Iterative Equalization using Improved Bloc DFE for Synchronous CDMA Systems Sang-Yic Leong, Kah-ing Lee, and Yahong Rosa Zheng Abstract Iterative equalization using optimal multiuser detector and trellis-based decoder in coded CDMA systems improves the bit error rate BER performance dramatically However, given large number of users employed in the system over multipath s causing significant multiple-access interference MAI and intersymbol interference ISI, the optimal multiuser detector is thus prohibitively complex Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered In this paper, a novel low-complexity bloc decision feedbac equalizer DFE is proposed for the synchronous CDMA system Based on the conventional bloc DFE, the new method is developed by computing the reliable extrinsic log-lielihood ratio LLR using two consecutive received samples rather than one received sample in the literature At each iteration, the estimated symbols by the equalizer is then saved as apriori information for next iteration Simulation results demonstrate that the proposed low-complexity bloc DFE algorithm offers very good performance gain over the conventional bloc DFE Keywords: DFE, Iterative Equalization, Turbo Equalization I INTRODUCTION Iterative equalization which employs maximum a posteriori MA algorithm is a powerful tool to combat frequency selective fading [1] This so-called Turbo-principle [] can be achieved easily due to the serial concatenation of two steps that formed by the encoder at the transmitter and the discrete-time equivalent multipath s The performance of a wireless system can be enhanced in the fashion of exchanging the extrinsic information iteratively among the softinput/soft-output equalizer and decoder until convergence is achieved Unfortunately, these optimum algorithms are not usually applicable to the practical communication systems in use today due to their high computational complexity As a consequence, the study of low complexity suboptimal algorithms in turbo equalization are motivated In recent literature, the Turbo principle has been successfully applied to the code division multiple access CDMA systems to mitigate the multiple-access interference and intersymbol interference Specifically, Moher derived an optimal iterative multiuser detector for synchronous coded CDMA system based on the cross-entropy minimization [] In [], the near single user performance of the iterative multiuser detection is proposed by Reed, et al Later, Wang and oor developed a low-complexity S-Y Leong and K- Lee are with the Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO 01, USA YR Zheng is with the Department of Electrical and Computer Engineering, University of Missouri, Rolla, MO 09, USA, Email: zhengyr@umredu iterative receiver structure to decode the multiuser information data The minimum mean square error linear equalizer LE implemented in turbo equalization cancels the inter-symbol interference and multi-access interference successfully In this paper, we focus on the nonlinear multiuser bloc decision feedbac equalizer in the synchronous CDMA systems We address the drawbac of the conventional bloc DFE algorithm in turbo equalization, which has error propagation The effects of error propagation can be observed from the simulation results [], [] Hence we propose a new approach to mitigate the error propagation in the DFE algorithm when used in iterative equalization and retaining low computational complexity It estimates the data using the aprioriinformation gleaned from the decoder and also the aprioridetected data from last iteration to minimize error propagation From simulation results, we show that the bit error rate performance of the improved bloc DFE algorithm has very good improvement when compared with the conventional bloc DFE algorithm II SYSTEM MODEL Fig 1 shows a convolutional coded CDMA system with K users in total and one receiver antenna rior to transmission, a frame of binary data symbol b i {0, 1} of user, {1,,,K}, with length K b is first encoded through a convolutional encoder with constraint length M and rate r The output encoded data symbols of length K c are next interleaved into different ordering by a random permutation function to reduce the influence of error bursts Thereby, yielding a bloc of data symbols c n {1, 1}, where n {1,,,K c } denotes the symbol index of the interleaved symbols The operation is denoted as c n c i and its reverse operator de- is denoted as 1 At the final stage, each coded data symbol c n is then modulated by a spreading waveform s t The modulated sequence due to the th user can be written as KX c1 x t A s t n0 c ns t nt, 0 t K c 1T,1 N1 1 X w qψt qt c N q0 where A and s t are, respectively, the amplitude and th user s normalized signature waveform that is supported only on the interval [0,T] N is the processing gain and w q,q {0, 1,,N 1} is the signature code of user, T c is the chip period, T NT c is the symbol period, ψt is the chip waveform that is nonzero only on [0,T c ]
