Interference Rejection and Equalization forDS/CDMA Multiuser Communication

Hsin-Chang ChenDepartment of Electronic EngineeringChung Yuan Christian University

Chung-Li, 32023 Taiwan

Li-Der JengDepartment of Electronic EngineeringChung Yuan Christian University

Chung-Li, 32023 Taiwan

Chung-Hsuan WangDepartment of Communication Engineering

National Chiao Tung UniversityHsinchu, 30056 Taiwan

Abstract- In direct-sequence code division multiple access(DS/CDMA) mobile communication systems with time-varyingmultipath channels, both intersymbol interference (ISI) andmultiple-access interference (MAI) must be considered. It hasbeen shown that iterative equalization and decoding method is anefficient technique to combat ISI. Based on this approach, we pro-pose a turbo equalization-like receiver for multiuser DS/CDMAsystems in multipath channels. The proposed MAI-rejection/ISIsuppression filter is based on a cost function evaluated at thePN code despreader's and data detector's output. Besides, ourscheme does not require a training signal. Simulation results showthat the proposed iterative receiver performs better than that ofnon-iterative scheme, and the BER decreases with the numberof iteration increases.

I. INTRODUCTION

In wireless environments, the multipath fading is animportant problem for signal detection. These different pathswith different attenuations cause the signal to fade both inamplitude and in time. The adaptive filter receivers can beused to compensate this phenomenon and able to adapt todifferent channel characteristics. Adaptive receivers for singleuser detection performs better than conventional receivers.They perform interference rejection, despreading, and in somecases act as the RAKE receivers which combine the multipathcomponents of the signal. There have been considerableworks done in the past few years on adaptive multiuserdetection in [4] and [5] based on the minimization of meansquare error (MMSE) between the finite impulse response(FIR) filter output and the data.

A low complexity soft multiuser detector is proposed in[6], which uses the same decision statistic as the conventionalRAKE receiver and performs soft-interference cancellationand instantaneous MMSE filtering. MMSE linear filters forcontinuous transmission are presented in [13] which take intoaccount both ISI and MAI. To get the better performance, thedecision feedback equalizer (DFE) can be used for iterativeinterference cancellation. The structure of the receiver withthe chip-level DFE has been investigated. On the otherhand, Yihand [12] presented a design of iterative multiuserdetection for bit-interleaved coded modulation (BICM) signalsin CDMA systems over multipath Rayleigh fading channels.

In digital communication systems, error-correction

codes can improve the system performance. Furthermore,conventional solutions consider both equalization and channelcoding which are done separately. Recently, a novel techniqueconsidering the equalization and decoding jointly, is called"turbo equalization". Combining turbo coding and multiuserdetection in CDMA has shown to get the system performanceclose to single user bound with a few iterations of jointdetection and decoding.

It has been shown that iterative equalization and decodingmethod has proved a clever technique for combating ISI [3].Based on this approach, we propose a turbo equalization-likereceiver for multiuser DS/CDMA systems in multipathchannels. The proposed MAI-rejection/ISI suppression filteris based on a cost function evaluated at the PN codedespreader's and data detector's output. Besides, our schemedoes not require a training signal.

The rest of this paper is organized as follows. Section IIgives a general description of the transmitter and receiverscheme of our proposed system. In this section we also definetwo cost functions in the iterative process. Section III presentsthe log-likelihood ratio transmission for the new cost functionto update filter tap-weights. Numerical results and discussionare given in section IV. Finally, section V summarizes ourmajor results.

