errors. To solve this synchronization problem, in this paper, we propose a new data-aided timing and CFO synchronization scheme, that exploits the conjugate-symmetry property of a properly designed training sequence. In addition, the sliding window algorithm is applied to the proposed scheme to further improve synchronization performance in multipath fading chan- nels. Simulation results verify that the proposed scheme achieves good performance in AWGN channel and multipath fading channels, in terms of timing capture probability, minimum- square-error (MSE) of timing offset and CFO estimation and bit error rate (BER) versus signal-to-noise ratio (SNR). Moreover, it can achieve timing and frequency synchronization independently in steps with relatively lower implementation complexity. Keywords—FBMC-OQAM, Data-aided timing and CFO syn- chronization scheme, conjugate-symmetry property, sliding win- dow algorithm, lower implementation complexity. I. INTRODUCTION Recently, Filter bank multicarrier with offset quadrature amplitude modulation (FBMC-OQAM) have been attracting increasing attention, as a promising alternative to the con- ventional orthogonal frequency division multiplexing (OFDM) technique [1], [2]. Due to the use of the pulse shaping filter on each subcarrier, FBMC-OQAM systems have lower spectral sidelobes than OFDM systems [3]. In addition, compared to OFDM, FBMC-OQAM does not require the insertion of cyclic prefix (CP) [4], resulting in higher spectral efficiency. As a result, the FBMC-OQAM has been viewed as a promising physical layer technique for 5G wireless networks [5]. However, like all other multicarrier modulation schemes, FBMC-OQAM systems are in general more sensitive to syn- chronization errors than single-carrier systems [6]. In spite of the advantage of having well-localized filters, timing offset and carrier frequency offset (CFO) are very critical to the performance of the FBMC-OQAM system. The performance Copyright (c) 2016 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org. This work was supported in part by National High Technology Development 863 Program of China under Grant 2015AA01A710, the National Science Foundation (NSFC) for Distinguished Young Scholars of China with Grant number 61325004, the NSFC with Grant numbers 61301129, 61571200, the Key Project of Hubei Province in China with Grant 2015BAA074, the open research fund of National Mobile Communications Research Laboratory, , and Southeast University under Grant 2014D09. degradation resulting from synchronization errors is much more severe in low SNR scenarios due to the residual in- terference. In addition, the existence of CFO destroys the or- thogonality among subcarriers, then introduces inter-subcarrier interference (ICI). Therefore, a more accurate and reliable synchronization method must be proposed. Several synchronization algorithms have been investigated in connection with FBMC-OQAM systems. Among them, two categories were addressed. One category is blind schemes. A blind joint symbol timing and CFO estimator was firstly proposed by exploiting the unconjugated cyclostationarity of the received OFDM/OQAM signal [7]. Then, a blind CFO estimator based on the linear unbiased estimation principle was proposed in [8]. But the blind estimators requires wide observation window with long processing delay. Usually, we adopt data-aided schemes. Based on the identical structure of the training sequence, the TR1 and TR2 methods were firstly derived in [9]. Then, the MLS algorithm based on the least squares (LS) approach was investigated in [10]. Considering about multipath channels, the WBS scheme in [11] based on sliding window was proposed. The arrival time of the first path can be almost surely located in the WBS scheme, whatever the channel power profile is. However, the above schemes usually should jointly consider time and frequency synchronization, that is to say, timing offset estimation and CFO estimation are needed to conduct at the same time. This may bring relatively higher implementation complexity for synchronization. In this paper, we propose a new data-aided synchronization scheme, that exploits the conjugate-symmetry property of a properly designed training symbol. In multipath channels, we apply the sliding window algorithm to improve