b 1 i encoder spreader s 1 multipath nt b K i encoder spreader s K multipath L D c 1 n rt Soft decision multiuser detector Λc 1 n L E c 1 n de 1 L E c 1 i Softdecision decoder ˆb1 i Λc 1 i L D c 1 i Λc K n L D c K n L de E c K i ˆbK i L Softdecision D c K i 1 decoder L E c K n Λc K i Fig 1 Turbo Equalization system model consists of soft-decision equalizer and decoder Assume the data sequence of th user are transmitted in burst mode to the receiver and distorted by the multipath and additive white Gaussian noise AWGN The impulse response of the multipath propagated by the th user is given by h t L 1 h l δt τ l where L is the total number of paths in the th user and h l and τ l are, respectively, the complex gain and delay of the lth path signal of th user In this paper, we implement a special case of CDMA model, where the transmitted signals arrive at the receiver synchronously and the multipath impulse response is given by h t [h 1 δt h δt T h L δt L T ] and L 1 L L K L Therefore, the baseband representation due to the th user at the receiver is then given by y t x t h t K c1 A n0 L1 c n s t n lt h l where is the convolution operator As shown in Fig 1, the received signal rt at the multiuser receiver is the combination of the K users signal and the additive white Gaussian noise and written as follows, rt K y tvt 1 where vt N0,σ is the zero mean complex Gaussian noise process with variance σ III MULTIUSER DETECTION FOR SYNCHRONOUS CDMA In this section, we present the multiuser detection technique of the synchronous CDMA model described above The ey techniques developed in this paper later can be generalized to the general multipath CDMA such as asynchronous CDMA systems For this synchronous case, it is sufficient to demodulate the th user signal by choosing the output of a filter matched to s in the nth symbol interval, is given by y n ρ j n1t nt s t nt rtdt L1 A c n lh l L1 j,j A ρ j c j n lh jl zn 8 T 0 s ts j tdt 9 where zn is a Gaussian noise and ρ j is the cross-correlation of the signal set s 1,,s K Denote Yn [y 1 n y n y K n] T is the K- vector whose th component is the filter output given in and
[ ] T is the transpose operator Based on equation 8, the vector Yn can be arranged into the matrix form as follows Yn RAHCnZn 10 where R is the normalized cross-correlation matrix: [R],j ρ j and A diaga 1,,A K We further define other quantities into matrix form as follows where the conditional probability [Yn Ĉm n] is defined as [ 1 [Yn Ĉm n] exp 1 ] πσ σ nr 1 n 19 n Yn RAHĈm n 0 h [h 0 h 1 h L1 ] C 1 L 11 h 1 0 0 H 0 h 0 C K KL 1 0 0 h K C n [c n c n 1 c n L 1] C 1 L 1 C T 1 n C T Cn n CKL 1 1 C T K n Zn [ z 1n z n z Kn ] T C K 1 1 It is important to note that Zn is a Gaussian vector and Zn N0, R In the sequel, we derive the bloc DFE and the new algorithm to improve bloc DFE based on equation 10 in iterative multiuser detection A Conventional Bloc DFE In this section, we focus on the iterative multiuser detection using bloc DFE algorithm in the synchronous CDMA system Denote { C n [c 1 n,,c 1 n, 1,c 1 n,,c K n] } : c j n {1, 1},j 1 Similarly define C n We now define Ĉm n C n if Ĉ m n is given by [c 1n ĉ m 1 n 1 ĉ m 1 n L 1] T [ ] T [c bc m 1 n ĉ m 1 n 1 ĉm 1 n L 1]T n [1 ĉ m n 1 ĉ m n L 1] T 1 [c 1 n ĉ m 1 n 1 ĉm 1 n L 1]T [ ] T [c Kn ĉ m K n 1 ĉm K n L 1]T and the operator is the complex conjugate transpose Similarly, define [c n 1 Yn] Given that the a posteriori LLR of nth symbol Λc m n log [cm n1 Yn], substitute 18 into it with some mathematical manipulation, we [c m n1 Yn] have Λc m bc m n C [Yn C b m n log n n] j [c jn] bc m n C [Yn C b m n n] j [c jn] L E c m n log [cm n 1] 1 [c m n 1] L D c m n It is seen from 1 that the a posteriori LLR consists of two terms, the first term L E c m n is the extrinsic LLR computed by the bloc DFE, and the second term L D c m n is the a priori LLR from the decoder In the process of symbol detection, the bloc DFE, which relies on the soft information from 1, initially hard decides the th user s nth symbol ĉ m n {1, 1} Then, it is fed bac to the equalizer for ISI and MAI cancellation After the symbol detection, the bloc of extrinsic LLR is interleaved and delivered to the decoder as a set of aprioriinformation Unfortunately, the analysis and simulation results from [], [] indicate that DFE is not an