Communications and Network, 2013, 5, 249254 http://dx.doi.org/10.4236/cn.2013.53B2046 Published Online September 2013 (http://www.scirp.org/journal/cn) Signal Detection for OFDMIDMA Uplink over Doubly Selective Channels* Tao Peng1, Yue Xiao1, Shaoqian Li1, Huaqi an g S hu2, Eric Pierre Simon2 1Nation Key Lab of Sci. and Techno. On Commun. University of Electronic Sci. and Techno. of China, Chengdu, China 2IEMN Lab, TELICE Group, University of Lille, Lille, France Received June, 2013 ABSTRACT Orthogonal frequency division multiplexinginterleave division multiple access (OFDMIDMA) systems may suffer from serious intercarrier interference (ICI) in timeand frequencyselective (doubly selective) channels. In such case, the conventional OFDMIDMA detection algorithm for quasistatic channels will result in significantly performance degradation. In this paper, signal detection is investigated for OFDMIDMA uplink over doubly selective channels. Firstly, the impact of timevarying channels for OFDMIDMA uplink is analyzed, which leads to the failure of the con ventional algorithm. Secondly, a novel iterative detection algorithm is developed based on an integrated interference canceller, which can iteratively estimate and mitigate the ICI as well as multiple access interference (MAI) simultane ously. In addition, an improved detection algorithm is derived for reducing the complexity using an approximation to the mean and variance of the in terference. Simulation results indicate that the proposed algorithm can significan tly en hance the system performance to the conventional case, and the improved algorithm can strike a balance between per formance and complexity. Keywords: Interleave Division Multiple Access (IDMA); Orthogonal Frequency Division Multiplexing (OFDM); Doubly Selective Channel 1. Introduction As a kind of nonorthogonal multiple access scheme, interleave division multiple access (IDMA) was devel oped by Ping et al.[1,2], in which random interleavers are employed as the only means for user separation. In gen eral, IDMA outperforms conventional code division mul tiple access (CDMA) in terms of power and bandwidth efficiency. The key innovation of IDMA is the introduc tion of lowrate channel coding, chiplevel interleaving and lowcomplexity multiuser detection. On the other hand, orthogonal frequency division multiplexing (OFDM) is an attractive transmission technique for future wireless communication due to its high spectral efficiency and excellent robustness to frequencyselective fading. Based on the combination of IDMA and OFDM, OFDMIDMA was presented for achieving the advantages of both sys tems [3]. In OFDMIDMA systems, intersymbol inter ference (ISI) can be mitigated by OFDM and multiple access interference (MAI) can be suppressed by IDMA. Moreover, OFDMIDMA can achieve more throughput and reliability than conventional OFDMCDMA and orthogonal frequencydivision multiple access (OFDMA) [35]. In [3], an iterative multiuser detection scheme is de rived for OFDMIDMA, where the complexity of each user is independent of the channel length and number of users. However, it assumes that the frequencyselective channels are time invariant (quasistatic) within an OFDM block. In practice, high speed movement of mobile ter minals will cause Doppler spread and result in time varying multipath fading channels [6,7]. In this case, the channels will be time and frequencyselective (doubly selective), in which the length of an OFDM block is longer than th e coherent time. As a result, the time varia tion of doubly selective channels will destroy the or thogonal property among subcarriers and induce in tercarrier interference (ICI), which complicates the data detection in the receiver. *This work was supported by the Foundation Project of National Key Laboratory of Science and Technology on Communications under Grant 9140C020404120C0201, National HighTech R&D Program of China ("863" Project under Grant number 2011AA01A105), Na tional Grand Special Science and Technology Project of China under Grant No. 2010ZX0300600202, and the Fundamental Research Funds for the Central Universities. Due to this additional interference from other subcar riers, the conventional OFDMIDMA detection algo rithm [3] will degrade the system performance severely in the doubly selective channels. In [810], several inter carrier interference cancellation schemes were proposed C opyright © 2013 SciRes. CN