the synchro- nization performance. Moreover, the proposed scheme can acheive timing and frequency synchronization independently in steps, thus making the implementation complexity relatively lower. The derived estimator does not require the knowledge of the prototype filter with robust acquisition properties. The rest of this paper is organized as follows. In section II, after describing the system model of FBMC-OQAM systems, the receive signal model in the presence of timing offset and CFO and the detailed implement diagram of timing and carrier frequency synchronization are reviewed. In section III, the proposed timing offset and CFO estimation method is derived. The simulation results are finally presented in section IV and the conclusion is given in section V. 978-1-5090-2860-3/16/$31.00 ©2016 IEEE

2 Fig. 1. The equivalent baseband diagram of an FBMC-OQAM system. II. SYSTEM MODEL B. Review of Synchronization Procedure A. FBMC-OQAM System Model As shown in Fig. 1, we consider the equivalent baseband diagram of an FBMC-OQAM system, in which the subcarrier number is M and subcarrier spacing is 1/T , with T being the complex symbol interval. The transmitted symbol is real- valued with frequency index m and time index n, and T /2 is the interval of real-valued symbols. am,2k and am,2k+1 are obtained by taking the real and imaginary parts of a complex- valued symbol from 22K-quadrature amplitude modulation (QAM) constellation, respectively. g(k) is a symmetrical real- valued pulse shaping filter, with the length KM, K is over- lapping factor, usually takes as 4. We denote basis function as gm,n(k) = gk − n M ej2πmk/M ej(m+n)π/2. Therefore, the equivalent baseband FBMC-OQAM signal is written as 2 M−1 ej2πmk/M ej(m+n)π/2 . (1) k − n s (k) = am,n g M 2 gm,n(k) m=0 n∈Z In FBMC-OQAM systems, we denote ∞ k=0 ζ p,q m,n = gm,n(k)g∗ p,q(k). (2) In this part, we would have a detailed review of the received signal model in the presence of timing offset and CFO and the implement diagram of timing and carrier frequency synchronization. For brevity, we firstly take no account of the influence of channel. In the presence of the normalized timing offset τ and CFO ∆f, the received signal in AWGN channel can be written as r(k) = s(k − τ )ej2π∆f·k/M + n(k), (5) where s(k) is the transmitted FBMC-OQAM signal and n(k) denotes the zero-mean circular complex white Gaussian noise n. with power spectral σ2 In general, timing offset as well as carrier frequency offset exists in FBMC-OQAM systems. Usually we may adopt data- aided scheme based on training sequences. As shown in Fig. 2, we compare the implement diagram of proposed scheme with traditional schemes. In traditional synchronization schemes, we usually jointly consider time and frequency synchroniza- tion, i.e., timing offset estimation and CFO estimation are needed to conduct at the same time, such as the TR1, TR2 and WBS scheme. Compared with traditional synchronization schemes, we achieve timing and frequency synchronization independently in steps in this paper. In detail, in the first m,n = 1. Or ζ p,q Note that when (m, n) = (p, q), ζ p,q m,n is an imaginary-valued number. Specially, when |p − m| > 1 or |q− n| > 1, it can be considered that ζ p,q m,n ≈ 0 [2]. In FBMC- OQAM systems, the orthogonality condition can be written as 1 m = p, n = q ∞ gm,n(k)g∗ = δm,pδn,q = . (3) p,q(k) 0 others k=0 Through the channel, we can get the receive signal r (k) for demodulation. The receive module is in corresponding with transmit module. After the demodulation, it can be obtained as ˆam,n = r(k)g(k − n M 2 )e−j2πmk/M e−jπ(m+n)/2. (4) ∞ k=−∞ After channel equalization and taking the real part on ˆam,n, the original real symbols can be obtained. Fig. 2. The implement diagram of timing and frequency synchronization. 2jkMep2(1)jMkMep-[]sk[]gk0,ˆna1,ˆna1,ˆMna-[]gk[]gk2jnep-(1)2jnep+-(1)2jMnep-+-2jkMep-2(1)jMkMep--[]gk[]gk[]gk[]rkchannel2jnep(1)2jnep+(1)2jMnep-+2M2M2M2M2M2M0,na1,na1,Mna-Timing Offset compensatorCFO compensator()rk f ! ()synrkTiming Offset estimatorCFO estimator(a)The implement diagram of proposed synchronization scheme(b)The implement diagram of traditional synchronization scheme()rk Timing Offset compensatorTiming Offset estimator f CFOcompensatorCFOestimator()synrk

