IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 1, JANUARY 2004 71

Blind Multiuser Detection in Uplink CDMA WithMultipath Fading: A Sequential EM Approach

Qinghua Li, Costas N. Georghiades, Fellow, IEEE, and Xiaodong Wang

Abstract—We consider joint channel estimation and data detec-tion in uplink asynchronous code-division multiple-access systemsemploying aperiodic (long) spreading sequences in the presence ofunknown multipath fading. Since maximum-likelihood (ML) se-quence estimation is too complex to perform, multiuser receiversare proposed based on the sequential expectation-maximization(EM) algorithm. With the prior knowledge of only the signaturewaveforms, the delays and the second-order statistics of the fadingchannel, the receivers sequentially estimate the channel using thesequential EM algorithm. Moreover, the snapshot estimates of eachpath are tracked by linear minimum mean-squared error filters.The user data are detected by a ML sequence detector, given thechannel estimates. The proposed receivers that use the exact ex-pressions have a computational complexity (2 ) per bit, where

is the number of users. Using the EM algorithm, we derivelow-complexity approximations which have a computational com-plexity of ( 2) per bit. Simulation results demonstrate that theproposed receivers offer substantial performance gains over con-ventional pilot-symbol-assisted techniques and achieve a perfor-mance close to the known channel bounds. Furthermore, the pro-posed receivers even outperform the single-user RAKE receiverwith Nyquist pilot-insertion rate in a single-user environment.

Index Terms—Code-division multiple access (CDMA), multi-path fading, multiuser detection, sequential expectation-maxi-mization (EM).

I. INTRODUCTION

TO DATE, most research on code-division multiple access(CDMA) channel estimation has focused on the more

tractable pilot-assisted techniques and the short-code case,where the period of spreading codes is one symbol duration.Since long (aperiodic) spreading codes are employed in cur-rent and next-generation CDMA standards (such as IS-95,CDMA-2000 and W-CDMA), recent work has addressed blindchannel estimation for long-code CDMA. Of recent paperson blind channel estimation, only a handful [1]–[4] consideruplink CDMA, and only for time-invariant multipath channels.

Paper approved by N. C. Beaulieu, the Editor for Wireless CommunicationTheory of the IEEE Communications Society. Manuscript received March 13,2001; revised October 4, 2002; January 5, 2003; and June 19, 2003. This workwas supported in part by a grant from the Texas Telecommunications Engi-neering Consortium (TxTEC). This paper was presented in part at the VehicularTechnology Conference, Vancouver, BC, Canada, September 2002.

Q. Li was with the Electrical Engineering Department, Texas A&M Univer-sity, College Station, TX 77843-3128 USA. He is now with Intel Labs, SantaClara, CA 95052 USA.

C. N. Georghiades is with the Electrical Engineering Department, TexasA&M University, College Station, TX 77843-3128 USA (e-mail: c.georghi-ades@tamu.edu).

X. Wang was with the Electrical Engineering Department, Texas A&M Uni-versity, College Station, TX 77843-3128 USA. He is now with the ElectricalEngineering Department, Columbia University, New York, NY 10027 USA.

Digital Object Identifier 10.1109/TCOMM.2003.822172

In [2] and [3], channel estimation for quasi-synchronousCDMA is considered, where intersymbol interference (ISI)is ignored. Blind channel estimation of uplink and downlinkCDMA is addressed in [4], where the timing of each path andthe signature waveforms of all users are assumed known in theuplink.

Compared to batch processing, sequential processing reducesdata storage requirements and output latency. Short latency iscrucial for real-time applications, where data is received sequen-tially and up-to-date estimation is needed online. The sequen-tial expectation-maximization (EM) algorithm, first introducedin [5], performs sequential parameter estimation in the pres-ence of hidden data by maximizing the Kullback–Leibler in-formation measure [6]. Applications of the sequential EM algo-rithm to communications are reported in [7]–[9]. In [7], an adap-tive filter was proposed to suppress narrowband interference inCDMA, which combines the sequential EM algorithm and a re-cursive hidden Markov model estimator. The sequential EM al-gorithm is used for joint channel estimation and data detectionfor single-user channels in [8], and for single-user channel esti-mation in [9]. Applications of the sequential EM to other signalprocessing problems can be found in [6], [10], and [11].

