decision-feedback blind adaptive multiuser detector for synchronous cdma system

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 1, JANUARY 2000 159 Decision-Feedback Blind Adaptive Multiuser Detector for Synchronous CDMA System He Ping, Tjeng Thiang Tjhung, Senior Member, and Lars K. Rasmussen Abstract—In this paper, we develop a blind adaptive multiuser detector for synchronous code-division multiple access (CDMA) with a noise-whitening filter. The triangular structure of the noise- whitened model ensures complete resolution of detection ambigui- ties. To further improve the symbol error probability performance, we introduce decision feedback in our detector similar to the decor- relating decision-feedback detector (DDFD), thus forming the de- cision-feedback blind adaptive multiuser detector (DFBD). Simu- lations indicate that the performance of the DFBD is very close to that of the DDFD in additive white Gaussian noise (AWGN) chan- nels. In Rician fading channels, the DFBD can track the slowly varying channels well and has symbol error probability perfor- mance approaching that of the DDFD, which requires the knowl- edge of users' energies. The blind adaptive and decision-feedback blind adaptive multiuser detectors proposed here do not, however, require that knowledge. Index Terms—Blind adaptive multiuser detection, decision feed- back, symbol error probability, synchronous CDMA system. I. INTRODUCTION C ODE-division multiple access (CDMA) is a multiplexing technique where several independent users share a common channel by modulating preassigned signature wave- forms. The receiver then observes the sum of the transmitted signals over an additive white Gaussian noise (AWGN) channel. A conventional receiver simply consists of a bank of single-user matched filters followed by quantizers. Its performance, how- ever, deteriorates rapidly due to multiple-access interference (MAI) as the number of users increases. The optimum receiver in this CDMA multiuser scenario makes decisions based on the Viterbi algorithm where the complexity grows exponentially with the number of users. A multitude of suboptimum detectors have been proposed for obtaining a tradeoff between perfor- mance and complexity. Most such multiuser detectors are based on coherent detection and hence assume a priori knowledge of each user's received amplitude, channel coefficient and timing. In mobile communication environments, however, the amplitudes of the received signals usually vary with the motion of mobile stations and with changes in the multipath propagation. Detectors must therefore estimate and update the parameters adaptively for each decision. Recently, blind adaptive multiuser detection has received some attention and several blind adaptive detectors have been Manuscript received January 18, 1997; revised December 10, 1998. H. Ping and T. T. Tjhung are with the Centre for Wireless Communications, Department of Electrical Engineering, National University of Singapore, 119260, Singapore. L. K. Rasmussen is with the Chalmers University of Technology, Sweden. Publisher Item Identifier S 0018-9545(00)00636-8. proposed [1]–[6]. The main motivation for employing a blind detector is to avoid the requirements of a training sequence which is commonly required in most of the adaptive multiuser detectors proposed previously [7]–[10]. Blind detection relaxes the requirements for prior knowledge of system parameters, and its performance does not degrade remarkably when compared to detectors requiring a training sequence. For example, the blind detector based on the anchored minimum output energy proposed in [1] is shown to converge to a scaled version of the MMSE detector without requiring a training sequence. Other blind detectors apply the constant modulus algorithm (CMA) [3]–[6]. The CMA has been widely applied to cancel intersymbol interference (ISI) for digital transmission through band-limited channels [11]–[16]. Based on the combined channel and equalizer parameter space, an infinite tap filter with CMA tap updates will always converge to a global minimum re- gardless of the initial tap weight settings. However, the CMA has also been proven to have local stable points when a finite number of tap weights is used [17], [18]. In this case, the algorithm can inadvertently converge to an undesired equilibrium. When the CMA is applied in a CDMA system, it is therefore possible that an interferer is recovered rather than the desired signal. Even when the desired signal is captured, there are pos- sible phase ambiguities that can lead to an erroneously recov- ered signal. Some constraints must therefore be enforced to re- solve these permutation and phase ambiguities. In [6], three con- straints are derived to ensure convergence to the desired solution. This, however, involves inversion of the resulting filter matrix which is not desirable. Zecevic and Reed [4] suggest an anchored CMA approach similar to [1] which also resolves the ambigui- ties. In this paper, we suggest an alternative approach based on the noise-whitened CDMA model first presented in [19]. The model is characterized by a triangular structured MAI which directly re- solves any permutation ambiguities. Additionally enforcing that the main tap be greater than zero, all ambiguities are avoided. The convergence rate of the CMA is in general known to be slow. The anchored MOE detector in [1] is expected to have faster convergence. However, this detector converges to a scaled version of the MMSE detector, leading to a MSE performance loss as compared to training-based schemes. CMA schemes pre- viously considered in the literature, closely approximate the per- formance of the training-based equivalents [4], [5]. A potential advantage of the CMA algorithm as compared to the anchored MOE is therefore an improved bit error rate performance at the expense of noticeably slower convergence. The above detectors are fundamentally limited by their linear structure. At best, they reach the performance of the best linear detectors. In heavily loaded systems, the performance can thus 0018–9545/00$10.00 © 2000 IEEE