TI. SYSTEM MODELThe block diagram of the proposed scheme is shown in

Fig. 1, where the number of active users is K. A binarydata sequence of each user is encoded by a convolutionalencoder and then fed into an interleaver. After interleaving, thecoded data sequence is spreaded by the user-specific signaturesequence of length A1. Finally, the transmitted data sequenceis modulated by a standard binary phase-shift keying (BPSK)modulator. In this paper, we assume a coherent receiver suchthat the multipath channel can be modeled as a finite impulseresponse (FIR) filter with impulse response [ho, hl,..., hp],and the transmitted signal is corrupted by thermal noise andMAI as well. The thermal noise in the channel is the so-called additive white Gaussian noise (AWGN) with the powerspectral density (PSD) No. The received sample sequence isfiltered and decoded by a adaptive filter and convolutional

0-7803-9206-X/05/$20.00 ©2005 IEEE 284

decoder respectively. In order to make better performance of asour system, iterative algorithm is employed in the proposedreceiver.

user data #1

p

Zq,m (n) = , hps',m_p (n)p=o

K P

+ , S hpsj mn-p (n) + Nq,m (n)j=2,jok p=O

'Zq(n) L

algorivh spreadingcodes LOE (bq(n))

I iter hinterleaver!iterative scheme

Fig. 1. Block diagram of the proposed system.

A. TransmitterFor the proposed multiuser DS/CDMA communication sys-

tems, assume the k-th user is the desired user. The desireduser transmit a sequence of binary information, whose el-ements take on values of 0 or 1 equiprobably, then thedata vector for n-th block can be expressed as bk (n) =

[bk (n) , bk (n), bk (n)], k = , ,K, where k denotesthe k-th user, Q is the number of elements in a block. Thisdata is first encoded by a recursive systematic convolutionalcode with rate 1/2 shown in Fig. 2. The generator matrix

used in this paper isG [i,1+D+D2. The encoded data

Xk,q (n), 1, 2, is the codeword of the k-th user, n-th block,q-th bit. Then the encoded data is feed into the interleaver withsize Q. In this paper, we consider both the block interleaverand S-random interleaver. After interleaving, the coded datasequence is spreaded by the user-specific signature sequence oflength Al. The transmitted data sequence eventually is modu-lated by a standard BPSK modulator, i.e., +1,0 -1}.Finally, these data sequences are combined by a multiplexerand transmit over the multipath channel.

where si,m (n),j = 1,2, , K is the binary input signals{+1, -1} with equal probabilities; the second term is the MAIsequence; Nq,m (n) is the AWGN sequence with variance o2.

Considering the proposed MAI/ISI rejection scheme illustratedin Fig. 1, we define the number of taps of the transversal filterbe t and the tap-weight vector as

Wq (n) = [Wq,l (n) Wq,2 (n) Wq,t (n)]TAssuming

Zq (n) = [ZAl(q-1)+l (n) ZM(q-1)+2 (n) ZA(q-1)+,N (n)]Tand

ZA(q-1) (n) ZAI(q-1)+AI-1 (n)

ZM>(q-1)-1 (n) ZAI(q-l)+AI-2 (n)Uq (n) = . (2)

LZAI1(q-1)-(t-1) (n) ... ZAI(q-l)+A,I-t (n)i

the estimated interference (MAI+ISI) can be obtained in thefollowing

Iq (n) = [IM(q-1)+1 (n) iM(q-1)+2 (n) *A.*Z(q-1)+M (nt)]

= U (n) Wq (n). (3)

Let C = [Cl C2 CM 1T be the signature sequence of thedesired user, we have CTC = M. For iterative interferencerejection and decoding, our multiuser receiver utilizes theadaptive filter output and the a priori information of desireduser data to get the soft estimates. In the first iteration, no a

priori probability is available, so Pr {dE (n) = ±1} = 1/2 isused for soft outputs. It is desired that the adaptive filter outputgives a perfect MAIMISI estimation so that the normalizeddespreader output

dq (n) = (n)-Iq (n)TC/M (4)

behaves like a desired user's output. In other words, we hopethat signal at the despreader output has the same statistic as

an ideal BPSK signal. To achieve the goal we formulate thecost function

Fig. 2. Recursive systematic convolutional encoder.