The classic EM algorithm and its variant, the space-al-ternating generalized expectation-maximization (SAGE)algorithm, are applied to multiuser receivers in [12]–[16]. In[12], the EM algorithm is applied to the estimation of staticchannels using batch processing. The EM algorithm in [13] andthe SAGE algorithm in [14] are applied to multiuser detectionfor synchronous CDMA. In [15], the EM algorithm is appliedto channel estimation for CDMA over multipath fading. TheSAGE algorithm is applied to joint channel estimation and datadetection for synchronous CDMA in [16].

In this paper, two sequential multiuser receivers are devel-oped for the asynchronous long-code CDMA uplink over un-known multipath fading channels. Since data modulation is em-ployed, neither maximum-likelihood (ML) nor minimum mean-squared error (MMSE) estimation of the data or the channelcan be accomplished by the Kalman filter [11]. Although theper-survivor processing and per-branch processing algorithms[17] provide a practical means of joint estimation and detectionfor time-variant channels, the computational complexity of ap-plying them in CDMA channels is prohibitive for systems with amedium-to-large number of users. With the prior knowledge ofonly the signature waveforms, the delays, and the second-orderstatistics of the fading channel, the receivers sequentially esti-mate the channel using the sequential EM algorithm. The snap-shot estimates for each path are tracked by linear MMSE fil-ters, and the user data are detected by ML sequence estimation

0090-6778/04$20.00 © 2004 IEEE

72 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 1, JANUARY 2004

(MLSE) conditioned on the channel estimates. The proposed re-ceivers that use the exact sequential EM algorithm have a com-putational complexity per bit, where is the numberof users. Using the EM algorithm, we derive low-complexityapproximations which have a complexity per bit at abit-error rate (BER) penalty of less than 1 dB compared with theexact, and less than 0.2 dB compared with the known channelbound for bandwidth time (BT) product less than 0.005.

In Section II, we briefly introduce the sequential EM algo-rithm. In Section III, the signal model and decision statistics arepresented. Sequential multiuser receivers based on the sequen-tial EM algorithm are derived in Section IV, and simulation re-sults are presented in Section V. Finally, Section VI concludes.

II. SEQUENTIAL EM ALGORITHM

Following the description and notation in [5], [10], and [11],we briefly summarize the sequential EM algorithm. Suppose

are a sequence of observations with probability den-sity function (pdf) , where is a time-variant pa-rameter vector, for some . A class of sequential estimators de-rived from the ML principle is given by

(1)

where is the estimate of at the th step, is a smallpositive constant, is an matrix later in thissection, and

(2)

is the score (i.e., the gradient of the log-likelihood function). Letdenote the Hessian matrix of , where

(3)

Let denote a “complete” data related to , for .The complete data is not unique, and is such that can beobtained through a many-to-one mapping . We denotethe Fisher information matrix of the data and , respectively,as

III. SYSTEM DESCRIPTION

We consider the uplink of a -user asynchronous CDMAsystem signaling through multipath fading channels, where eachuser employs binary phase-shift keying (BPSK) spread-spec-trum modulation with random aperiodic spreading. The blockdiagram of the system is illustrated in Fig. 1.

A. Signal Model

The transmitter is shown in the upper left part of Fig. 1.The bit stream , for user ,

, consists of independent and equiprobablebits. The th bit of the th user is modulated by a signaturewaveform of duration , , which is nonzero only on

and has unit energy . That is,is mapped to , and is mapped to

. Letting be the number of bits in a signal block, theth user’s transmitted signal is

(4)

is transmitted through a multipath channel with impulseresponse

(5)

where is the number of paths in the th user’s channel;and are, respectively, the complex fading processes

and the delay of the th user’s th path. It is assumed that onlythe second-order statistics of the fading processes are known tothe receiver. Also, fading can vary from symbol to symbol butremains constant over a symbol interval

(6)

Using (4), (5), and (6), the received signal due to the th user is( denotes convolution)

(7)

Letting be complex white Gaussian with spectral density, the received signal is then

(8)

B. Decision Statistic

We derive an explicit expression for the decision statistic interms of the channel parameters and the transmitted symbols,which is used in developing multiuser receivers in subsequentsections. Using the Cameron–Martin formula [18], we can showthat the sufficient statistics for detecting multiuser symbols canbe obtained by passing the received signal through a bankof path matched filters (i.e., RAKE fingers), as shown in Fig. 1.Detailed derivations can be found in [19]. We next derive anexplicit expression for this sufficient statistic in terms of themultiuser channel parameters and the transmitted symbols.