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Page 1: Decision-feedback blind adaptive multiuser detector for synchronous CDMA system

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 1, JANUARY 2000 159

Decision-Feedback Blind Adaptive MultiuserDetector for Synchronous CDMA System

He Ping, Tjeng Thiang Tjhung, Senior Member, and Lars K. Rasmussen

Abstract—In this paper, we develop a blind adaptive multiuserdetector for synchronous code-division multiple access (CDMA)with a noise-whitening filter. The triangular structure of the noise-whitened model ensures complete resolution of detection ambigui-ties. To further improve the symbol error probability performance,we introduce decision feedback in our detector similar to the decor-relating decision-feedback detector (DDFD), thus forming the de-cision-feedback blind adaptive multiuser detector (DFBD). Simu-lations indicate that the performance of the DFBD is very close tothat of the DDFD in additive white Gaussian noise (AWGN) chan-nels. In Rician fading channels, the DFBD can track the slowlyvarying channels well and has symbol error probability perfor-mance approaching that of the DDFD, which requires the knowl-edge of users' energies. The blind adaptive and decision-feedbackblind adaptive multiuser detectors proposed here do not, however,require that knowledge.

Index Terms—Blind adaptive multiuser detection, decision feed-back, symbol error probability, synchronous CDMA system.

I. INTRODUCTION

CODE-division multiple access (CDMA) is a multiplexingtechnique where several independent users share a

common channel by modulating preassigned signature wave-forms. The receiver then observes the sum of the transmittedsignals over an additive white Gaussian noise (AWGN) channel.A conventional receiver simply consists of a bank of single-usermatched filters followed by quantizers. Its performance, how-ever, deteriorates rapidly due to multiple-access interference(MAI) as the number of users increases. The optimum receiverin this CDMA multiuser scenario makes decisions based on theViterbi algorithm where the complexity grows exponentiallywith the number of users. A multitude of suboptimum detectorshave been proposed for obtaining a tradeoff between perfor-mance and complexity. Most such multiuser detectors are basedon coherent detection and hence assumea priori knowledgeof each user's received amplitude, channel coefficient andtiming. In mobile communication environments, however,the amplitudes of the received signals usually vary with themotion of mobile stations and with changes in the multipathpropagation. Detectors must therefore estimate and update theparameters adaptively for each decision.

Recently, blind adaptive multiuser detection has receivedsome attention and several blind adaptive detectors have been

Manuscript received January 18, 1997; revised December 10, 1998.H. Ping and T. T. Tjhung are with the Centre for Wireless Communications,

Department of Electrical Engineering, National University of Singapore,119260, Singapore.

L. K. Rasmussen is with the Chalmers University of Technology, Sweden.Publisher Item Identifier S 0018-9545(00)00636-8.

proposed [1]–[6]. The main motivation for employing a blinddetector is to avoid the requirements of a training sequencewhich is commonly required in most of the adaptive multiuserdetectors proposed previously [7]–[10]. Blind detection relaxesthe requirements for prior knowledge of system parameters, andits performance does not degrade remarkably when comparedto detectors requiring a training sequence. For example, theblind detector based on the anchored minimum output energyproposed in [1] is shown to converge to a scaled version of theMMSE detector without requiring a training sequence.

