A novel interleaving scheme for multiuser detection of coded CDMA systems

A Novel Interleaving Scheme for Multiuser Detection

of Coded CDMA Systems

Ayman Y. Elezabi, Alexandra Duel-Hallen

North Carolina State University

Department of Electrical and Computer Engineering

Raleigh, NC 27695-7911

Phone/Fax: (919) 515-7352/2285

email: [email protected], [email protected]

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 de-modulation method of choice in CDMA receivers despite many shortcomings due to its simplicity. Multiuser detectors on the other hand have the po-tential 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 alterna-tive receiver structures for two stage detectors in coded systems and present a novel 'user' interleav-ing 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 de-spite its inherent limitations. The complexity of the Maximum-likelihood (optimum) detector 1] is pro-hibitive even for systems with a moderate number of users. Many suboptimum detectors have there-fore 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 com-pare it to that of the conventional and other sub-optimum detectors. We nd that it has has very good performance on the fading channel when

sim-This research was supported by NSF grant NCR-9410227 and the Center for AdvancedComputingandCommunicationat North 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 bet-ter rst stage decisions. We call it the "complex" scheme as opposed to the "simple" scheme where a single decoder for each user follows a multi-user detector. As we reported in 6] however, the per-formance is limited by error dependence introduced in the receiver chain by the rst set of Viterbi de-coders._{For that, we propose a new method for} inter-leaving the user bits relative to each other (i.e. not just in time) to randomize the error bursts going into the second stage. Results for a 2-user sys-tem on the additive white Gaussian noise (AWGN) channel show up to two orders of magnitude im-provement in average 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

) = K X

k=1

c

k

b

k

s

k(

t

) +

n

(

t

) (1)

where

s

k(

t

) denotes the

k

th user's signature

wave-form,

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 su-cient statisticyfor estimating the user bitsbgiven

r

(

t

). Thus,

y=RCb+n (2)

where n is a zero-mean complex Gaussian

K

;vector with the covariance matrix 2Rfor both

real and imaginary components. We do not con-sider the problem of channel estimation here. We use BPSK modulation with coherent detection in a 4-user bit-synchronous system with a set of sig-nature waveforms derived from Gold sequences of length seven that result in a normalized cross-correlation matrixRas 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 se-quences g1 = 101] and g2 = 111]. It has a

mini-mum free distance,

d

_{free, of 5 and its encoder}

mem-ory,

m

, is equal to 2. At the receiver, we imple-ment 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 detec-tors.

3 Comparison of Multiuser

De-tectors

Figures 1(a) and 1(b) show the BER plots ver-sus average SNR for the uncoded and coded sys-tems, respectively, for single- and multi-user de-tectors. 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 two-stage with the decorrelating rst two-stage (TSDFS) de-tector 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.

Next, 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 Fig-ure 2(b) we show the performance of the TSCFS detector with and without coding for both the mod-erate 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 SNR case. However, the performance of the coded system is very acceptable, and the er-ror 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

Detec-tor 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, er-ror correction is applied to the decisions of the rst stage detector in an attempt to make them more re-liable. The decoding delay of the complex scheme is twice that of the simple.

Depending on SNR, user cross-correlations, and the channel characteristics one or the other of the complex and simple schemes shows better perfor-mance. The complex scheme may perform poorly because of the bursty nature of the uncorrected errors coming out of the rst bank of Viterbi de-coders. 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 er-rors in second stage decisions. The second bank of Viterbi decoders no longer provides optimum de-cisions 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 SNR and the complex scheme will do better for low cross-correlations be-tween 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 Fig-ure 3 shows the performance for theRused earlier.

5 Complex Scheme with User

In-terleaving

To overcome the problem described above for the complex scheme, an interleaving method is pro-posed where the relative order of the bits in the in-terleaved 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 interleaver are

P

, the period of the delay sequence, and

D

, the num-ber of bit positions by which each bit in the original sequence is separated from the next. A correspond-ing 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.

in-tended interference cancelation to occur. Note that since we are using a half-rate code, the actual in-formation bit delay for an interleaver-deinterleaver pair will be (

P

;1)

D=

2.

Figure 5(a) shows the BER of the TSCFS de-tector for a 2-user system over the AWGN chan-nel 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 out-performs the complex scheme if no interleaving is used virtually over the entire SNR range. An in-terleaver 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 stor-age) occurring when we go from

P

=

D

= 5 to

P

=

D

= 10. Note 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 inter-leaving. For the largest interleaver (

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. Note that interleaving is required in any wireless environment to mitigate the eects of fading. The complex scheme requires that operation to be re-peated 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 SNR increases (exceeding two orders of magnitude) for moderate interleaver depths. A more powerful code is required on the fading channel to realize the po-tential 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 vi-able alternative in multiuser detection considering its simplicity, excellent performance, and robust-ness in near-far situations. It also improves greatly with lower user cross-correlations. For the coded system, it outperforms the decorrelator for an av-erage SNR 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 decor-relator is that is does not require cross-correlation matrix inversion at the receiver.