M 4 −1 4 −1 m0=0 M step, we use received signal to estimate time offset parameters and take corresponding compensation; then, according to the timing compensated signal, we conduct CFO estimation and compensation. After the above two steps, we finally utilize the synchronized signal for post-processing at the receiver, such as demodulation, equalization etc. III. PROPOSED TIMING AND CARRIER FREQUENCY OFFSET ESTIMATOR A. Training Sequence Design with Conjugate-Symmetry Prop- erty Firstly, this subsection aims to obtain a properly designed training sequence satisfying conjugate-symmetry property, which is similar to that in OFDM systems [12], namely s(A − B) = s∗(A + B) , where A is the conjugate-symmetry center and B is the width. Specially, pilot symbols are trans- mitted every fourth subcarrier at the n0th instant, i.e., on the (m = 4m0)th subcarrier with m0 = 0, 1, ..., M/4 − 1, the sequence can be obtained as s0(k) = a4m0,n0 g(k − n0M 2 j2π·4m0·k M e )e j(4m0+n0)π 2 = a4m0,n0 g(k − n0M 2 . By substituting k = KM + n0M − k to (6), we obtain j2π·4m0·k m0=0 jπn0 )e e M 2 (6) s0(KM + n0M − k) 4 −1 M = a4m0,n0g(KM + n0M 2 − k)e j2π·4m0·(−k) M jπn0 2 e . (7) m0=0 In general, g(k) is a real-valued symmetrical pulse shaping filter with the length of KM, i.e., g(k) = g(KM − k). Then, it can be obtained as g(k − n0M 2 ) = g(KM − k+ n0M 2 ). (8) For simplification, assume that n0 is odd, then e 2 = ±1. Comparing above equations (6), (7) and (8), it can be 0(KM + n0M−k). To easily illustrate the obtained s0(k) = s∗ symmetry of training sequence, for k = 0, 1, ..., M/2− 1, it can be rewritten as jπn0 KM + n0M s0( 2 − k) = s∗ 0( KM + n0M + k). (9) 2 Obviously, the training sequence is conjugate-symmetry with , which is suitable for timing offset respect to k = KM +n0M 2 and CFO estimations. However, due to the overlapping structure of the adjacent FBMC-OQAM symbols, we should separate the pilot symbols and data symbols by inserting zero-valued symbols. When the number of zero-valued symbols is larger, the interference to pilot symbols is smaller. However, the insertion of zero-valued symbols introduces large overhead, thus reduces spectrum efficiency. Therefore, we should choose the appropriate num- ber of zero-valued symbols to maintain good synchronization performance while keeping number of zero-valued symbols as small as possible. B. Timing Offset Estimation 3 According to the above training sequence, we propose the timing offset estimator as follows. Firstly, we denote −k+τ )r( KM + n0M KM + n0M 2 2 +k+τ ). (10) M/2−1 R(τ )= r( k=0 Substituting (5) to (10) and extending it, we can obtain four terms, including one signal term, one noise term and two cross terms. In high SNR condition, the power of noise w(n) is much lower than signal power, the noise and cross terms can be ignored for simplicity. When the estimated timing offset equals the real value, i.e., τ = τ, according to the conjugate- symmetry property, it can be obtained R(τ )≈ KM + n0M + k) ej 4π( KM +n0M 2 M +τ )∆f . 2 (11) It can be noted that, each sum item has the same phase , then the amplitude of their vector sum ej R(τ ) is relatively larger. Besides, we define 4π(KM + +τ )∆f n0M 2 M s( M/2−1 k=1 2 Q(τ ) = max M/2−1 k=0 τ = arg maxτ = arg maxτ M (τ + m) D−1 MD(τ ). m=0 (15) 2 − k +τ ) 2 + k +τ ) , 2 KM + n0M KM + n0M r( r( |R(τ )|2 M (τ ) = Q(τ )2 . τ = arg maxτ M (τ ). to normalize R(τ ), then the final timing metric function can 2 be expressed as , (12) (13) Therefore, we get the estimated timing offset as (14) When τ = τ, R(τ ) is the linear in-phase superposition of M/2− 1 samples and M (τ ) should be the largest. Whenτ = τ, R(τ ) is the nonlinear superposition of M/2 − 1 samples, and it is obvious smaller than that when τ = τ. Thus, it symmetry property, M (τ ) is very sharp for accurate detection. can be regarded as noise. In conclusion, due to the conjugate- Moreover, considering the fact that the first path is not always the instantaneous power strongest path in actual multi- path fading channels, we should combine the above estimation algorithm with sliding window algorithm [11] to improve the accuracy of the timing synchronization. The core idea of the sliding window algorithm is applying the final timing metric function M (τ ) to a sliding window with fixed length D(D > τmax) to obtain a new timing metric MD(τ ) , where τmax is the maximum delay of the multipath channel, the timing estimator is obtained as 

