Blind Synchronization for Cooperative MIMO OFDM Systems

Transcription

1 Blind Synchronization for Cooperative MIMO OFDM Systems C. Geethapriya, U. K. Sainath, T. R. Yuvarajan & K. M. Manikandan KLNCIT Abstract - A timing and frequency synchronization is not easily achieved in cooperative multiple-input multipleoutput (MIMO) orthogonal frequency division multiplexing (OFDM) systems. In current scenarios, usingspecial preamble (training sequence) or cyclic prefixalong with synchronization algorithms, have been proposed for both data-aided and non-data-aided systems. Among these data-aided approaches, here, atiming synchronization scheme utilizing unequal period synchronization patterns (UPSPs) was proposed. In this paper, from a blind synchronization perspective, we propose a generalized interleaved carrier assignment scheme (CAS) that develops a blind timing synchronization scheme and also CFO estimation was done for frequency synchronization.simulation results show that through the application of the proposed methods, cooperative systems result in significant performance gains even in presence of impairments. Keywords - non-data-aided; cooperative communications; multiple-input multiple-output (MIMO); orthogonal frequency division multiplexing (OFDM); carrier assignment scheme (CAS); synchronization; carrier frequency offset (CFO). I. INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM),the method of transmitting multiple data streams over a common broadband medium by splitting the radio signal into multiple smaller sub-signals that are then transmitted simultaneously at different frequencies to the receiver and it is more sensitive to carrier frequency offsets (CFO). In the meantime, multipleinput multiple-output (MIMO) systems have been demonstrated to be one of the most promising technologies for the future wireless communications. MIMO can be realized in a centralized or a cooperative (distributed) manner. In conventional MIMO systems, the antenna elements are co-located on a single device, which results in a single timing and carrier offset [1].In centralized MIMO systems [2]- [7],have multiple antennas and multiple radios. It takes advantage of multipath effects, where a transmitted signal arrives at the receiver through a number of different paths. Each path can have a different time delay, and the result is that multiple instances of a single transmitted symbol arrive at the receiver at different times. All transmit-receive links are characterized by a different carrier frequency offset (CFO) because the antennas at the transmitter/receiver are driven by the different oscillator. For some wireless applications, due to hardware or cost limitations, planting multiple antennas on a single device may be impractical. In such cases, cooperative communications have been proposed to exploit the spatial diversity gains inherent in multiuser wireless systems without the need of multiple antennas at each node. The signals transmitted by sparsely distributed cooperating nodes arrive at the receiver on distinct timing due to diverse propagation delays and are characterized by different CFOs. This makes synchronization even more challenging in cooperative MIMO systems than in centralized MIMO configurations. Recent developments of synchronization techniques for cooperative MIMO systems are mainly based on special preamble (training sequence) designs [8]-[11]. Guo et al. [8] introduced the idea of using unequal period synchronization patterns (UPSPs) to distinguish the training sequences of different cooperating transmitters. With the knowledge of the unique repetitive training structure of a particular cooperating transmitter, the corresponding timing synchronization can be accomplished through utilizing conventional correlation-based methods. Later, Cheng et al. [9] adopted the preamble design in [8] for timing synchronization and added another two identical training sequences (each has duration of an OFDM symbol) to assist multi-cfo estimation. The direct combination of different types of training sequences, however, significantly decreases the system efficiency. Afterward, Yang et al. [10] developed another preamble that is feasible for both timing synchronization and multi-cfo estimation, yet the preamble still contains two identical training sequences (each has duration of an OFDM symbol). Recently, Wang and Wang [11] designed a low-overhead preamble that only has the 33