Assume that and the multipathspread of any user signal is limited to, at most, symbol inter-vals for some positive integer . That is, ,

LI et al.: BLIND MULTIUSER DETECTION IN UPLINK CDMA WITH MULTIPATH FADING: A SEQUENTIAL EM APPROACH 73

Fig. 1. Uplink of an asynchronous CDMA system.

, . Define the following correlation of the delayeduser-signaling waveforms:

(9)

Since and is nonzero only for, it follows that , for . The

output of the RAKE finger for the th user’s th path is givenby

(10)

where is a sequence of zero-mean complex Gaussianrandom variables with covariance

(11)

We can then express (10) as

(12)Next, we have1 the first equation shown at the bottom of thenext page. We can then express (12) as

(13)

1All vector subscripts are functions of time index i. For simplicity, weomit the time index in all subscripts. For instance, we simplify RRR (i) and

��� (i) using instead RRR (i) and ��� (i), respectively.

74 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 1, JANUARY 2004

and from (11), the covariance matrix of the complex Gaussianvector sequence is as shown in (14) at the bottom of thepage. Equation (13) is the signal model used to develop mul-tiuser receivers below.

IV. SEQUENTIAL BLIND MULTIUSER RECEIVERS

A. Receiver Structure

In this section, we present sequential blind multiuser re-ceivers based on the signal model (13) and the sequentialEM technique outlined in Section II. In these receivers, theparameters to be estimated are the fading processes .The observations are the output of RAKE fingers , andthe complete data will be defined in Section IV-C. The receiverstructure is schematically shown in the lower half of Fig. 1.

For the th snapshot, , we have the followingsteps.

1) Localization:

(15)

where is a one-step prediction of provided byStep 3.

2) Multiuser detection:

(16)

3) Tracking:

(17)

where is a -order linear MMSE filter for.

Note that we use instead of , because is a betterestimate of than by exploiting the second-orderstatistics of the channel and the data .

Computation of , , , and andtheir low-complexity approximations are derived in the rest ofthis section. Computation of the score is presentedin Section IV-B, and derivation of the information matrices

in Section IV-C. An approximation tobased on the EM algorithm is developed in Section IV-D. A MLdetector of the data based on and a low-complexitydetector are presented in Section IV-E. The instantaneousMMSE filter is derived in Section IV-F. Finally, thesequential multiuser receivers developed in Section IV aresummarized in Tables I and II.

B. Computing the Score

From (13), the likelihood function of the decision statisticis given by

(18)

where is a scalar independent of , ,and . Though arbitrary can be handled,for simplicity, here we assume that , i.e. each user’s mul-tipath delay spread is within one symbol interval. We define thefollowing quantities ,

......

......

matrix

matrix

vector

vector

vector

vector

......

......

matrix (14)

LI et al.: BLIND MULTIUSER DETECTION IN UPLINK CDMA WITH MULTIPATH FADING: A SEQUENTIAL EM APPROACH 75

TABLE ISEQUENTIAL EM-BASED ALGORITHM

USING EXACT EXPRESSIONS. COMPLEXITY IS O(2 ) PER BIT,DOMINATED BY THE COMPUTATION OF SCORE AND MULTIUSER DETECTION

TABLE IISEQUENTIAL EM-BASED ALGORITHM USING APPROXIMATIONS. COMPLEXITY

IS O(K ) PER BIT, DOMINATED BY INVERTING THE MATRIX (i)IN (52), (53), AND (54)

, . Forsimplicity of notation, we assume the fading process is slow and

does not vary within three bit intervals for the current snap-shot processing. Namely, in the processing snapshot of , weassume hereafter. The slow fadingassumption is reasonable for most data applications in next-gen-eration wireless systems. Then, the log-likelihood function of

is given by

(19)

