A ovel Interleaving Scheme for Multiuser Detection of Coded CDMA Systems Ayman Y. Elezabi, Alexandra Duel-Hallen orth Carolina State University Department of Electrical and Computer Engineering Raleigh, C 27695-7911 Phone/Fax: (919) 515-7352/2285 email: ael-eza@eos.ncsu.edu, sasha@eos.ncsu.edu Abstract Code Division Multiple Access (CDMA) is one of the main players in the wireless market expected to ll the need for higher capacity. Conventional or single-user detection has thus far been the demodulation method of choice in CDMA receivers despite many shortcomings due to its simplicity. Multiuser detectors on the other hand have the potential for dramatically higher capacity at the cost of increased complexity. In this paper, we consider two-stage detection schemes in a coded system, and compare them to other suboptimum detectors. We focus on the relatively simple two-stage with the conventional rst stage detector and show that it has very good performance over the fading channel and is robust against the "near-far" problem when error correction is used. We then describe alternative receiver structures for two stage detectors in coded systems and present a novel 'user' interleaving scheme which oers even further performance improvement over previous implementations. 1 Introduction Practical implementation issues have mainly been responsible for the prevalence of the conventional, or single-user detector, in most CDMA systems despite its inherent limitations. The complexity of the Maximum-likelihood (optimum) detector [1] is prohibitive even for systems with a moderate number of users. Many suboptimum detectors have therefore been proposed with a few results reported for coded systems (e.g. [2, 3, 4]). In this work we are particularly interested in the two-stage with the conventional rst stage (TSCFS) detector [5]. We evaluate its performance for a 4-user system over a fading channel, and compare it to that of the conventional and other suboptimum detectors. We nd that it has has very good performance on the fading channel when sim- This research was supported by SF grant CR-9410227 and the Center for Advanced Computing and Communicationat orth Carolina State University ple error correction is used and is robust against the so-called "near-far" problem. We then describe an alternative implementation for the TSCFS detector where decoders are placed between the rst and second stages to provide better rst stage decisions. We call it the "complex" scheme as opposed to the "simple" scheme where a single decoder for each user follows amulti-user detector. As we reported in [6] however, the performance is limited by error dependence introduced in the receiver chain by the rst set of Viterbi decoders. For that, we propose a new method for interleaving the user bits relative toeach other (i.e. not just in time) to randomize the error bursts going into the second stage. Results for a 2-user system on the additive white Gaussian noise (AWG) channel show uptotwo orders of magnitude improvement inaverage bit error rate (BER) over the simple scheme.a 4-user system on a fading channel is currently being studied. 2 CDMA Channel Model We assume a frequency-nonselective channel and slow Rayleigh fading which leads to the following expression for the received signal, r(t) = KX k=1 c k b k s k (t)+n(t) (1) where s k (t) denotes the kth user's signature waveform, b k its transmitted bit, n(t) is a realization of a zero-mean complex white Gaussian process with power spectral density 2, and c k 's are independent complex zero-mean Gaussian random variables. At the receiver, a bank of lters matched to the signature waveforms of each user provides a sucient statistic y for estimating the user bits b given r(t). Thus, y = RCb + n (2) where n is a zero-mean complex Gaussian K;vector with the covariance matrix 2 R for both 1
real and imaginary components. We do not consider the problem of channel estimation here. We use BPSK modulation with coherent detection in a 4-user bit-synchronous system with a set of signature waveforms derived from Gold sequences of length seven that result in a normalized crosscorrelation matrix R as in [5, 7]. We assume perfect channel estimation and that our interleaving is suf- ciently deep to render the fading coecients, c k, uncorrelated from one bit interval to another. For the coded channel, we use the half-rate four-state convolutional encoder with generator sequences g 1 = [101] and g 2 = [111]. It has a minimum free distance, d free, of 5 and its encoder memory, m, is equal to 2. At the receiver, we implement a hard-decision truncated best-state Viterbi decoder with a path memory of 10 branches. In our comparative analysis, we consider the conventional, decorrelating, and two-stage detectors. 