effective equalizer in turbo equalization It has only small improvement throughout the iterations when compared with a linear equalizer The loss of performance is mainly due to the residual interference in the presence of the severely multipath s and the incorrect symbols being fed bac during the equalization Therefore, we propose a novel bloc DFE which is shown to be a low-complexity and efficient equalizer for turbo equalization where ĉ m n 1 {1, 1} is the estimated n 1th symbol of user fed bac by the equalizer in mth iteration Based on the input-output relationship given in 10, we can write the a posteriori probability A of the nth symbol of th user being 1 as follows, [c n 1 Yn] bc m n C [Yn C b m n n] [c n 1] j [c jn] bc m [Yn b, C m n n] j [c jn] {j, {1,,,K}} 18 B Improved Bloc DFE It is obvious that the feedbac of incorrectly estimated symbols during equalization lead to loss of performance As a consequence, the ey idea of the proposed equalizer is increasing the reliability of the extrinsic information LLR by computing the extra metric We further define the vector Ĉm,m1 n 1 C n if
bc m,m1 n 1 1 n 1 c 1n ĉ m 1 n 1 L] T [ ] T 1 n 1 c 1 n ĉ m 1 n 1L]T n 1 1 ĉ m n 1 L] T 1 n 1 c 1 n ĉ m 1 n 1L]T [ ] T K n 1 c Kn ĉ m K n 1 L]T In the first iteration of turbo equalization, there is no apriori LLR delivered from the decoder and estimated symbols from previous iteration by the equalizer The equalizer thus detects the user symbols based on the a posteriori LLR calculated in the first term of 1 Starting from the second iteration, we define a new a posteriori probability of the nth symbol of th user given by, [c n 1 Yn, Yn 1] C n,n1 Y [c n 1] j [c jn] C n,n1 Y j [c jn], {j, {1,,,K}} n,n1 Y [Yn, Yn 1 C b m n, C b m,m1 n 1] where C {Ĉm n, Ĉm,m1 n 1} and C {Ĉm n, Ĉm,m1 n 1} C n Similarly define [c n 1 Yn, Yn 1] Given that the received samples are independent, the probability of received samples Yn and Yn 1at mth iteration is obtained using 19 and given by [Yn, Yn 1 Ĉm 1 { πσ exp 1 [g σ 0 where g 0 Ĉ m n g 1 Ĉ m,m1 n 1 n, Ĉm,m1 Ĉ m n n 1] g 1 Ĉ m,m1 n 1 nr 1 n n1r 1 n1 n1 Yn 1 RAHĈm,m1 n 1 ]} Finally, let us define a new a posteriori LLR Λc m n ln [c n1 Yn,Yn1] [c n1 Yn,Yn1], and substituting into After some mathematical manipulation, the new a posteriori LLR of nth symbol at mth iteration is given by Λc m n h io C n log exp 1 σ g 0 bc m n g 1 bc m,m1 n 1 h io C n exp 1 σ g 0 bc m n g 1 bc m,m1 n 1 L E c m n log cm n 1 c m n 1 L D c m n It is obvious that the new algorithm considers the extra sample Yn 1in the process of computing L E c m n while compared with the conventional bloc DFE given in 1 However, it is important to note that in the first iteration, when computing L E c 1 n, neither the apriorillr Lc1 n nor symbol ĉ 0 n is available As a consequence, the computation of metric Yn 1is discarded and the new algorithm becomes the conventional bloc DFE algorithm given in the first term of 1 in the first iteration From the second iteration onward, the improved bloc DFE algorithm feedbac the estimated set of th user symbols Ĉ m [ĉ m 0 ĉ m n ĉ m K c 1] to the detector for interference cancellation It also eeps the data in memory for the computation of Yn 1in the next iteration m 1 In short, the new algorithm treated the detected symbols Ĉ m as another set of aprioriinformation besides Lc m n that is delivered from the decoder starting from the second iteration onward It is noted here that the new a posteriori probability can be calculated using J number of received samples, ie [c n 1 Yn, Yn1,, Ynj], where j 0, 1,,J1 Given that j equals to 0 and 1, the As are simplified to 18 and, respectively Due to the tradeoff between the computational complexity and system performance gain, we only compute the new a posteriori probability using j 0, 1 throughout this paper IV SIMULATION RESULTS In this section, we present several simulation results obtained using the bloc DFE and improved bloc DFE presented in Section III The entire scenario of iterative multiuser detection is depicted in Fig 1 In the users CDMA system, the binary data is first encoded through rate r 1/ and constraint length M convolutional encoder The generator code given in octal notation is G [, ] For the multipath, we consider a static ISI slow fading with L and the CIRs of the users are given in Table I, where i is 1 and the com- TABLE I CHANNEL IMULSE RESONSE IN CDMA SYSTEM δn δn 1 δn User 1 009 0i 00 00i 011 0099i User 088 01i 0 00i 0900 00i User 00 08i 09 019i 018 01i plex path gains are normalized such that L1 h l 1The additive white Gaussian noise added to the received symbols is determined by the desired E b /N o Based on the derivation given by the improved bloc DFE algorithm, it has the same performance as the conventional bloc DFE algorithm in the first iteration due to the lac of apriori information from the decoder and the equalizer From the second iteration onward, the conventional bloc DFE algorithm has only a small improvement throughout the iterations shown