The score, conditioned on the channel prediction of currentsnapshot , is given by

(20)

To simplify (20), we use the following approximation forin (19)

(21)

where

(22)

Using (21), the score in (20) is simplified as

(23)

C. Computing the Information Matrix

The information matrices of both the incomplete andcomplete data, needed for the sequential EM algorithm, arebriefly introduced next. Detailed derivations can be foundin [19]. The information matrix of the incomplete datais , where

. Since com-putation of is prohibitive for large , the stochasticapproximation method cannot be applied, and the EM-basedalgorithms that substitute with the simplerbecome attractive.

By appropriately choosing the complete data, we can obtain acorresponding information matrix with low complexity. A com-plete data that leads to a simple information matrix is

(24)

(25)

where and; is AWGN with zero mean and

power spectral density , such thatand . The information matrix for thecomplete data is then given by

(26)A natural choice of is to let , ,

.

D. Estimating Using the EM Algorithm

It is seen from (23) that the bit vector is crucial to theapproximation of the score . As seen from (22),the computational complexity of finding by brute force is

, which is prohibitive for large . We next derive asolution to (22) based on the EM algorithm. Define the completedata as

(27)

(28)

where is AWGN with zeromean and power spectral density, such that and . A natural

choice of is . By choosing the complete data asabove,wedecomposethe -dimensionaloptimizationproblem

76 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 1, JANUARY 2004

in (22) into three-dimensional binary minimization problems.A similar technique is applied in [13] for multiuser detection insynchronous CDMA channels. By definition, we have

(29)where

Wehave the equation at the bottomof the page, where de-notes the th estimate of in the EM algorithm, de-notes the th estimate of , and is the number of EM itera-tions. The computation of the initial estimate is describedintheAppendix.TheEMalgorithmiteratesbetweenthefollowingE-step and M-step.

E-Step: We have (for brevity, we skipped some of the deriva-tions below)

(30)

where is a constant independent of . Since, and are jointly Gaussian

conditioned on . Thus

(31)

where

(32)

(33)

(34)

(35)

Substituting (32), (33), (34), and (35) into (31), we obtain

(36)M-Step: From (30) and (36), the M-step of the EM algorithm

is given by

(37)

Finally, by substituting in (22) with , the outputof the EM algorithm, we obtain the approximation of the scoreas

(38)

E. Multiuser Detectors

To reduce the data storage, we derive two sequential multiuserdetectors that use only the current snapshot observation in-stead of a sliding window of data. Both detectors exploit theintermediate results of the score computation. One is for the re-ceiver that computes the score using the exact expression (20)and the other for the receiver that uses the approximate expres-sion (38) for the score.

1) Detector Associated With the Exact Score: Based on thedecision statistic and the channel estimates , the MLestimation of the data based on can be written as

(39)

vector

vector

vector

vector

LI et al.: BLIND MULTIUSER DETECTION IN UPLINK CDMA WITH MULTIPATH FADING: A SEQUENTIAL EM APPROACH 77

From (13), the likelihood function of conditioned on thechannels and the data can be written as

(40)Then, the likelihood function is given by

(41)

where all the terms in the summation are already computed forthe score using (20). Substituting (41) into (39), wehave

(42)

2) Detector Associated With the Approximate Score: Thecomputational complexity of the detector above is

. To reduce the complexity, we exploit theoutput of the EM algorithm in (37), , to form an estimateof as

(43)

F. MMSE Filter

We model in (15), the output of Step 1 (localization), asthe sum of fading process and additive observation noise

as

(44)

where the second-order statistics of are assumed known;

is assumed to be coloredGaussian noise independent of . The independence as-sumption is reasonable because the observation noise is mainlyfrom the independent strong MAI from the other users andother paths. To form the linear MMSE filter and predictor for

, we need to estimate the covariance matrix of asfollows.