T. PENG ET AL. 250 for OFDMA and OFDMCDMA in doubly selective chan nels. However, due to different system structure, these schemes cannot be extended to OFDMIDMA. Therefore, signal detection of OFDMIDMA uplink over doubly selective channels becomes a challenging problem due to the complex interference from MAI and ICI. In order to overcome the above problems over the doubly selective channels, signal detection for OFDM IDMA uplink is investigated in this paper. Firstly, the impact of doubly selective channels for OFDMIDMA uplink is analyzed, which results in the failure of the conventional algorithm. Then a new iterative detection algorithm is developed based on an integrated interfer ence canceller, which considers the influence of not only multiple users but also intercarrier interference. It can eliminate ICI from other subcarriers as well as MAI in an iterative way. Moreover, an improved detection algo rithm is also derived based on an approximation to the mean and variance of the interference for reducing the complexity. Finally, simulation results verify that the proposed detection algorithm can greatly improve the performance of the conventional one, and the improved algorithm can achieve performance close to the proposed one while keeping the computational complexity low. The rest of this paper is organized as follows. Section II introduces the system model of OFDMIDMA uplink adopted in this paper. In Section III, three detection algo rithms are presented for OFDMIDMA uplink over dou bly selective channels. Simulation results are provided in Section IV to demonstrate the effectiveness of the pro posed algorithms. The conclusions are drawn in Section V. 2. System Model 2.1. Transmitter of OFDMIDMA Uplink The system model of OFDMIDMA uplink with K si multaneous users is shown in Figure 1, where each user communicates with the base station through independent doubly selective channels. For the transmitter of userk, information data dk is first encoded and interleaved to generate a lowrate permutated sequence Xk, which is then fed into an inverse fast Fourier transform (IFFT) modulator. After IFFT and cyclic prefix (CP) insertion, the time domain transmitted signal from userk can be represented as 12 0 1 1, NjunN kk ug xnXuN ne NN (1) where N is the total number of subcarriers and Ng is the length of CP. 2.2. Receiver of OFDMIDMA Uplink As illustrated in Figure 1, the OFDMIDMA receiver consists of one elementary signal estimator (ESE) detec tor and K softinput softoutput (SISO) decoders (DECs), which are used to solve the multiple access channel con straint and the coding constraint respectively. The out puts of ESE and DECs are the extrinsic loglikelihood ratios (LLRs), which are updated via the interleavers and deinterleavers iteratively. More detailed description of OFDMIDMA receiver can be found in [3]. 3. Detection Algorithms of OFDMIDMA Uplink over Doubly Selective Channels In the OFDMIDMA receiver, since the SISO DECs are standard a posteriori probability (APP) decoding, the distinction between different detection algorithms lies in the ESE detector. In what follows, three different ESE detection algorithms will be given for OFDMIDMA up link over doubly selective channels. 3.1. Impact of Doubly Selective Channels for OFDMIDMA The doubly selective channel model considered in this paper is the timevarying multipath fad ing channel with a d elay spread L. The channel may vary within each OFDM block, depending on the velocity of the user’s motion. C Decoder (DEC) Doubly Selective Channels ESE Detector Transmitter for user1 Transmitter for userK 1ESE eX r 1 d K d 1 d K d 1 c1 K 1DEC eX 1ESE ec 1DEC ec ESE K eX DEC K eX ESE K ec DEC K ec CK c 1 1 1 K K 1 K IFFT IFFT FFT 1 X XK 1 Decoder (DEC) Figure 1. Transmitter and receiver structures of OFDMIDMA uplink. Copyright © 2013 SciRes. CN