Other blind detectors apply the constant modulus algorithm(CMA) [3]–[6]. The CMA has been widely applied to cancelintersymbol interference (ISI) for digital transmission throughband-limited channels [11]–[16]. Based on the combinedchannel and equalizer parameter space, an infinite tap filter withCMA tap updates will always converge to a global minimum re-gardless of the initial tap weight settings. However, the CMA hasalso been proven to have local stable points when a finite numberof tap weights is used [17], [18]. In this case, the algorithm caninadvertently converge to an undesired equilibrium.

When the CMA is applied in a CDMA system, it is thereforepossible that an interferer is recovered rather than the desiredsignal. Even when the desired signal is captured, there are pos-sible phase ambiguities that can lead to an erroneously recov-ered signal. Some constraints must therefore be enforced to re-solve these permutation and phase ambiguities. In [6], three con-straints are derived to ensure convergence to the desired solution.This, however, involves inversion of the resulting filter matrixwhich is not desirable. Zecevic and Reed [4] suggest an anchoredCMA approach similar to [1] which also resolves the ambigui-ties. In thispaper,wesuggestanalternativeapproachbasedon thenoise-whitened CDMA model first presented in [19]. The modelis characterized by a triangular structured MAI which directly re-solves any permutation ambiguities. Additionally enforcing thatthe main tap be greater than zero, all ambiguities are avoided.

The convergence rate of the CMA is in general known to beslow. The anchored MOE detector in [1] is expected to havefaster convergence. However, this detector converges to a scaledversion of the MMSE detector, leading to a MSE performanceloss as compared to training-based schemes. CMA schemes pre-viously considered in the literature, closely approximate the per-formance of the training-based equivalents [4], [5]. A potentialadvantage of the CMA algorithm as compared to the anchoredMOE is therefore an improved bit error rate performance at theexpense of noticeably slower convergence.

The above detectors are fundamentally limited by their linearstructure. At best, they reach the performance of the best lineardetectors. In heavily loaded systems, the performance can thus

0018–9545/00$10.00 © 2000 IEEE

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160 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 1, JANUARY 2000

be unacceptable. A possible solution is to introduce decisionfeedback. The triangular structure of the noise-whitened modelis especially suited for decision feedback as exploited in [19].The same approach is clearly applicable to the CMA detectorbased on the noise-whitened model. Decision feedback is nothowever, easily incorporated into the anchored MOE as sug-gested in [1]. The algorithm is based on a chip-level repre-sentation while effective blind decision feedback without priorknowledge of the received signal amplitudes requires a bit-levelrepresentation. It is therefore necessary to derive an equivalentalgorithm on bit level in order to facilitate decision feedback.This is however, beyond the scope of this paper and thereforedecision feedback is only considered for the CMA-based de-tector, i.e., we focus on developing a blind CMA decision feed-back detector based on a structure similar to the DDFD in [19].

The rest of the paper is organized as follows. In Section II,the matched filtered and noise-whitened system models for syn-chronous CDMA are briefly restated. The noise-whitened-basedblind CMA detector is formalised in Section III. The extensionof the suggested blind detector to include decision feedback isconsidered in Section IV and the performance of all the detectorstructures are compared in Section V through computer simula-tions. Conclusions are offered in Section VI.

II. SYSTEM MODEL

In a synchronous CDMA system, users share a commonchannel by modulating preassigned signature waveforms,

, where each waveform is restrictedto a symbol interval of duration with normalized energy

. These signature waveforms are linearly inde-pendent. The input symbol of each user takes on independentantipodal binary values [1, 1] with equal probability. Theinput bit sequence for each user is independent of those of theother users. Under the assumption of an AWGN channel, thereceived signal can be expressed as

(1)where is an AWGN process with two-side power spectraldensity , and and are the information bit andthe energy of theth user at theth instant, respectively. In syn-chronous transmission, each user produces exactly one symbolwhich interferes with the desired symbol, so without loss of gen-erality, it is sufficient to consider the signal received in only onesymbol interval. Therefore, dropping the time index maybe rewritten as

(2)

The output of a bank of filters matched to each user's signa-ture waveform is

(3)

represents the cross correlation of the received signal withthe th signature waveform, and the term

(4)

represents the cross correlation between signature waveformand . The noise component is given as

(5)

is a zero-mean Gaussian variable with variance

(6)

where denotes the expectation of. Let

denote, respectively, the input data vector and the output vectorconsisting of the match filter outputs. Superscript “” denotestranspose. The outputcan be expressed as

(7)

where

(8)

is a positive definite matrix of signature waveform crosscorrelations, and is a diagonal matrix with diagonal entries

is a Gaussian noise vector with a autocorrelation matrix.