We then introduced an alternative implementa-tion for the coded system (the complex scheme), and analyzed its behavior in comparison to the sim-ple scheme. Finally, a novel interleaving scheme for the complex two-stage detector was proposed, and shown to provide large improvements over the sim-ple scheme in preliminary results for a 2-user sys-tem. More work is needed to study systems with a larger number of users on the fading channel,

but preliminary results indicate that more power-ful 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 Chan-nels". IEEE Transactions on Information The-ory, IT-32(1):85{96, Jan. 1986.

2] T.R. Giallorenzi and S.G. Wilson. "Multistage Decision Feedback and Trellis-Based Multiuser

Receivers for

Convolu-tionally Coded CDMA Systems". SEAS Report No. UVA/538341/EE93/102. May 1993. 3] M. Nasiri-Kenari and C.K. Rushforth. "An

Ecient Soft-Decision Decoding Algorithm for Synchronous CDMA with Error-Control Cod-ing". In Proceedings of the IEEE International Symposium on Information Theory, Trond-heim, Norway, 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 Vehicu-lar Technology Conference Proceedings, Vol. 1, pages 382{386, April 1996.

5] M. K.

Varanasi and B. Aazhang. "Near-Optimum De-tection in Synchronous Code-Division Multiple-Access Systems". IEEE Transactions on Com-munications, 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 Communica-tion, Control, and Computing, Monticello, Illi-nois, pages 1{10, October 1995.

7] A. Duel-Hallen.

"Decor-relating Decision-Feedback Multiuser Detector for Synchronous Code-Division Multiple-Access Channel". IEEE Transactions on Communica-tions, COM-41(2):285{290, Feb. 1993.

8] Ayman El-Ezabi. "Combined Multiuser De-tection and Error Correction for Code Divi-sion Multiple Access Systems over Gaussian and Rayleigh Fading Channels". Master's thesis, North Carolina State Univ., June 1995.

0 5 10 15 20 25 30 35 10−5

10−4 10−3 10−2 10−1 100

SNR(i) dB, i=1,2,3,4

BER of User 1 __x__: Conventional __o__: Decorrelator

__+__: 2−stage conv. 1st stage

__*__: 2−stage decorr. 1st stage

−−−−−: Single User Bound

(a) Uncoded Case

0 5 10 15 20 25 30 35 40

10−6 10−5 10−4 10−3 10−2 10−1 100

SNR(i) dB, i=1,2,3,4

BER of User 1

__x__: Conventional __o__: Decorrelator

__+__: 2−stage, conv. 1st stage __*__: 2−stage, decorr. 1st stage −−−−−: Single User Bound

(b) Coded Case

Figure 1: BER for 4-user Systems on a Rayleigh Fading Channel

0 5 10 15 20 25 30 35 40

10−6 10−5 10−4 10−3 10−2 10−1 100

SNR(i) dB, i=1,2,3,4

BER of User 1

__x__: Conventional, Uncoded

__o__: Conventional,Coded __+__: TSCFS, Uncoded

__*__: TSCFS, Complex

−−*−−: TSCFS, Simple

(a) Low User Cross-correlations System

0 5 10 15 20 25 30 35 40 10−6

10−5 10−4 10−3 10−2 10−1 100

SNR(1) dB

BER of User 1

__x__: TSCFS, Uncoded,−3 dB

__o__: TSCFS, Coded,−3 dB

__+__: TSCFS, Uncoded,−6 dB

__*__: TSCFS, Coded,−6 dB

(b) TSCFS Detector Performance in Two Near-Far Cases

0 5 10 15 20 25 30 35 40 10−6

10−5 10−4 10−3 10−2 10−1 100

SNR(i) dB, i=1,2,3,4

BER of User 1

__x__: TSCFS,complex __o__: TSCFS,simple

__+__: TSDFS,complex __*__: TSDFS,simple

Figure 3: BER of "Simple" and "Complex" Schemes for Two-stage Detectors with Coding in a Fading Channel

r(t) FirstStage

Detector

-+

+ −

−

y₁

y₂

bˆ2( )2

bˆ1( )2

w12

w₂₁

Symbol Decoder

Symbol Decoder Deinter

leaver Deinter

leaver leaver Inter

leaver Deinter

Decoder

Decoder Encoder

Encoder

leaver Inter

M O D U L A T I O N

C H A N N E L b1

b2

& S U M M I N G

Delay Delay

Matched Filter 1

Matched Filter 2

2 4 6 8 10 12 14 16 10−6

10−5 10−4 10−3 10−2 10−1 100

SNR(i) dB

BER

x : P=D=5 o : P=D=10 + : P=D=15 * : P=D=20

−−− : Simple scheme ___ : No interleaving (Complex)

(a) TSCFS, r=0.75

Complex, No interleaving Complex, P=D=10 Complex, P=D=20 Simple

2 4 6 8 10 12 14 16 10−6

10−5 10−4 10−3 10−2 10−1 100

SNR(i) dB

BER of user 1

(b) TSDFS, r=0.9