T. PENG ET AL. 251 The received signal from userk without noise can be described as 1 0 12 0 , 1, L kkk l N un N kk u rn hnlxnl XuHnue N (2) where hk(n,l) stands for the channel impulse response (CIR) of path l at time n for userk, and Hk(n,u) is the channel frequency response at the uth subcarrier. Equation (2) can be rewritten in a matrix form as t kk rHX k w (3) where rk=[rk(0), rk(1),…, rk(N1)]T, Xk=[Xk(0), Xk(1),…, Xk(N1)]T, and is given by (4), shown at the bottom of the page. t k H Thus the received signal from all users can be given by 11 KK t kkk kk rrwHX (5) where w is the additive white Gaussian noise (AWGN) with zero mean and variance 2 . After the CP removal and fast Fourier transform (FFT) of r in (5), the received signal in the frequency domain is as follows 1 Kt NNkk k RFrFHX W (6) where W is the noise in the frequency domain, and FN is the FFT matrix defined as NN 2 1,1, 0,1. jmnN Nmn emnN F (7) Furthermore, denoting t k FH by k H in (6), the re ceived signal can be rewritten as 1. Kf kk k RHXW (8) In (8), k H is the equivalent channel response matrix of the doubly selective channel for userk. 3.2. Conventional Detection Algorithm In [3], the conventional detection algorithm of OFDM IDMA was proposed, which can effectively cancel the MAI of quasistatic channels. When the channel is as sumed to be time invariant within an OFDM block, the channel matrix k H in (8) can be simplified to a diago nal matrix denoted as k . In this case, the frequency domain received signal (8) is simplified as 1,0 1 Kf k static k k Rm HmXmWmmN (9) For the subcarrier m of userk, the received signal can be rewritten as '' '1,' K ff kk static kk kkk fMAI kkk RmHmXm HmXmWm HmXm m (10) where MAI km is the total interference term with re spect to userk on subcarrierm, consisted of both MAI and noise. Without loss of generality, BPSK modulation and real valued channel coefﬁcients are assumed for simplifying the expression. Furthermore, the principle here can be easily extended to other cases such as complex channels, higher order modulations and multiple receive antennas [3]. According to the central limit theorem, MAI km is approximated as a Gaussian random variable with mean MAI k Em and variance . Based on the definition of extrinsic LLRs, the output of ESE de tector is calculated by MAI k Var m 2 MAI fstatic k k ESE kMAI k RmEm eXmHmVar m (11) where MAI k Em and can be ob tained by the mean and variance of Xk’(m). MAI k Var m By the priori LLRs EC k eX feedback from the DECs, the mean and variance of Xk(m) can be calculated as follows tanh2 , kDECk EX meX m (12) 2 1. kk VarXmEX m (13) In the above conventional detection algorithm, the MAI MAI km of quasistatic channels can be eliminated effectively. However, in the doubly selective channel, the channel matrix k H is not a diagonal matrix and the frequency domain received signal cannot be expressed 2 21 2 21 21 0,10, 1 1, 01,11,1 1 1, 01, 0,0 11,1 kk k jN j N kk k t k jN jN NN kk k HHN HHe HNe N HNHN eH H NNe H N (4) Copyright © 2013 SciRes. CN
T. PENG ET AL. 252 simply as (9). More specifically, an additional interfer ence from other subcarriers will be introduced, resulting from the timevarying characteristics of the channel. Therefore, the performance will be degraded signifi cantly if the conventional algorithm is adopted in the doubly selective chan nels. 3.3. Proposed Detection Algorithm To alleviate this problem, a novel ESE detection algo rithm is proposed to enhance the system performance of OFDMIDMA uplink over doubly selective channels. It takes into account the additional intercarrier interference and utilizes an iterative soft interference canceller to suppress the MAI and ICI jointly. With increasing itera tion number, the additional interference can be mitigated and the transmitted signal of the desired user can be re covered gradually. For analyzing the interference of userk, the received signal on s ubcarrier m in (8) is expressed as 1 10 1 10, , ,, ,. KN f kk kn KN ff kk kkk knnm fICIMAI kkkk RmHmnX nWm HmmXmHmnXn m HmmXmmm MAI (14) As shown in (14), the interference term includes not only the MAI from other users on subcarrierm, but also the ICI from other subcarriern of all users. Compared to (10), an additional in terference term will be appeared in the doubly selective channels, which is neglected in the conventional algo rithm. This explains the performance degradation for OFDMIDMA uplink when using the conventional algo rithm. Consequently, this additional interference should also be cancelled in the ESE detector. Based on an inte grated interference canceller, the output of the proposed ESE detector can be obt a i ned by ,0 1nm nN ICI km 2, proposed ESE k MAI ICI kk f kMAI ICI kk eXm Rm Em Em Hmm VarmVarm . (15) In the proposed detection algorithm, all the interfer ence included MAI and ICI can be suppressed and the system performance can be improved. For suppressing the additional in terference , the computation in the proposed detection algorithm is more complicated than the conventional