In the steady state of tracking, we assume ,for the receiver using (20) and for the

receiver using (38). Comparing (15) and (44), we have

(45)

From (29), we have

(46)

Define

(47)

For Clarke’s Rayleigh fading model, where

is the symbol-rate normalized Doppler shift and is thezero-order Bessel function. In (46),is a deterministic matrix, and the covariancematrix of the random variable is given by (14). Thus, theautocorrelation of , , can be obtained. Since

and are independent for and ,for . Further, define (48) at the bottom of

the next page, where is the MMSE filter order. A linearMMSE one-step prediction of is [18]

(49)

(50)

The two sequential EM-based receivers are summarized inTables I and II.

V. SIMULATION RESULTS

In this section, we demonstrate the performance of the se-quential EM and the approximate sequential EM multiuser re-ceivers in an unknown multipath fading CDMA channel. Themultipath channel model is given by (5). The delays of users’paths were randomly generated, as listed in Table III, and thenfixed for the simulation. Each user has two equal-en-ergy paths. The time-variant fading coefficients were randomlygenerated from Clarke’s model to simulate fading channels withthe same BT product on each path.

We consider the uplink of an asynchronous CDMA systemwith five users . The spreading sequences and databits of each user are independently and randomly generated.The processing gain is . All users have equal signalamplitudes, i.e., . To remove the signambiguity of the tracked fading process, the transmitted bits are

78 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 1, JANUARY 2004

TABLE IIISIMULATED MULTIPATH DELAYS

differentially encoded. Differential encoding is not required inthe pilot-assisted receivers.2

In the following example, the performances of the blind mul-tiuser receivers and the pilot-assisted receivers are compared.The pilot-assisted receivers estimate the channel using only thepilot symbols, where the channel estimation is processed inbatch. A block of data of size 10 000 symbols is received. Usingthe RAKE receiver’s assumption that ignores ISI and MAI,the pilot-assisted receiver estimates each fading path using thematched-filter output of the pilot symbols on that path. TheMMSE estimates of the channel coefficients are obtained bysolving the Wiener–Hopf equations [18] using all the pilotsin the block. The minimum pilot insertion rate correspondingto the Nyquist sampling rate of the fading channel is .After the channel estimates are obtained, the pilot-assistedreceiver uses the estimates as if they were perfect. In a mul-tiuser environment, the data pilot-assisted multiuser receiverperforms EM estimation for data using (43). In a single-userenvironment, the pilot-assisted receiver detects data using themaximum ratio combiner (MRC) output. The first and last 200transition symbols in the 10 000 symbol block are ignored incomputing BER for the pilot-assisted receivers. Since the blindreceivers perform sequential channel estimation, the signal doesnot need to be sent in block, and the signals are sent throughcontinuous fading processes. After the first 300 symbols atthe very beginning of the fading processes, the sequential EMreceivers’ output are employed to compute BERs.

The number of EM iterations in the approximate sequentialEM receiver is fixed to three. The initial value of the channel

2Differential encoding is not necessary if a special frame header is present atthe start of each frame.

Fig. 2. BER performance comparison between the proposed multiuserreceivers and the pilot-assisted multiuser receivers in a multipath fadingchannel, with the number of users K = 5 and 1, the number of paths L = 2,processing gain N = 12, BT = 0:001.

coefficients in the sequential EM channel estimation is set to. The order of the finite impulse response (FIR) MMSE

filters and predictors is 100 and . Simulation resultsindicate that after 200 symbols, the channel estimators reachsteady state.

The average BERs of five users versus signal-to-noise ratio(SNR) per bit are plotted in Fig. 2. The figure showsthe performance of the pilot-assisted multiuser receiver withpilot insertion rates 1/500, 1/100, and 1/50 reaches an error floordue to ISI and MAI. The figure also shows the performance ofthe pilot-assisted single-user RAKE receiver in a single-user en-vironment with pilot insertion rate 1/500 and the performance ofthe proposed sequential EM and approximate sequential EM re-ceivers, including the known channel performance for each. It isseen that significant performance gains are achieved by the pro-posed receivers, compared with pilot-assisted receivers. Boththe performance of the approximate sequential EM receiver withthree iterations and the performance of the sequential EM re-ceiver are very close to that for known channels. This can beattributed to the quality of the channel estimation for both re-

......

. . ....

.... . .

. . .. . .

...