2 duration of one OFDM symbol to support both timing synchronization and multi-cfo estimation. In contrastive manner, we propose a non-data-aided timing and frequency synchronization scheme for cooperative MIMO OFDM systems. The proposed approach is based on a new carrier assignment scheme (CAS), i.e., generalized interleaved CAS, which makes the resultant random OFDM data symbols themselves become UPSP-like. Accordingly, non-data-aided timing synchronization can be carried out in a similar fashion as in [8], but without any known training sequence. Simulation results show that through the application of the proposed methods, cooperative systems result in significant performance gains even in presence of impairments. The rest of this paper is organized as follows. In Section II, we briefly introduce a typical cooperative MIMO system model. In Section III, we summarize a UPSP-based timing synchronization scheme. In Section IV, we propose a generalized interleaved CAS, along with a non-data-aided timing synchronization scheme.in Section V, simulation results are presented. Finally, in Section VI, some conclusions are drawn. II. SYSTEM DESCRIPTION In this section, we briefly describe a typical cooperative MIMO system, along with its synchronization problems. We consider a cooperative communication system with one source node one destination node and relay nodes [14], all equipped with a single antenna, as shown in Fig. 1. In the broadcasting phase, the source node broadcasts a training sequence to the relay nodes. In the relaying phase, the relay nodes transmit distinct training sequences to the destination node. The received superimposed training sequences at the destination node are then used to estimate the CFO and channel coefficients of each relay-destination link. Fig. 1 : A cooperative MIMO OFDM system. In Fig. 1, S represents source node, N 1, N 2,, N T represents relay nodes and D represents destination node. In this paper, we consider synchronization for the relaying phase. Suppose that we have N T single-antenna transmitters sparsely distributed in space to form a virtual multi-antenna array, where the multiple cooperative terminals have different distances to the destination terminal and thus the cooperative transmission may be time-asynchronous and also each cooperative terminal has its own oscillator and thus the cooperative transmission is frequency-asynchronous. Accordingly, we may model the baseband signal received by an antenna as N T 1 r n = e j 2π N ℇ m n τ m m=0 L 1 l=0 h m l s m n τ m l + w n, where the notations with subscript m are related to the m-th transmitter,h m = [h m 0,.., h m (L 1)] represents an L-tap channel impulse response vector, s m (n) is the transmitted signal,τ m denotes the propagation delay normalized to the sampling period, ℇ m denotes the CFO normalized to the subcarrier spacing, N is the fast Fourier transform (FFT) size, and w(n) characterizes the complex additive white gaussian noise. Briefly, synchronization in cooperative MIMO systems is to estimate the distinct propagation delay and CFO between each cooperating transmitter and the receiver. III. A CONVENTIONAL DATA-AIDED TIMING SYNCHRONIZATION SCHEME In this section, we discuss a data-aided timing synchronization scheme that is based on UPSPs [8]. To produce UPSPs, the synchronization sequence for the m-th transmitter, Z ss m, is constructed as follows: m m Z ss n = Z sp n mod L sp, (2) m {1, 2,., N T }, n = 0, 1,., L sp 1, where the notation a mod b denotes the residual of a divided by b, Z sp is a basic synchronization pattern to construct Z m m ss,and L sp is the length of the synchronization pattern assigned to the m-thtransmitter, m i.e., the period of Z ss as depicted in Fig.2. Note that m thel sp, should be equal to or longer than the largest L sp, m m and no L sp should be a multiple of another L sp for m {1, 2,., N T },m m. In addition,l ss represents the length ofz m ss. With the knowledge of the period of the synchronization sequence associated with the m-th cooperating transmitter, i.e., L m sp, the corresponding timing estimate can be determined as (1) 34