one. ICI km 3.4. Improved LowComplexity Detection Algorithm As described above, the proposed detection algorithm can obtain more satisfied performance than the conventional one. But the computation complexity of the mean and variance of the interference is much higher than the con ventional one. In the follow, an improved detection algo rithm is proposed for reducing the complexity by an ap proximation to the mean and variance of the interference. In the proposed algorithm, the interference ICI km consists of the equivalent channel matrix k H and the transmitted signal on other subcarriers. This indicates that the value of the channel matrix k H will affect the computation of the mean and variance of Im IC k . By analyzing the property of the chann el matrix k H, it can be found that the values of offdiagonal elements become smaller and smaller with increasing distance to the main diagonal elements. And when these offdiagonal ele ments are far from the main diagonal ones, their values will be quite small that can be approximated to zero. As a result, the rowm (1mN ) of the channel matrix k H (1kK ) can be approximated by using the following vector: ,0,,12,,, ,120 fff kkk f k HmHmmP Hmm HmmP (16) where P is the number of elements that are not set to zero. In this case, the interference CI k only from P subcar riers needs to be calculated instead of all subcarriers in the ESE detector. Furthermore, by the expression in (15), the variance of interference only affects the magnitude of the output of ESE detector. Thus the variance of can be neglected for reducing the computation complexity. ICI km Consequently, the improved algorithm can reduce the complexity in two aspects. Firstly, the computation com plexity of the mean of the interference is reduced to P/N as the proposed algorithm by the approximation to the channel matrix. Secondly, the computatio n complexity of the variance o f th e in terferen ce is reducing to the same as the conventional one. 4. Simulation Results In this section, computer simulations are carried out to verify the effectiveness of the proposed detection algo rithms over doubly selective channels. Simulations are performed for OFDMIDMA uplink with four users, em ploying BPSK modulation. A repetition code of rate1/8 is adopted for all users, and the total number of subcarri ers is 128. The channel model used here is the extended vehicular A (EVA) channel [11]. The normalized Dop pler frequency is denoted as fDT, where fD represents the maximum Doppler frequency shift and T is an OFDM symbol period. In the simulations, channel estimation is not considered and perfect channel information is as sumed to be known at the receiver. Figure 2 shows the biterrorrate (BER) performance of the conventional detection algorithm in the doubly Copyright © 2013 SciRes. CN
T. PENG ET AL. 253 selective channels with different velocities (i.e., corre spondingly fDT = 0.001, 0.01, 0.05, 0.1, and 0.2, respec tively). It can be found that the system performance de grades with the increase of users’ velocity. The perform ance is relatively poor at fDT =0.2 and fDT =0.1 compared with fDT =0.01. This is because the conventional algo rithm doesn’t take into account the additional interfer ence from other subcarriers, which becomes larger with the increase of normalized Doppler frequency. Figure 3 depicts the BER performance results of the proposed and conventional detection algorithms in the doubly selective channels with different normalized Doppler shift. From this figure, it can be found that the proposed algorithm can enhance the performance obvi ously in the doubly selective channels. More specifically, it can be found that the performance gap between the proposed algo rithm and the convention al one is very sig nificant when fDT =0.2. And the performance of the pro posed algorithm with fDT =0.1 is very close to the per formance of the conventional one with fDT =0.001. Figure 4 and Figure 5 show the BER performance of the improved lowcomplexity algorithm with different value of parameter P, where the performance of the con ventional and proposed algorithms is also included for comparison. It can be observed that the performance gap between the improved algorithm and conventional one becomes greater with the increasing value of P. When P = 3, at the cost of little complexity, the performance of the improved algorithm is sig nificantly better th an that of the conventio nal one. And while P = 17 for the improved algorithm, the performance is almost the same as that of the proposed one. 101 Eb/N0(dB) R 103 010121416 102 1820 Conv ention al algorithm, fDT=0. 