(48)

LI et al.: BLIND MULTIUSER DETECTION IN UPLINK CDMA WITH MULTIPATH FADING: A SEQUENTIAL EM APPROACH 79

Fig. 3. BER performance of the proposed multiuser receivers and thepilot-assisted multiuser receivers in a multipath fading channel, with thenumber of usersK = 5, the number of paths L = 2, processing gainN = 12,BT = 0.005, 0.001, 0.005, and 0.01.

ceivers. Moreover, the performance difference between the se-quential EM receiver and the approximate sequential EM re-ceiver is small in the low and medium SNR regions, and it isabout 1 dB at high SNRs. Furthermore, it is seen from the simu-lation results that the proposed multiuser receivers in a multiuserchannel even outperform the RAKE receiver in a single-userchannel. This is because the RAKE receiver makes the assump-tion that the delayed signals from different paths for each userare orthogonal, which effectively neglects the ISI.

The performances of the approximate sequential EM receiverand the pilot-assisted receiver in channels with different fadingrates are shown in Fig. 3. High error floors are seen in the per-formances of the pilot-assisted receiver with 1/50 and 1/100pilot insertion rates for fast fading ( ) andslow fading ( ), respectively. The approx-imate sequential EM receiver has performances almost exactlythe same as the known channel bound for slow fading (

) and 0.2 dB, and less than 2-dB degradations fromthe bound for , respectively. The performancedegradations are roughly constant over the practical range of0–16 dB.

The performance sensitivity of the approximate sequentialEM receiver with respect to the step size in (15) is shownin Fig. 4. The simulation parameters are the same as the onesin Fig. 3, except that varies from 0.001 to 1. It is seen thatthe that deliver lowest BERs at SNR dB are 0.5, 0.2,0.1, and 0.05 for 0.01, 0.005, 0.001, and 0.0005, respec-tively. The BER sensitivity to increases as the fading rate in-creases, and low BER can be obtained in large regions for slowfading. The optimal can then be approximately computed as

.The performance of the approximate sequential EM receiver

with no iterations using (53), and after three EM iterations, isshown in Fig. 5. The improvement of the EM iteration is about0.1–0.3 dB, which may not be worth the iteration complexity.The initial estimator is essentially a parallel-cancellation mul-tiuser detector.

Fig. 4. Performance sensitivity of the proposed multiuser receivers withrespect to the step size � in a multipath fading channel, with the number ofusers K = 5, the number of paths L = 2, processing gain N = 12, BT =

0.005, 0.001, 0.005, and 0.01, SNR = 16 dB.

Fig. 5. BER performance difference between the initial estimates and the onesafter EM iterations of the proposed receivers in a multipath fading channel, withthe number of users K = 5, the number of paths L = 2, processing gainN = 12, BT = 0.001 and 0.01.

VI. CONCLUSION

We have proposed blind sequential multiuser receivers forasynchronous direct sequence/CDMA systems using aperiodicspreading sequences. The receivers are derived based onthe sequential EM algorithm. The multiuser detector usesthe output of conventional RAKE fingers. The ones derivedfrom the exact expressions run in computational complexity

per bit, where is the number of users and themaximum delay spread is less than symbols duration. Theapproximate sequential EM algorithm has a low complexity

per bit. Simulation results demonstrate that, in unknownasynchronous multipath fading channels, the proposed blindmultiuser receivers significantly outperform a pilot-assistedmultiuser receiver with pilot insertion rate much higher thanthe Nyquist rate. Moreover, the performance of the proposed

80 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 52, NO. 1, JANUARY 2004

receivers in a multiuser environment is even better than that ofa single-user RAKE receiver in a single-user environment.

APPENDIX

INITIAL ESTIMATE OF

The initial estimate that starts the EM iteration forcan be obtained from a decision-feedback decorrelating

detector. Other than , a sufficient statistic for data is, the output of the MRC, which is given by

(51)

where is a sequence of zero-mean complex Gaussian vec-tors with covariance matrix

matrix

matrix

Let , ,, . Substituting

with its estimate , we have the estimate of as

. Based on , we are going to obtain the .First, the ISI from the previous bits is cancelled as

. Ignoring the ISI from and, a decorrelator for is given by

(52)

where . Further, by can-celling the interference from and , the initialestimate of can be obtained by

(53)

Finally, we reestimate by cancelling the interferencefrom as

(54)where . Thus, we obtainthe initial estimate as

(55)

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Qinghua Li was born in Guangzhou, China, in 1970.He received the M.E. degree from Tsinghua Univer-sity, Beijing, China, in 1995, and the Ph.D. degreefrom Texas A&M University, College Station, TX, in2001.