in all the figures In Fig, we assume that there is no correlation between the users; ρ j 0,j DFE denotes the BER performance computed by the conventional DFE at th iteration The conventional bloc DFE has BER of 000 at dbe b /N o after iterations We obtain only an 1dB gain if compared to the BER after the first iteration Nevertheless, after iterations, the improved bloc DFE algorithm has BER of 0000 at db E b /N 0, and achieve extra 1dB gain than the conventional bloc DFE algorithm Fig depicts the simulation results that the correlation of the users is ρ j 0 After one iteration, the receiver achieve a BER of 00 at db E b /N o Obviously, the gain of the new method is thus db while the conventional DFE only produces the gain of 1dB after iterations It is apparent in Fig and Fig that the improved DFE algorithm requires only iterations to achieve overall better performance when compared to that computed by the conventional DFE algorithm 10 0 V CONCLUSION In this paper, the bloc DFE algorithms are introduced and analyzed for iterative multiuser receiver in synchronous CDMA system We first address the computational complexity of the MA equalizer and the ineffectiveness of the conventional bloc DFE algorithm to mitigate the MAI and ISI in the multipath CDMA s A novel low-complexity improved bloc DFE algorithm is proposed for iterative multiuser detection The new method improves the BER performance by computing the extrinsic LLR using two consecutive received samples At each iteration, the hard detected symbols are fed bac to cancel MAI and ISI in equalization, they are also saved as another set of a priori data for next iteration We verified the proposed algorithm through the simulation results in the users synchronous CDMA system The simulation results indicate that the proposed low complexity bloc DFE algorithm improves the BER performance throughout the iterations when compared to the conventional bloc DFE algorithm 10 1 ACKNOWLEDGMENT The authors are grateful to Dr Chengshan Xiao for his helpful discussions Bit Error Rate BER 10 10 DFE 1 DFE DFE DFE Improved DFE Improved DFE Improved DFE 10 Eb/No db Fig BER performance of the Turbo multiuser detector while ρ j 0 Bit Error Rate BER 10 0 10 1 10 10 DFE 1 DFE DFE DFE Improved DFE Improved DFE Improved DFE 10 Eb/No db Fig BER performance of the Turbo multiuser detector while ρ j 0 REFERENCES [1] C Douillard et al, Iterative correction of intersymbol interference: Turbo-equalization, Euro Trans Telecommun, vol, no, pp0-11, Sept-Oct 199 [] C Berrou, A Glavieux, and Thitimajshima, Near Shannon limit errorcorrecting and decoding: Turbo codes 1, in roc IEEE Int Conf Commun, vol, May, 199, pp 10-100 [] M Moher, An iterative multiuser decoder for near-capacity communications, IEEE Trans Commun, vol, pp 80-880, July 1998 [] M C Reed et al, Iterative multiuser detection for CDMA with FEC: Near single user performance, IEEE Trans Commun, vol, pp 19-199, Dec 1998 [] X Wang and HV oor, Iterative Turbo soft interference cancellation and decoding for coded CDMA, IEEE Trans Commun, vol, no, pp 10-101, July 1999 [] M Tuchler, AC Singer, and R Koetter, Minimum mean squared error equalization using a priori information, IEEE Trans on Signal rocessing, vol 0, no, pp -8, Mar 00 [] M Tuchler, R Koetter and AC Singer, Turbo equalization: principles and new results, IEEE Trans Commun, vol 0, no, May 00 [8] Strauch et al, Turbo equalization for an 8-SK modulation scheme in a mobile TDMA communication system, in roc IEEE Veh Technol Conf, vol, Sept 1999, pp 10-109 [9] G Bauch and V Franz, A comparison of soft-in/soft-out algorithms for Turbo detection, in roc Int Conf Telecomm, June 1998,pp9- [10] C Berrou, Adde, E Angui, and S Faudeil, A low complexity softoutput Viterbi decoder architecture, in roc IEEE Int Conf Commun, May 199, pp -0 [11] A Dejonghe and L Vandendorpe, Turbo-equalization for multilevel modulation: an efficient low complexity scheme, in roc IEEE Int Conf Commun, May 00, pp 18-18 [1] SL Ariyavisitaul and Y Li, Joint coding and decision feedbac equalization for broadband wireless s, IEEE J Select Areas Commun, vol 1, no 9, pp 10-18, Dec 1998 [1] Jingxian Wu, Chengshan Xiao, and Khaled B Letaief, Multiuser estimation for CDMA systems over doubly selective fading s, roc IEEE Veh Technol Conf, vol, Oct 00, pp 11-1181