It is easy to see thatis a sufficient statistic for estimating theinput bits . The objective of a multiuser detector is to recoverthe input bits based on the output. Since the cross-corre-lations matrix can be factored as [19], whereis a lower triangular matrix, we can apply a filter with response

to the output of the matched filters (7) to obtain the whitenoise model of CDMA systems as

(9)

where is a white Gaussian noise vector with the autocorrela-tion matrix ( is a identity matrix).

III. B LIND ADAPTIVE MULTIUSER DETECTORS

Consider the th component of at the th instant, which canbe written as

(10)

In (10), the first term is the desired information, and thesecond and third terms are the MAI and white Gaussian noise,respectively. Obviously, the MAI has a form similar to ISI,resulting from the transmission of digital signals through a

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PING et al.: DECISION-FEEDBACK BLIND ADAPTIVE MULTIUSER DETECTOR 161

Fig. 1. Blind adaptive multiuser detector.

Fig. 2. Decision-feedback blind adaptive multiuser detector.

band-limited channel. Therefore, adaptive equalization algo-rithms can be employed to cancel MAI, especially when, intime-variant mobile channels, the received amplitudesare unknown to the receiver. We should also note that in(10) does not involve the multiuser interference from the userscorresponding to , therefore, a blind adaptivemultiuser detector can consist of a bank of equalizers followedby quantizers as shown in Fig. 1. The output of the equalizerfor the th user can be expressed as

(11)where

represent the tap coefficient vector and the input signal vector ofthe equalizer at theth instant, respectively. Since the informa-tion bits have been assumed to take on antipodal binary values

, the Godard cost function [12] has the form as follows:

(12)

The objective of the blind equalizer is to minimize the costfunction (12) by adjusting the tap coefficients adaptively. As-suming at the th time instant are known, the recursiveformula for the next decision can be written as

(13)

where is the step-size parameter. By differentiatingand dropping the expectation operation, we can get the recursiveformula as follows:

(14)

Obviously, in (11), only the signal contains the desiredinformation bit of user , the minimization of the costfunction (12) naturally results in an optimal solution for useronly if the main tap coefficient is not equal to zero. Besides,the tap coefficients track the variation of the signal energies, themain tap coefficient should be restricted to be larger than zero.So this blind equalization algorithm is naturally proved to befree of the phase and permutation ambiguities. After conver-gence of the blind equalizer, the decision for userat the thinstant can be made by taking the sign of

(15)

Although the blind adaptive multiuser detector has a goodconvergence performance, it is clear from (11) that the noisehas been enhanced in the process of the equalization. In fact, byusing the approach proposed in [6], it is very easy to prove theblind adaptive multiuser detector converges to the decorrelatordetector of the white noise model of CDMA systems (9), so itssymbol error probability performance is the same as that of thedecorrelator detector of CDMA systems.

IV. DECISION-FEEDBACK BLIND ADAPTIVE

MULTIUSER DETECTOR

Decision feedback introduces a nonlinear process which hasthe potential of improving performance beyond the constraintsimposed by linear detectors. Such detectors are, however, proneto error propagation in case of erroneous decisions. It is there-fore important to detect users according to received amplitude.For the blind detector such a user ordering can crudely be ob-tained based on the matched filter outputs. In [19], Duel-Hallen

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162 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 1, JANUARY 2000

suggested the DDFD detector based on the noise-whitened sta-tistics. It was later shown that this approach corresponds to com-plexity-constrained maximum-likelihood trellis detection [20]where only one survivor is retained at each trellis stage. Forthis approach, error propagation can be virtually eliminated bykeeping two or more survivors which is equivalent to the im-proved DDFD suggested in [21] and [22]. The blind CMA de-tector based on the noise-whitened statistics can naturally beextended to include decision feedback. At convergence, this de-tector will closely approximate the DDFD. The development ofthe algorithm progresses as follows.