B. ReceiverThe received sample sequence Zq,m (n) of the desired user

in n-th block, q-th bit, and m-th chip can be thus expressed

Jq (n) = E{ d, (n)-dq (n) }

where

dE (n) = {+1 dq (n) > 0

-1, otherwise

(5)

(6)

is the hard decision for the despreader output using for thepseudo training signal. Employing Least Mean Square (LMS)

285

(1)

algorithm to minimize the cost function Jq (n) for updatingthe set of weight every bit interval. we need to evaluate

Wq+j (n) =Wq (n) - uaJ(t (n)o9Jq (n)

-W, (n)-HL [M (d (n) -dq (n)) Uq (n) C] (7)

where At is the step size.

During the signal detection, the bit reliabilities must becomputed as a priori information of the soft-input soft-output(SISO) channel decoder. To get the bit reliabilities, the statis-tics

={[b, (n)-dq (n)] lb, (n) =+1} P {b,(n) = +l

+ {[bq(n)-dq (n)] Ibq(n)-l1} P{bq(n)=-1}. (12)

Similarly, using the LMS algorithm to minimize the costfunction Jq (n), we have

aJq' (n)&Wq (n)

={ [(bq (n) dq(n))Uq(nI bq(n)+1} P{bq(n)=+1}

p (n) E {dq (n)}and

(n)-=Et dq(n) }-E{dq(n)}

of the set of bits dq (n) , q = 1, 2, * , Q, are required. Let

d (n) = di (n) d2 (n) ..dQ (n)the bit reliability is given as

{ q(n)Idd(n) =+1} 2LA(dq (n)) = ln = } = 2dq (n) (10)

P {dq (n) jd~E (n)--1 ¢d

After MAP decoding algorithm [2], the a posterior informa-tion can be obtained from the channel decoder in the following

Lo bq (n) Idq (n))

= Lc- dq (n) + LA (dq (n)) + LOE (dq (n) Ibq (n)) (11)

and hard decision will be made for bit estimates bq (n)of the desired user. Later, the bit estimates take the placeof the hard decision for the despreader output using foranother pseudo training signal. Consequently, we can see thatthe a-posteriori LLR, i.e., soft output, Lo (bq (n) Idq (n))calculated with the aid of the MAP algorithm can beviewed as comprising three additive soft-metric terms:LA (dq (n)), Lc 4q (n) , LOE (dq (n) Ibq (n)). The extrinsic

information LOE (dq (n) Ibq (n)) which contains the softinformation of the current bit is re-interleaved and fed backinto the adaptive filter to update the a prior informationto get better soft information. The iteration process, whichrefines the soft output Lo (bq (n) iq (n)), q = 1 2, ... , Q,continues until the result converges. At the last iteration, thedecoder makes a hard decision for the user's data bits.

III. LOG-LIKELIHOOD RATIOAs mentioned above, we calculate the bit reliabilities of

filter's output dq (n) and expressed as LA (dq (n)). The re-liabilities are used as the a priori information in the SISOMAP decoder. The a posteriori information of the decoded

Zq(n) dq(n) - -> LA(dq(n))Equa1izer Decde,i'~~~~~~~ A

(^

-))

-Lo (dq (n) bq (n))'4bq(n)1*-±((f)(lJ

Fig. 3. Log-Likelihood Ratio transmission diagram.

bit bq (n) is expressed as Lo (bq (n) ldq (n)) which includesa priori information LA (dq (n)), extrinsic information andLOE (dq (n) lbq (n) ). After first iteration, the extrinsic infor-mation will be transformed into the a priori information for thefilter tap-weights updating. The LLR of the data bit bq (n) isdenoted as Lu bq (n)) and is defined to be the log of the ratioof the probabilities of the bit taking its two possible values,i.e.,

Lu (bq (1)) =ln (P (q (1) +)Pr (bq (n) = -1))

(15)