C. CFO Estimation 4 In order to achieve accurate CFO estimation with a low implementation complexity, an identical training symbol part in the above subsetion III-A is proposed. After achieving timing offset estimation, we should consider about the identical property of the proposed training sequence, then the following correlation expression can be obtained R1(τ ) = M−1 k=0 r∗( KM + n0M 2 · r( KM + n0M 2 − M 2 − M 2 + k +τ ) + d + k +τ ), (16) where d is the number of interval samples between two identical training symbol parts. As a result, the CFO can be estimated as ∆f (τ ) = ∠{R1(τ )}. M d · 1 2π (17) Fig. 3. Capture probability of timing synchronization in AWGN and 802.22 A channels. exactly estimate timing offset in per trial without errors. The above results illustrate that the proposed estimator is unbiased and can achieve perfect timing offset estimation in AWGN channel. In 802.22 A channel, with the increase of SNR, the capture rate grows rapidly, and especially when SNR ≥ 10 dB, it is up to a high value of 0.98. The proposed timing estimator can reach almost same performance with the WBS scheme [11] when SNR ≥ 10 dB, although a little but acceptable gap may exist in low SNR. However, in the WBS scheme, one should jointly consider timing offset estimation and CFO estimation at the same time, while the proposed scheme can achieve the above synchronization independently in steps with relatively lower implementation complexity. IV. SIMULATION RESULTS In this section, the performance of the proposed synchro- nization algorithm via computer simulations in both AWGN and 802.22 A channel, the simulation parameters of FBMC- OQAM systems are shown in Table I. The values of the CFO ∆f normalized to subcarrier spacing and the timing offset τ normalized to sampling interval are uniformly distributed in the range of [−1/4, 1/4] and {−M/4, ..., M/4}, respectively. In order to present the performance of the proposed syn- chronization scheme, we give key indicator of synchronization estimator as follows. The capture rate of exactly estimating timing offset per trial, P catch, is used to evaluate the performance of the proposed timing offset estimation. Usually, the capture rate can be statistically illustrated and defined as P catch = Nt/Ntotal, where Ntotal (large enough) is the number of timing offset estimation trials and Nt is the number of exact timing offset estimation. In multipath channels, the mean squared error of timing offset estimator is defined as M SE ST O=(τ − τ )2. Besides, the mean squared error of CFO estimator is defined as M SE CF O=(∆f − ∆f )2. TABLE I SIMULATION PARAMETERS. System Parameter Number of subcarriers (M) Modulation scheme Prototype function Number of pilot symbols Value 256 QPSK IOTA filters(length: 4M) 6 802.22 A Channel Delay of Channel (Ts) Gain of Channel (dB) [ 0 2 4 7 11 14 ] [ 0 -7 -15 -22 -24 -19 ] Fig. 4. MSE of timing offset estimation in 802.22 A Channel. A. Performance of timing offset estimator Fig. 3 shows the performance of timing offset estimation P catch versus SNR in AWGN and 802.22 A channels. It is obvious that in AWGN channel, the capture rate remains 1 for all SNRs, which means that the proposed algorithm can Fig. 4 shows the mean squared error of proposed timing esti- mator in 802.22 A channel. When SNR ≥ 10 dB, MSE STO is less than 100, which means that the mean error of per-trial is lower than 1 sample. Therefore, the receiver needs to perform proper channel estimation to complete demodulation. 05101520253000.10.20.30.40.50.60.70.80.91SNR dBP_catch Proposed(AWGN)Proposed(802.22 A)WBS(802.22 A)05101520253010−210−1100101102SNR dBMSE of timing offset estimation