From 1993 to 1996, he was with GuangdongTelecommunication Academy of Science andTechnology, China, where he was involved in thedevelopment of telephone exchange networks. From1996 to 2001, he was a Research Assistant in theWireless Communications Laboratory, Texas A&M

University, doing research in CDMA, turbo coding, and CMOS RF circuitdesign. In the summer of 2000, he was an intern with Nokia Americas, Irving,TX, developing simulation tools for HDR CDMA. Since February 2001, hehas been with the Wireless Research Group of Intel Corporation, Santa Clara,CA. His research interests are in the area of MIMO, SDMA, UWB, wirelesschannel modeling, multiuser detection, CDMA communications, and mediaaccess control protocols.

LI et al.: BLIND MULTIUSER DETECTION IN UPLINK CDMA WITH MULTIPATH FADING: A SEQUENTIAL EM APPROACH 81

Costas N. Georghiades (S’82–M’82–SM’90–F’98)was born in Cyprus in 1955. He received the B.E. de-gree with distinction from the American Universityof Beirut, Lebanon, in 1980 and the M.S. and D.Sc.degrees from Washington University, St. Louis, MO,in 1983 and 1985, respectively, all in electrical engi-neering.

Since September 1985, he has been with the Elec-trical Engineering Department, Texas A&M Univer-sity, College Station, where he is a Professor and in-augural holder of the Delbert A. Whitaker Endowed

Chair (2002). His general interests are in the application of information, com-munication, and estimation theories to the study of communication systems.

Dr. Georghiades received the 1995 Texas A&M University College of En-gineering Halliburton Professorship, and in 2002, the E. D. Brockett Profes-sorship. From 1997 to 2002, he was the J. W. Runyon, Jr. Professor. He is amember of Sigma Xi and Eta Kappa Nu and a registered Professional Engi-neer in Texas. He served as an Associate Editor for the IEEE TRANSACTIONS

ON COMMUNICATIONS, as Publications Editor and Associate Editor for Com-munications for the IEEE TRANSACTIONS ON INFORMATION THEORY, as GuestEditor for the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, andas an Associate Editor for the IEEE COMMUNICATIONS LETTERS. He has beeninvolved in organizing a number of conferences, including as Technical Pro-gram Chair for the 1999 IEEE Vehicular Technology Conference and the 2001Communication Theory Workshop, and as Program Chair for the Communica-tion Theory Symposium within Globecom 2001.

Xiaodong Wang received the B.S. degree inelectrical engineering and applied mathematics(with highest honors) from Shanghai Jim TongUniversity, Shanghai, China, in 1992, the M.S.degree in electrical and computer engineering fromPurdue University, West Lafayette, IN, in 1995,and the Ph.D. degree in electrical engineering fromPrinceton University, Princeton, NJ, in 1998.

From July 1998 to December 2001, he wasan Assistant Professor with the Department ofElectrical Engineering, Texas A&M University. In

January 2002, he joined the Department of Electrical Engineering, ColumbiaUniversity, New York, NY, as an Assistant Professor. His research interests fallin the general areas of computing, signal processing, and communications. Hehas worked in the areas of digital communications, digital signal processing,parallel and distributed computing, nanoelectronics, and bioinformatics, andhas published extensively in these areas. His current research interests includewireless communications, Monte Carlo-based statistical signal processing, andgenomic signal processing.

Dr. Wang received the 1999 National Science Foundation CAREER Awardand the 2001 IEEE Communications Society and Information Theory SocietyJoint Paper Award. He currently serves as an Associate Editor for the IEEETRANSACTIONS ON COMMUNICATIONS, the IEEE TRANSACTIONS ON WIRELESS

COMMUNICATIONS, and the IEEE TRANSACTIONS ON SIGNAL PROCESSING.