Based on the noise-whitened statistics, equalization for user1 is not necessary because is not perturbed by MAI fromthe other users. The decision for user 1 is made directly as

Hence, the symbol error performance of user 1 is the same asthat of the decorrelator and the DDFD [19]. For user 2, sincethe decision for user 1 has been made, the equalization for theuser can be realized by feeding back the decisionas

the decision for user 2 can be obtained as

Similarly, for user , the output of the equalization can beexpressed as

(16)

where

is the input vector of the equalizer at theth instant. Therefore,the decision for user can be made by

(17)

Substituting (16) into (12)–(14), we get the decision feedbackblind equalization algorithm. The recursive formula of the tapcoefficients for the blind equalizer can be rewritten as

(18)

Combining (16)–(18), we obtain the decision-feedback blindadaptive multiuser detector (DFBD). It can be expected thatthe performance of the DFBD is superior to that of the blindadaptive multiuser detector described in Section III, because thenoise of the feedback signals can be cancelled completely pro-vided that the decisions for the former users are correct. Similarto the blind adaptive multiuser detector, the DFBD is also freeof the phase and permutation ambiguities.

V. SIMULATION RESULTS

In this section, the performance of the blind adaptive mul-tiuser detector (BD) and the DFBD is estimated by simulationsfor synchronous CDMA systems. Since the expectation opera-tion in the cost function (12) is very difficult to do in practice, theconvergence performance of both of the detectors is considered

Fig. 3. Convergence performance of the BD and DFBD for user 4 of thefour-user system with identical energies and SNR= 10 dB,� = 10 .

using the time average cost function in each segment observa-tion interval defined as

The symbol error performance is then estimated after the con-vergence of the equalizers has been reached.

Case I. AWGN Channels:In AWGN channels, the energiesof the received signals for all users are assumed to be constants.The performance of both detectors is evaluated for a four-userand a 15-user synchronous CDMA systems.

The cross-correlation matrix of the four-user system is thesame as example (2) in [19] as

Fig. 3 shows the convergence performance of the BD and theDFBD for the fourth-user assuming that the energies of all theusers are identical, the signal-to-noise ratio (SNR) is 10 dB, andthe step size of the blind equalizers is . From Fig. 3,we can see that the equalizer converges in about 2000 iterations.The larger the step size, the faster is the convergence, howeverthe residual error will increase. Considering the tradeoff be-tween the error and the convergence, we divide the equalizationprocess into two steps. When the iteration number is less thansome number , we set a larger step size, otherwise, we seta smaller one. Fig. 4 depicts the convergence performance foruser 4 with and the initial procedure with step size

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PING et al.: DECISION-FEEDBACK BLIND ADAPTIVE MULTIUSER DETECTOR 163

Fig. 4. Convergence performance of the BD and DFBD for user 4 of thefour-user system with identical energies and SNR= 10 dB,� = 10 whenk � 500; � = 10 whenk > 500.

, the stable procedure with step size . Theequalizers have converged after 1000 iterations this time.

The symbol error probability performance of the two detec-tors are shown in Figs. 5 and 6 for all the four users with iden-tical energies. For the sake of comparison, we have simulatedthe performance of the DDFD proposed in [19] with the sameconditions and results are also drawn as dotted lines in Figs. 5and 6. The performance of user 1 is the same for all the detec-tors. For the DDFD, since user 2 suffers the least MAI and errorpropagation, its performance is the best. User 3 then basicallyis the same as that of user 2. The performance of user 4 is infe-rior to that of users 2 and 3 because of the presence of increasedMAI and error propagation. As was pointed out in [19], onlywhen the other users' energies grow very much stronger, thenits performance approaches the single-user bound and will intheory be almost the same as that of users 2 and 3. User 1 hasthe worst performance. Using the BD, as shown in Fig. 5, theperformance of user 4 is the worst. It is because user 4 suffersthe strongest MAI, and the noise has also been enhanced by thelargest amount in the equalization. If we decrease the MAI, theperformance of user 4 will be improved significantly and willapproach the performance of user 1, which has been proven bysimulations. Users 2 and 3 have almost the same performanceand are inferior to the DDFD. Fig. 6 shows that the DFBD has aperformance nearly the same as the DDFD for all four users inthe AWGN channels.