5 B. Performance of CFO estimator Furthermore, in Fig. 5 we present the performance of the proposed CFO estimator. Numerical results show that with the increase of SNR, the mean square error decreases rapidly, maintaining at a lower level for a relatively higher SNR level. For the condition that MSE CFO reaches lower than 10−5, we need to guarantee SNR ≥ 10dB in 802.22 A channel while SNR ≥ 7dB in AWGN channel. The proposed CFO estimator can reach almost same performance with the WBS scheme when SNR ≥ 10dB. The proposed algorithm can achieve good CFO estimation both in AWGN and 802.22 A channel. Fig. 6. BER performance of FBMC-OQAM system in AWGN and 802.22 A channels. The performance of the proposed estimator, that does not require the knowledge of the prototype filter, has been assessed via computer simulation both in AWGN and multipath chan- nels. Simulation results have shown that the proposed scheme can assure accurate timing offset and CFO estimation with relatively lower implementation complexity due to that timing and frequency synchronization can be achieved independently in steps and robust acquisition properties. Fig. 5. MSE of CFO estimation in AWGN and 802.22 A channels. REFERENCES C. BER Results To gain some insight about the sensitivity of the FBMC- OQAM signal in terms of BER on timing and carrier frequency synchronization, Fig. 6 shows the BER verus SNR in AWGN channel and 802.22 A channel due to the fact that the capture rate remains 1 for all SNRs and excellent performance of CFO estimator. Simulation results show that, the proposed synchro- nization scheme can reach almost the same performance with perfect synchronization in AWGN channel. Furthermore, in 802.22 A channel, when SNR ≥ 10 dB, the proposed syn- chronization scheme can reach almost the same performance with perfect synchronization. When SNR < 10 dB, there is only a acceptable performance gap between them due to the fact that the timing offset estimation error of per-trial is relatively large as well as CFO estimation. In conclusion, the proposed algorithm can achieve good synchronization, and improve the system performance. V. CONCLUSIONS In this paper, we consider about the problem of timing and carrier frequency synchronization for the FBMC-OQAM sys- tems. In particular, we have derived a new data-aided symbol timing and frequency synchronization scheme, that exploits the conjugate-symmetry property of a properly designed training symbol. Furthermore, in multipath channel, we apply the sliding window algorithm to improve timing offset estimation. [1] P. Siohan, C. Siclet and N. Lacaille, “Analysis and Design of OQAM- OFDM Systems based on Filterbank Theory,” IEEE Trans. Signal Process., vol. 50, no. 5, pp. 1170-1183, May 2002. [2] D. Kong, D. Qu, and T. Jiang, “Time Domain Channel Estimation for OQAM-OFDM Systems: Algorithms and Performance Bounds,” IEEE Trans. Signal Process., vol. 68, no. 2, pp. 322-330, Jan. 2014. [3] D. Chen, D. Qu, T. Jiang and Y. He, “Prototype Filter Optimization to Minimize Stopband Energy With NPR Constraint for Filter Bank Multicarrier Modulation Systems,” IEEE Trans. Signal Process., vol. 61, no. 1, pp. 159-169, Jan. 2013. [4] D. Qu, S. Lu and T. Jiang, “Multi-Block Joint Optimization for the Peak- to-Average Power Ratio Reduction of FBMC-OQAM Signals,” IEEE Trans. Signal Process., vol. 61, no. 7, pp. 1605-1613, Apr. 2013. [5] M. Bellanger, “Physical Layer for Future Broadband Radio Systems,” in Proc. IEEE RWS, pp. 436-439, Jan. 2010. [10] T. Fusco, A. Petrella, and M. Tanda, “Data-aided Symbol Timing and CFO Bank Multicarrier Systems,” IEEE Trans. Wireless Commun., vol. 8, no. 5, pp. 2705-2715, May 2009. [11] G. Yang, H. Chen, S. Hu, G. Wu and S. Li, “Data-aided Joint Symbol Timing and CFO Estimation for OFDM/OQAM systems,” in Proc. IEEE ICICS, pp. 1-5, Dec. 2011. [12] B. Park, H. CHEON, C. KANG, “A Novel Timing Estimation Method for OFDM Systems,” in Proc. IEEE GLOBECOM, pp. 269-272, Nov. 2002. [6] W. Chung, B. Kim, M. Choi, H. Nam, H. Yu, S. Choi, and D. Hong, “Synchronization Error in QAM-based FBMC System,” in Proc. IEEE MILCOM, pp. 699-705, Oct. 2014. [7] H. Bolcskei, “Blind Estimation of Symbol Timing and Carrier Frequency Offset in Wireless OFDM Systems,” IEEE Trans. Commun., vol. 49, no. 6, pp. 988-999, Jun. 2001. [8] T. Fusco, A. Petrella, and M. Tanda, “Blind CFO Estimation for Noncritically Sampled FMT Systems,” IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2603-2608, Jun. 2008. [9] A. Tonello and F. Rossi, “Synchronization and Channel Estimation for Filtered Multitone Modulation,” in Proc. IEEE WPMC, pp. 590-594, Sept. 2004. 05101520253010−710−610−510−410−3SNR dBMSE of CFO estimation Proposed(AWGN)Proposed(802.22 A)WBS(802.22 A)05101520253010−410−310−210−1100SNR dBBER Perfect Syn.(AWGN)Syn.(AWGN)Perfect Syn.(802.22 A)Syn.(802.22 A PCI)