3 Comparison of Multiuser Detectors Figures 1(a) and 1(b) show the BER plots versus average SR for the uncoded and coded systems, respectively, for single- and multi-user detectors. Figure 2(a) shows the performance of the conventional-based detectors for a system with user cross-correlations equal to 0.2. Returning to Figures 1(a) and 1(b), the twostage with the decorrelating rst stage (TSDFS) detector provides practically single-user performance over both the uncoded and coded channels but it is too complex. In this work, therefore, we are mainly interested in the TSCFS detector due to its relative simplicity. ext, we study the important near-far situation where user 1's energy is, on average, one half (3 db lower than) and then one quarter (6 db lower than) that of each of the other three users. In Figure 2(b) we show the performance of the TSCFS detector with and without coding for both the moderate and the severe near-far cases. We observe that the TSCFS detector's performance is only slightly worse in the moderate near-far case than in the equal average SR case. However, the performance of the coded system is very acceptable, and the error oor is quite low. The performance in the severe near-far situation is very close to that of the milder near-far case, proving the resilience of the TSCFS detector in a fading environment when simple error correction is employed. 4 Two-Stage Detector Implementations for Coded Systems An alternative, and more complex, implementation (we refer to it as the complex scheme) than the one implied earlier (we refer to it as the simple scheme) for two-stage detectors is now described. Here, error correction is applied to the decisions of the rst stage detector in an attempt to make them more reliable. The decoding delay of the complex scheme is twice that of the simple. Depending on SR, user cross-correlations, and the channel characteristics one or the other of the complex and simple schemes shows better performance. The complex scheme may perform poorly because of the bursty nature of the uncorrected errors coming out of the rst bank of Viterbi decoders. And since the noise components of all users are correlated (Equation 2), these error events may occur at the same time, leading to clusters of errors in second stage decisions. The second bank of Viterbi decoders no longer provides optimum decisions in that case. A more detailed performance comparison of both schemes can be found in [8]. Generally, the simple scheme outperforms the complex scheme for higher SR and the complex scheme will do better for low cross-correlations between users. For our system of interest, the simple scheme is always at least as good as the complex scheme for the fading channel, indicating that the potential of the complex scheme is poorly utilized. Figure 2(a) compares both schemes for a system with low user cross-correlations (0.2), while Figure 3 shows the performance for the R used earlier. 5 Complex Scheme with User Interleaving To overcome the problem described above for the complex scheme, an interleaving method is proposed where the relative order of the bits in the interleaved sequences of the users is also scrambled, i.e. the interleaving function is dierent for each user. We introduce a periodic sequence of delays in the bit stream coming out of the rst encoder bank following the interleaving method outlined in [9]. The two parameters of the inter are P, the period of the delay sequence, and D, the number of bit positions by which each bit in the original sequence is separated from the next. A corresponding set of delays is required at the receiver to set the sequence back to its original ordering, with a pure delay of(p ; 1)D intervals. For illustrative purposes, we look at a two user system in which the inter-deinter pairs are introduced in the path of only one user as shown in Figure 4. The rst and second pair of inters and deinters must be identical since the same interleaving operation must be performed before the second stage of detection in order for the in-
tended interference cancelation to occur. ote that since we are using a half-rate code, the actual information bit delay for an inter-deinter pair will be (P ; 1)D=2. Figure 5(a) shows the BER of the TSCFS detector for a 2-user system over the AWG channel with a user cross-correlation of 0.75 when P = D = 5 10 15 and 20, and for the case of no interleaving as well as for the simple scheme. We notice that for this example the simple scheme outperforms the complex scheme if no interleaving is used virtually over the entire SR range. An inter with P = D = 5 does not adequately improve the complex scheme's performance. For P = D =10 15 and 20, we have signicant gains, with the largest gain per additional delay (and storage) occurring when we gofromp = D = 5to P = D = 10. ote also that the dierence between the last two cases (P = D = 15 and P = D =20) is not enough to warrant the additional delay and storage requirement. This is because the length of most error events does not require such deep interleaving. For the largest inter (P = D = 20), the BER drops to about two orders of magnitude below that for the simple scheme. This shows the huge advantage of the complex scheme over the simple scheme when its potential is fully exploited. ote that interleaving is required in any wireless environment to mitigate the eects of fading. The complex scheme requires that operation to be repeated one more time in the receiver. Figure 5(b) shows the performance of the TS- DFS detector. Again we see a large improvement in performance over the simple scheme as the SR increases (exceeding two orders of magnitude) for moderate inter depths. A more powerful code is required on the fading channel to realize the potential of the complex scheme. A 4-user system on the fading channel is currently being studied. 