In the simulations of the 15-user system, we considerGold-like sequences of length 15, i.e., the corresponding

Fig. 5. Symbol error probability performance of the BD and DDFD for thefour-user system.

Fig. 6. Symbol error probability performance of the DFBD and DDFD for thefour-user system.

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164 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 1, JANUARY 2000

Fig. 7. Symbol error probability performance of the BD, DFBD, and DDFDfor the 15-user system.

correlation matrix has identical off-diagonal elements equalto 1/15. Similar to the four-user system, equalizers convergein 1000–2000 iterations. The symbol error probability perfor-mance is estimated only for user 1 and user 15 and all users areassumed to have the same energies. The results are shown inFig. 7 for the BD, DFBD, and DDFD. From Fig. 7, we can seethat the performance of the DFBD is close to that of the DDFD.For the BD, as every user has the same energy and suffers thesame MAI, when the SNR increases, the performance of everyuser is almost the same and inferior to the DDFD. When theSNR is small, user 15 suffers the most error propagation andthus has the worst performance.

Case II. Rician-Fading Channels:In Rician-fading chan-nels, assuming that the variations due to path loss and lognormalshadowing have been eliminated by power control, the energiesof the received signals vary slowly due to the Rician-fadingprocess. This assumption is made here because the blindequalizer based on the LMS algorithm has a slow convergencefeature, and is not appropriate for the fast varying channels. Theslow-varying Rician process can be realized by simulating theenvelope of each signal at theth symbol interval according to

where is a constant representing the nonshadowing line-of-sight (LOS) component in the received signals. andare independent band-limited Gaussian processes with mean0 and variance , which simulate the in-phase and quadra-ture multipath components, and can be obtained by passing the

Fig. 8. Convergence performance of the BD and DFBD for user 15 of the15-user system with identical energies and SNR= 10 dB,K = 10; f =

0:01.

white Gaussian processes through low-pass filters. In the sim-ulations, we have used second-order Butterworth filters withtransfer function given by

where is the normalized cutoff frequency,is the cutoff frequency of the low-pass filters, which

decides the fading rate, and is the sampling interval.For the mobile radio channels, the fading rate is about30–40 Hz. If the bit rate for each user is 100–200 kb/s,the varies in the range . Assuming

, the Rician fading channelsare characterized by . When , no LOScomponent exists, this is the Rayleigh fading channel. When

, there is no fading in the channel, this is the AWGNchannel.

Following the examples above, we still consider the four-userand the 15-user systems with the same cross-correlation matrix.Simulations indicate that, even though under the conditions of

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PING et al.: DECISION-FEEDBACK BLIND ADAPTIVE MULTIUSER DETECTOR 165

Fig. 9. Symbol error probability performance of the DFBD and DDFD for user4 of the four-user system.

severe fading channels, both the BD and the DFBD can convergeand track the slow-varying processes, and show a better conver-gence performance as shown in Fig. 8 for user 15 of the 15-usersystem with SNR dB, and . The equal-izers converge in 1000–2000 iterations with in initialprocedure and in stable procedure, respectively. Thesymbol error performance is evaluated for only the DFBD. Inthe estimates of symbol error performance, we adopt the averagesignal-to-noise ratio defined asSNR (average power of the re-ceived signals)/(average power of the noise), where the averagepower of signals is calculated by . Thesymbol error probability performance of the DFBD depends onthe parameters and . The larger the , the better is theperformance. The symbol error performance of both the DFBDand the DDFD is shown in Figs. 9 and 10 with the same condi-tions for user 4 of the four-user system and user 15 of the 15-usersystem, respectively. When is larger, the performance of theDFBD approaches that of the DDFD, which requires accurateestimates of users' energies. If we decrease, the performanceof the DFBD will degrade. Therefore, in time-varying environ-ments, the performance of the DFBD is slightly inferior to thatof the DDFD with accurate estimates of users' energies. Addi-tionally, we should note that the performance of DDFD can beimproved by ranking users in the order of decreasing energies.In the blind equalization of the DFBD, because of restriction ofthe blind algorithms, the order of users can not be changed inthe whole detection procedure, but the DFBD does not requirethe knowledge of users' energies.