Given the LLR value Lu (bq (n)), it is possible to calculateFurthermore, when the first iteration is finished, we use the the probability that bq (n) = +1 or bq (n) =-1 as follows.

following cost function for more iterations We know that

Jq (n) = E {[bq (n)-dq (n)] } Pr (bq (n) = -1) = 1-Pr (bq (n) = +1)

286

(8)and

(9+1 (n) = ) (n)-p i 4 (n)

(13)

(14)

(16)

and take the exponent of both sides in Equation (15), we have

r(bq

Pr (bq (n) = +1)exp 1Lu (bq (n))} 1- Pr (bq (n) = +1) (17)

and

exp {Lu 1q (n)) ErPr bq (ni) = *1) (18)

m

Similarly,

7-1- {L I{ \ 11

Vr bq rn) = -1) = ^eL )1+exp{ Lu(bq(n))}t

Once the decoding process is finished, the soft informa-tion LOE (dq (n) lbq (n)) can be fed into the filter as a

priori information. With the help of Pr (bq (n) = +±) and

Pr (bq (n) = -1) from LOE (dq (n) 1bq (n)), we can utilize

it in Equation (12) and Equation (13) for tap-weights updating.Then, we have accomplished one iteration for our proposedsystem.

IV. NUMERICAL RESULTSWe present BER performance results for the proposed

receiver by simulations. The system parameters for simulationare described as follows. The spreading code used in thispaper is the orthogonal Walsh code of length 16. Thefilter length is 16 taps. The transmission channel response

for simulation is [0.65, -0.52,0.39, 0.33, -0.19,0.06]. Inaddition, we consider two R = 1/2 convolutional codeswhose generator matrices are [1, 1++D2] (degree = 2), and

[i 1+D+2+D3+D42 (degree = 4). Two kinds of interleaverare used: S-random interleaver and block interleaver of size16384.

Shown in Fig. 4 is the performance comparison betweenthe different number of iteration, where the active user

number is 16 for convolutional codes of degree 2. S-randominterleaver is used for interleaving. Simulation results showthat the more the number of iteration, the performance isbetter. Fig. 5 shows the performance comparison betweenthe different number of active user for non-iteration withconvolutional codes of degree 2. Also, the S-randominterleaver is used in this case. The simulation results showthat the more the number of active users, the performance isworse. Fig. 6 shows the performance comparison betweenthe conventional scheme and the proposed scheme. Theactive user number equals 16, and S-random interleaveris used. Convolutional codes of degree 2 and 4 are alsoconsidered. Simulation results indicate that performance ofthe proposed system is better than that of the conventionalsystem. Fig. 7 shows the performance difference between

two cost functions Jq (n) = E { dq (n) - dq (n) } and

10

'.5 8.5Eb/No(dB)

9.5 10

Fig. 4. Performance comparison between different number of iterations: 16active user, convolutional codes degree = 2, S-random interleaver.

Non-iterative with Convolutional Codes degree = 2 and S-random interleaver

10-2

a)(a

m

5 8 9 10Eb/No(dB)

Fig. 5. Performance comparison between different number of active users:

non-iteration, convolutional codes degree = 2, S-random interleaver.

Jq (n) = E {[bq (n)-dq (n)]} We find that in the

non-iterative case, the performance of using cost functionJq (n) is identical to that using cost function J' (n). But inthe iterative case, the performance of using cost functionJ' (n) is better than that using cost function Jq (n).

Fig. 8 illustrates the performance comparison between blockinterleaver and S-random interleaver. Simulation results showthat S-random interleaver is better than block interleaver.

V. CONCLUSIONS

In this paper, we have presented an efficient interferencecancellation scheme which combines a filter and an iterative

287

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5 6 7 8 9Eb/No(dB)

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10

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................................ ....................................................... .... ............................................. ...............................

os;- -....,.........................' ' ' ' ' +. ..'.'.'..'.''.'.'.'.' '."'.-....................