6 Conclusions We show that the TSCFS detector is a very viable alternative in multiuser detection considering its simplicity, excellent performance, and robustness in near-far situations. It also improves greatly with lower user cross-correlations. For the coded system, it outperforms the decorrelator for an average SR of up to a 23 db, and its BER saturates at 10 ;6. Moreover, its performance in a simulated near-far situation is almost unaected. The crucial advantage of the TSCFS detector over the decorrelator is that is does not require cross-correlation matrix inversion at the receiver. We then introduced an alternative implementation for the coded system (the complex scheme), and analyzed its behavior in comparison to the simple scheme. Finally, a novel interleaving scheme for the complex two-stage detector was proposed, and shown to provide large improvements over the simple scheme in preliminary results for a 2-user system. More work is needed to study systems with a larger number of users on the fading channel, but preliminary results indicate that more powerful codes are needed to realize the potential of the coded scheme in a fading environment. References [1] S. Verdu. "Minimum Probability of Error for Asynchronous Gaussian Multiple-Access Channels". IEEE Transactions on Information Theory, IT-32(1):85{96, Jan. 1986. [2] T.R. Giallorenzi and S.G. Wilson. "Multistage Decision Feedback and Trellis-Based Multiuser Receivers for Convolutionally Coded CDMA Systems". SEAS Report o. UVA/538341/EE93/102. May 1993. [3] M. asiri-kenari and C.K. Rushforth. "An Ecient Soft-Decision Decoding Algorithm for Synchronous CDMA with Error-Control Coding". In Proceedings of the IEEE International Symposium on Information Theory, Trondheim, orway, page 227, June 1994. [4] Abdulrauf Hafeez and Wayne E. Stark. "Combined Decision-Feedback Multiuser Detection/Soft-Decision Decoding for CDMA Channels". In IEEE VTS 46th Vehicular Technology Conference Proceedings, Vol. 1, pages 382{386, April 1996. [5] M. K. Varanasi and B. Aazhang. "ear-optimum Detection in Synchronous Code-Division Multiple- Access Systems". IEEE Transactions on Communications, COM-39(5):725{736, May 1991. [6] Ayman El-Ezabi and Alexandra Duel-Hallen. "Combined Error Correction and Multiuser Detection for Rayleigh Fading Synchronous CDMA Channels". In Proceedings of the 33rd Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, pages 1{10, October 1995. [7] A. Duel-Hallen. "Decorrelating Decision-Feedback Multiuser Detector for Synchronous Code-Division Multiple-Access Channel". IEEE Transactions on Communications, COM-41(2):285{290, Feb. 1993. [8] Ayman El-Ezabi. "Combined Multiuser Detection and Error Correction for Code Division Multiple Access Systems over Gaussian and Rayleigh Fading Channels". Master's thesis, orth Carolina State Univ., June 1995. [9] M. Vedat Eyuboglu. "Detection of Coded Modulation Signals on Linear, Severely Distorted Channels Using Decision-Feedback oise Prediction with Interleaving". IEEE Transactions on Communications, COM-36(4):401{ 409, April 1988.
x : Conventional x : Conventional o : Decorrelator + : 2 stage, conv. 1st stage * : 2 stage, decorr. 1st stage : Single User Bound o : Decorrelator + : 2 stage conv. 1st stage * : 2 stage decorr. 1st stage : Single User Bound 0 5 10 15 20 25 30 35 SR(i) db, i=1,2,3,4 SR(i) db, i=1,2,3,4 (a) Uncoded Case (b) Coded Case Figure 1: BER for 4-user Systems on a Rayleigh Fading Channel x : Conventional, Uncoded x : TSCFS, Uncoded, 3 db o : Conventional,Coded + : TSCFS, Uncoded + : TSCFS, Uncoded, 6 db * : TSCFS, Complex * : TSCFS, Simple SR(i) db, i=1,2,3,4 (a) Low User Cross-correlations System o : TSCFS, Coded, 3 db * : TSCFS, Coded, 6 db SR(1) db (b) TSCFS Detector Performance in Two ear-far Cases Figure 2: Conventional-based Detector Performance
x : TSCFS,complex o : TSCFS,simple + : TSDFS,complex * : TSDFS,simple SR(i) db, i=1,2,3,4 Figure 3: BER of "Simple" and "Complex" Schemes for Two-stage Detectors with Coding in a Fading Channel b1 Encoder b2 Encoder Inter M O D U L A T I O & S U M M I G C H A E L r(t) Matched Filter 1 Matched Filter 2 y 1 y 2 First- Stage Detector Delay Deinter Delay Symbol Symbol Inter + + w 21 w 12 Deinter bˆ 1 ( 2) bˆ 2 ( 2) Figure 4: Complex Two-stage Detector with User Bit Interleaving for 2 Users.
: Simple scheme : o interleaving (Complex) BER x : P=D=5 o : P=D=10 BER of user 1 + : P=D=15 * : P=D=20 Complex, o interleaving Complex, P=D=10 Complex, P=D=20 Simple 2 4 6 8 10 12 14 16 SR(i) db (a) TSCFS, r=0.75 2 4 6 8 10 12 14 16 SR(i) db (b) TSDFS, r=0.9 Figure 5: Complex Scheme with Interleaving vs. Simple, 2 users, AWG