3 τ m = arg max { Φ m (n) }, L ss Lm sp 1 Φ m n = r n + i i=0 m {1, 2,., N T }, r m n + i + L sp, (3) where r*(.) denotes the complex conjugate of r(.). IV. PROPOSED NON-DATA-AIDED APPROACH A. Key Observations on a UPSP-Based Timing Synchronization Scheme As described in (2), the UPSPs are designed in time domain. However, a frequency-domain preamble design may be advantageous because training data for different transmitters should be loaded on disjoint sets of subcarriers in cooperative MIMO OFDM systems to prevent mutual interference. By transforming the timedomain preamble design into frequency domain, however, it can be shown that the training data for different transmitters do not occupy disjoint sets of subcarriers. For example, consider the case associated withl ss =120, L 1 sp =120/6, and L 2 sp =120/4, where Z 1 ss and 2 Z ss, respectively, have 6 and 4 identical parts in time domain as depicted in Fig. 2. Due to FFT/IFFT properties, subcarriers with indexes belonged to the set {0, 12, 24,,120} are occupied by both transmitters, where 12 is the least common multiple of 6 and 4. Using unequal periods in UPSPs design which is known by the receiver is needed for timing synchronization. The above-mentioned observations have given idea to develop a new CAS in frequency domain, which produces UPSP-like random OFDM data symbols in time domain. Accordingly, the UPSP-like structure can be effectively used to realize non-data-aided timing synchronization for cooperative MIMO OFDM systems.. TABLE I Some feasible parameter setting for the proposed new CAS N T =2 (d1,r1) = (6,0), (d2,r2) = (4,3) N T =3 N T =4 (d1,r1) = (6,0), (d2,r2) = (9,2), (d3,r3) = (15,4) (d1,r1) = (8,0), (d2,r2) = (12,1), (d3,r3) = (18,3), (d4,r4) = (20,2). Fig. 2 : An illustration of unequal period synchronization patterns (UPSPs) B. Proposed New Carrier Assignment Scheme In Fig. 3, we describe the proposed new CAS, along with three typical CASs that represent subband CAS, interleaved CAS, and generalized CAS, respectively. For illustration, we consider a simplified case of N = 50 and N T = 4. In subband CAS, adjacent subcarriers are grouped as disjoint subbands that are assigned to different transmitters. In interleaved CAS, the subcarriers assigned to each transmitter are uniformly spaced over the system bandwidth at a distance d, which is common for all transmitters, e.g., d = 8 in Fig. 3(b). In generalized CAS, each subcarrier can be assigned to any transmitter, which provides maximal carrier assignment flexibility. On the other hand, the proposed new CAS may be viewed as a generalized interleaved CAS, where the subcarriers assigned to the m-th transmitter are uniformly spaced over the system bandwidth at a unique 35

4 distanced m, so as to produce a unique time-domain repetition structure. For example, consider the carrier assignment shown in Fig. 3(d) with d 1 = 8, d 2 = 12,d 3 = 18 and d 4 = 20 the resultant time-domain repetition structures are shown in simulation results. Note that d m is selected as a factor of N, i.e., d m N, and the N-point time-domain signal thus contains exactly d m identical parts. Also note that for any CAS, it is essential that each subcarrier should only be assigned to a single transmitter, which can be easily accomplished in conventional interleaved CAS as shown in Fig. 3(b). In the proposed new CAS, however, both the distance (d m ) and the index of the first subcarrier (r m ) assigned to the m-th transmitter should be jointly chosen to fulfill the fundamental requirement of CASs. To