Fig. 10. Symbol error probability performance of the DFBD and DDFD foruser 15 of the 15-user system.

VI. CONCLUSION

In this paper, we have presented a BD and a DFBD and theirperformance has been evaluated by simulations for synchronousCDMA systems. Since we adopted the white noise model ofCDMA systems, the blind equalizers are free of the phase andpermutation ambiguities, which arise in most blind equalizers.So our detectors can recover the signals of each user withoutthese ambiguities. The blind equalizers show a better conver-gence performance. The symbol error performance of both de-tectors is evaluated after convergence of the equalizers. Thesymbol error performance of the BD is inferior to the perfor-mance of the DDFD, which requires a knowledge of each user'senergies. The symbol error performance of the DFBD is provento be close to the performance of the DDFD and thus is a goodchoice for multiuser detection. However, we should note thatthe performance of the DDFD can be improved by ranking theusers' order in decreasing received energies, which needs moreaccurate estimates of the users' energies for each bit detection.For the BD and the DFBD, after ordering the users, the ordercan not be changed in the whole detection procedure becauseof the restriction of the blind equalization algorithms. Hence,the performance of the DFBD is slightly inferior to that of theDDFD in Rician-fading channels. But the blind detectors do notrequire the estimates of the users' energies.

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He Pingreceived the B.Sc. and M.Eng. degrees fromthe University of Electronic and Science Technologyof China, Chendu, China, in 1983 and 1986, respec-tively, and the Ph.D. degree from Xidian University,Xian, China, in 1994.

From 1986 to 1996, he was with the Departmentof Electrical and Communication Engineering,Xidian University. Since 1996, he has been withthe Centre for Wireless Communications, NationalUniversity of Singapore, Singapore, where he is nowa Member of Technical Staff of a group specializing

in modulation and multiple-access technology. His current research interests arein mobile radio digital communications such as multiuser detection of CDMA,modulation/demodulation of OFDM, and synchronization and equalization ofcommunication systems.

Tjeng Thiang Tjhung (SM'84) received the B.Eng.and M.Eng. degrees in electrical engineering fromCarleton University, Ottawa, Ont., Canada, in 1963and 1965, respectively, and the Ph.D. degree fromQueen's University, Kingston, Ont., Canada, in 1969.

From 1963 to 1968, he was a Consultant withAcres-Inter-Tel Ltd., Ottawa, where his work wasconcerned with FSK system design for secure radiocommunication. In 1969, he joined the Departmentof Electrical Engineering, National Universityof Singapore, Singapore, where he is currently a

Professor. His present research interests are in bandwidth efficient digitalmodulation techniques for mobile radio and in multicarrier and CDMAsystems. From 1977 to 1983, he was a Consultant to Singapore Telecom on theplanning and implementation of their optical fiber wideband network.

Dr. Tjhung is a Fellow of the Institution of Engineers of Singapore and amember of the Association of Professional Engineers of Singapore.

Lars K. Rasmussenwas born in Denmark on March 8, 1965. He received theB.S. and M.Eng. degrees in electrical engineering in 1988 and 1989, respec-tively, from the Technical University of Denmark. In 1993, he received the Ph.D.degree in electrical engineering from the Georgia Institute of Technology, At-lanta. His dissertation work was in the area of error control coding and errorsensitive data transmission over fading channels.

From November 1993 to November 1995, he was with the Mobile Commu-nications Research Centre at the Institute for Telecommunications Research,University of South Australia, Australia, as a Research Fellow and Deputy Di-rector. From November 1995 to November 1998, he was the Research Leaderof the Modulation and Multiple Access Strategic Research Group at the Centrefor Wireless Communications, National University of Singapore, Singapore.He then spent three months as a Visiting Research Fellow at the University ofPretoria before starting as an Associate Professor in March 1999 at ChalmersUniversity of Technology, Sweden, where he currently resides. His research in-terests include multiuser CDMA detection, channel estimation, acquisition andtracking, multipath searching, and joint detection and decoding.