2 100 104 105 2684 Conventional algorithm, fDT=0.1 Conventiona l algorithm, fDT=0.05 Conventiona l algorithm, fDT=0.01 Conventiona l algorithm, fDT=0. 001 Figure 2. BER performance of the conventional algorithm in the doubly selective channels with different normalized Doppler frequency fDT. 101 Eb/N0(dB) BER 103 01012 14161820 102 Conventional algorithm, fDT=0.2 100 104 105 2684 Conventional algorithm, fDT=0.1 Conventional algorithm, fDT=0.001 Proposed algorithm, fDT=0.2 Proposed algorithm, fDT=0.1 Figure 3. Performance comparison of the proposed algo rithm and the conventional one in the doubly selective channels with different nor m alized Doppler frequency fDT. 101 Eb/N0(dB) BER 103 010121416 102 1820 Conventional algorithm 100 104 105 2684 Proposed algorithm Improv ed al go ri th m, P=3 Improv ed al go ri th m, P=5 Improv ed al go ri th m, P=17 Figure 4. BER performance of the improved algorithm in the doubly selective channels (fDT =0.2) with different pa rameter P. 101 Eb/N0(dB) BER 103 010121416 102 1820 Conventional algorithm 100 104 105 2684 Proposed alg orit hm Impr oved algo ri thm , P=3 Impr oved algo ri thm , P=5 Impr oved algo ri thm , P=17 Figure 5. BER performance of the improved algorithm in the doubly selective channels (fDT =0.1) with different pa rameter P. Copyright © 2013 SciRes. CN
T. PENG ET AL. Copyright © 2013 SciRes. CN 254 5. Conclusions In this paper, three different detection algorithms are derived for OFDMIDMA uplink over doubly selective channels. Among all the three detection algorithms, the conventional algorithm suffers from performance loss due to neglect of the additional interference from other subcarriers, and the proposed algorithm delivers the best performance but at the cost of higher complexity. And the improved algorithm can achieve performance close to the proposed on e but with a low co mputational co mplex ity. Consequently, it is optimal to adopt the improved lowercomplexity algorithm to obtain a tradeoff between performance and complexity. REFERENCES [1] P. Li, L. H. Liu, K. Y. Wu and W. K. Leung, “A Unified Approach to Multiuser Detection and Spacetime Coding with Low Comple xity and Nearly Optimal Performance,” in Proc. 40th Allerton Conference, 2002, pp. 170179. [2] P. Li, L. H. Liu, K. Y. Wu and W. K. Leung, “Interleave Division Multiple Access,” IEEE Transactions Wireless Communications, Vol. 5, No. 4, 2006, pp. 938947. [3] P. Li, Q. H. Guo and J. Tong, “The OFDMIDMA Ap proach to Wireless Communication Systems,” IEEE Wireless Communications Mag., Vol. 14, No. 3, 2007, pp. 1824. [4] R. Zhang and L. Hanzo, “Three Design Aspects of Multi carrier Interleave Division Multiple Access,” IEEE Transactions Vehicular Technoogy, Vol. 57, No. 6, 2008, pp. 36073617. doi:10.1109/TVT.2008.918724 [5] P. Hammarberg, F. Rusek and O. Edfors, “Channel Esti mation Algorithms for OFDMIDMA: Complexity and Performance,” IEEE Transactions Wireless Communica tions, Vol. 11, No. 5, 2012, pp. 17221732. [6] Y. Li and L. J. Cimini, “Bounds on the Interchannel Inter ference of OFDM in Timevarying Impairments,” IEEE Transactions Communications, Vol. 49, No. 3, 2001, pp. 401404. doi:10.1109/26.911445 [7] P. Schniter, “LowComplexity Equalization of OFDM in Doubly Selective Channels,” IEEE Transactions Com munications, Vol. 52, No. 4, 2004, pp. 10021011. [8] Y. X. Peng, K. Zheng, W. Wang, Y. Kim and Y. S. Lee, “Iterative PartialInterferenceCancellationbased Detec tor for OFDM Systems over DoublySelective Rayleigh Fading Channels,” in Proc. IEEE International Symp. On Personal, Indoor and Mobile Radio Comm., 2007, pp. 15. [9] T. Zemen, C. F. Mecklenbrauker, J. Wehinger and R. R. Muller, “Iterative Joint Timevariant Channel Estimation and Multiuser Detection for MCCDMA,” IEEE Trans actions Wireless Communications, Vol. 5, No. 4, 2006, pp. 938947. [10] S. W. Hou and C. C. Ko, “Intercarrier Interference Sup pression for OFDMA Uplink in Timeand Fre quencySelective Fading Channels,” IEEE Transactions Vehicular Technoogy, Vol. 58, No. 6, 2009, pp. 27412754. doi:10.1109/TVT.2008.2010550 [11] 3GPP Technical Specification 36.104, 2010, “Evolved Universal Terrestrial Radio Access (EUTRA): Base Sta tion(BS) Radio Transmission and Reception,” Version 9.3.0, Mar. 2010.