further explain the idea of the proposed CAS, let us start with two cooperating transmitters and consider Where Ω 1 = { k 1 d 1 + r 1 : k 1 N 0 }, Ω 2 = k 2 d 2 + r 2 : k 2 N 0, Ω 3 = k 3 d 3 + r 3 : k 3 N 0, Ω 4 = k 4 d 4 + r 4 : k 4 N 0, d 1, d 2, d 3, d 4 N, 0 r 1 < d 1, 0 r 2 < d 2, 0 r 3 < d 3, 0 r 4 < d 4 Ω 1 toω 4 - subcarrier index sets assigned to Transmitter 1 to 4, respectively. In addition, represents the set of natural numbers. We claim that Such that k 1, k 2, k 3, k 4 N 0, k 1 d 1 + r 1 k 2 d 2 + r 2 k 3 d 3 + r 3 k 4 d 4 + r 4 gcd d 1, d 2, d 3, d 4 r 4 r 1 where a b denotes that a is not a factor of b, and gcd(d 1,d 2, d 3, d 4 ) denotes the greatest common divisor of d 1,d 2, d 3 and d 4. A proof for two transmitters is given in the Appendix. Note that the carrier assignment shown in Fig. 3(d) corresponds to the case of (d 1,r 1 ) = (8,0), (d 2,r 2 ) = (12,1), (d 3,r 3 ) = (18,3), and (d 4,r 4 ) = (20,2), which guarantees Ω 1 Ω 2 Ω 3 Ω 4 =, i.e., the intersection of Ω 1, Ω 2, Ω 3 and Ω 4 is an empty set. More generally, let Ω m = k m d m + r m : k m N 0,dm N, 0 rm<dmdenote the subcarrier index set assigned to the m-th transmitter, the proposed CAS for multiple transmitters can be implemented in many ways as long as the following constraints are satisfied: gcd d m, d m r m r m, m m. where some feasible choices are listed in Table I. Analogous to (3), different from data-aided approaches, where the receiver has a single chance to perform synchronization using the known preamble at the beginning of each packet, the proposed approach can utilize an arbitrary number of random OFDM symbols to perform timing synchronization as well as to improve estimation accuracy through combining multiple estimates. C. Performance analysis using frequency offset estimation In the cooperative system, CFO estimation is essential as timing estimation. Each relaying phase nodes have different CFOs. In order to analysis the performance of the frequency synchronization, the received signal s offset is estimated. The received offset is calculated as r m = S m exp (j ℇ m ) wheres m (n) is the transmitted signal,ℇ m denotes the CFO for m-th transmitter. Here the additive white gaussian noise (AWGN) is added with the signal. The receiver knows the fixed offset and it is compared with estimated offset whose difference is considered as error. For the various signal to noise ratio (SNR), the mean square error (MSE) is estimated. The performance analysis is plotted for SNR vs. MSE.. Fig.3 : An illustration of the proposed new CAS and conventional CAS 36

5 Fig. 4(a) : Estimation of timing offset of transmitter 1 Fig. 4(e) : SNR vs. MSE plot V. SIMULATION RESULTS Fig. 4(b) : Estimation of timing offset of transmitter 2 Fig. (c) : Estimation of timing offset of transmitter 3 In our project, we have considered four transmitters (N T =4) for a cooperative system. The new proposed CAS was designed as described in IV.b with (d 1, r 1 ) = (8,0), (d 2, r 2 ) = (12,1), (d 3, r 3 ) = (18,3) and (d 4, r 4 ) = (2,20). The timing synchronization scheme based on UPSP described in III and the data modulated in BPSK was also simulated using L ss =256, L 1 sp =8, L 2 sp = 12, L 3 sp = 18, L 4 sp =20 and the basic synchronization pattern Z sp is chosen as a Zadoff-Chu sequence [12], [13]. After the CAS pattern the data is represented for 64 time indexes. For these four transmissions the offset is also given manually. Note that under the above parameter setting, the random OFDM symbols in the proposed approach and the UPSPs share the same repetition structure. Simulation results indicate that the proposed approach leads to advanced timing more frequently, it may be more desirable for OFDM-based systems.from the Fig. 4,the maximum correlation value of the corresponding timing index is considered as timing offset.themean square error (MSE) is calculated as the difference of fixed offset and estimated offset which is iterated for thousands of times. For the different signal to noise ratio (SNR), the mean square error (MSE) is calculated. The performance analysis is plotted in Fig. 5, for SNR vs. MSE. VI. CONCLUSION Fig. 4(d) : Estimation of timing offset of transmitter 4 In this paper, we have proposed a generalized interleaved CAS for cooperative MIMO OFDM systems to enable non-data-aided timing synchronization. Unlike data-aided approaches, it uses proposed CAS scheme instead of using the preamble at the beginning of each packet to perform timing synchronization. Simulation results have shown that the proposed non-data-aided approach can achieve better performance than the UPSP-based timing synchronization scheme and by 37

6 using the estimated offset, the MSE vs. SNR is plotted for performance analysis. This Appendix proves that VII. APPENDIX k 1, k 2 N 0, d 1, d 2 N, 0 r 1 < d 1, 0 r 2 < d 2, such that k 1 d 1 + r 1 k 2 d 2 + r 2 gcd d 1, d 2 r 2 r 1 Proof: Let gcd d 1, d 2 = h, we have (d 1 = d 1 h) and (d 2 = d 2 h) with gcd d 1, d 2 = 1 ( ) k 1 d 1 + r 1 k 2 d 2 + r 2 k 1 d 1 k 2 d 2 (r 2 r 1 ) h(k 1 d 1 k 2 d 2 ) (r 2 r 1 ) since gcd d 1, d 2 = 1 by Euclidean algorithms. k 1, k 1 εn 0,such that k 1 d 1 k 2 d 2 = 1or -1, k 1, k 2 N 0,we can represent k 1 d 1 k 2 d 2 = m k 1 d 1 k 2 d 2, m N hm k 1 d 1 k 2 d 2 (r 2 r 1 ) hm (r 2 r 1 ) h (r 2 r 1 ) h = gcd d 1, d 2 r 2 r 1 there exists no m ε Z, such that hm (r 2 r 1 ), where Z represents the set of integers. k 1, k 2 N 0,we can take m k 1 d 1 k 2 d 2 Z h k 1 d 1 k 2 d 2 (r 2 r 1 ) k 1 d 1 k 2 d 2 (r 2 r 1 ) k 1 d 1 + r 1 k 2 d 2 + r 2 VIII. REFERENCES [1] G. G. Raleigh and J. M. Cioffi, Spatio-temporal coding for wireless communication, IEEE Trans. Commun., vol. 46, no. 3, pp , Mar [2] A. N. Mody and G. L. Stüber, Synchronization for MIMO OFDM systems, in Proc. IEEE Global Telecommun. Conf., vol. 1, Nov. 2001, pp [3] G. L. Stüber, J. R. Barry, S. W. Mclaughlin, Y. Li, M. A. Ingram, and T. G. Pratt, Broadband MIMO- OFDM wireless communications, Proc. IEEE, vol. 92, no. 2, pp , Feb [4] Allert van Zelst and Tim C. W. Schenk, Implementation of a MIMO OFDM-based wireless LAN system, IEEE Trans. Signal Processing, vol. 52, no. 2, pp , Feb [5] Y. Jiang, H. Minn, X. You, and X. Gao, Simplified frequency offset estimation for MIMO OFDM Systems, IEEE Trans. Veh. Technol., vol. 57, no. 5, pp , Sept [6] C.-L. Wang and H.-C. Wang, Optimized joint fine timing synchronization and channel estimation for MIMO systems, IEEE Trans. Commun., vol. 59, no. 4, pp , Apr [7] C.-L. Wang and H.-C.Wang, Low-complexity joint timing synchronization and channel estimation for MIMO OFDM systems, in Proc IEEE Veh. Technol. Conf. - Spring (VTC 2011-Spring), Budapest, Hungary, May [8] F. Guo, D. Li, H. Yang, and L. Cai, A novel timing synchronization method for distributed MIMO- OFDM system, in Proc IEEE Veh. Technol. Conf. - Spring (VTC 2006-Spring), vol. 4, Melbourne, Australia, May 2006, pp [9] Y. Cheng, Y. Jiang, and X.-H.You, Preamble design and synchronization algorithm for cooperative realy systems, in Proc IEEE Veh. Technol. Conf. - Fall (VTC 2009-Fall), Alaska, USA, Sept [10] G. Yang, C.-L.Wang, H.-C.Wang, and S.-Q.Li, A new synchronization scheme for OFDM-based cooperative relay systems, in Proc IEEE Global Commun. Conf. (GLOBECOM 2010), Miami, Florida, USA, Dec [11] H.-C. Wang and C.-L.Wang, A compact preamble design for synchronization in distributed MIMO OFDM systems, in Proc IEEE Veh.Technol. Conf. - Fall (VTC 2011-Fall), San Francisco, California, USA, Sept [12] R. L. Frank and S. A. Zadoff, Phase shift pulse codes with good periodic correlation properties, IEEE Trans. Inform. Theory, vol. 8, no. 6, pp , Oct [13] C. Chu, Polyphase codes with good periodic correlation properties, IEEE Trans. Inform. Theory, vol. 18, no. 4, pp , July [14] Tao Liu and Shihua Zhu, Joint CFO and Channel Estimation for Asynchronous Cooperative Communication Systems, IEEE signal processing letters, vol. 19, no. 10, Oct [15] Wang, Hung-Chin, "Non-data-aided timing synchronization for cooperative MIMO OFDM systems", Communications (ICC), IEEE International Conference, pp on June