...

.. ..

... ... ...

.. .. .......,.,,

.5 . .. . .... ....,,,1., 11 11Eb:No(dB\

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Fig. 8. Performance comparison between different interleaver: 16 activeusers, non-iteration, convolutional codes degree = 2.

10-3

cc0

10-4

Comparson between original cost function and new cost function

8.5Eb/No(dB)

9.5

Fig. 7. Performance comparison between two different cost functions: 16active users, convolutional codes degree = 2, S-random interleaver

SISO decoder. We employ the LMS algorithm for the filtertap-weights updating and our system does not require thetraining signal. It can reduce the costs and complexities forthese kinds of systems.

From simulations, the iterative scheme performs better thanthe non-iterative scheme, and the BER decreases with the num-ber of iteration increases. Besides, we proposed two differentkinds of cost function in our iterative scheme. The simulationshows our proposed cost function J' (n) outperforms theconventional cost function Jq (n).

REFERENCES

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[2] J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary blockand convolutional codes," IEEE Trans. Inform. Theory, vol. 42, Issue 2,pp. 429 - 445, March 1996.

[3] Tuchler, M.; Koetter, R.; Singer, A.C., "Turbo equalization: principlesand new results," IEEE Trans. Commun., vol. 50, Issue 5, pp: 754 - 767,May 2002 .

[4] S. Miller, "An adaptive direct-sequence code-division multiple-accessreceiver for multiuser interference rejection," IEEE Transactions onCommunications, vol. 43, Issue 234, pp: 1746 - 1755, Feb./March/April2002.

[5] Dao Sheng Chen and S, Roy,"An adaptive multiuser receiver for CDMAsystems," IEEE Transactions on Selected Areas in Communications, vol.12, Issue 5, pp: 808 - 816, July 1994.

[6] Qinghua Li, Xiaodong Wang, and Costas N. Georghiades, "Turbo Mul-tiuser Detection for Turbo-Coded CDMA in Multipath Fading Channels," IEEE Transactions on Vehicular Technology. vol. 51, No. 5, Sept 2002.

[7] Jinho Choi, Seong Rag Kim, and Cheng-Chew Lim, "Receivers WithChip-Level Decision Feedback Equalizer for CDMA Downlink Chan-nels," IEEE Transactions on Wireless Communications, vol. 3, No. 1, Jan2004.

[8] M. Abdulrahman, A. U. H. Sheikh, and D. D. Falconer, "Decisionfeedback equalizer for CDMA in indoor wireless communications," IEEEJ. Select. Areas Commun., vol. 12, pp. 698-706, May 1994.

[9] J. E. Smee and S. C. Schwartz, "Adaptive feedforward/feedback architec-tures for multiuser detection in high data rate wireless CDMA networks,"IEEE Trans. Commun., vol. 48, pp. 996-1011. June 2000.

[101 Padam. L. Kafle, and Abu. B. Sesay, "Performance of turbo codedmulticarrier CDMA with iterative multiuser detection and decoding,"Electrical and Computer Engineering, 2001. Canadian Conference, onvol. 1, pp. 105-110, 13-16 May 2001.

[11] Garg, Vijay Kumar, IS-95 CDMA and cdma2000: cellular/PCS systemsimplementation, Upper Saddle River, NJ : Prentice Hall PTR, 2000.

[12] Chi-Hsiao Yihand, and E. Geraniotis, "Iterative multiuser detectionfor bit-interleaved coded modulation based CDMA signals in fadingchannels," Spread Spectrum Techniques and Applications, 2002 IEEESeventh International Symposium, on vol. 2, pp. 485 - 489 , 2-5 Sept.2002.

[13] Z. Xie, R.T. Short, and C.K. Rushforth, "A family of suboptimaldetectors for coherent multiuser communications," IEEE J. Sel. AreasCommun., vol. 8, no. 4, pp. 683 - 690, May. 1990.

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