**Abstract—A****robust** **iterative** **multicarrier** **code-division**
**access (MC-CDMA) receiver with adaptive **
**multiple-access interference (MAI) suppression is proposed for a pilot**
**symbols assisted system over a multipath fading channel with**
**frequency offset. The design of the receiver involves a two-stage**
**procedure. First, an adaptive filter based on the generalized**
**sidelobe canceller (GSC) technique is constructed at each finger**
**to perform despreading and suppression of MAI. Second, pilot**
**symbols assisted frequency offset estimation, channel estimation**
**and a RAKE combining give the estimate of signal symbols. In**
**order to enhance the convergence behavior of the GSC adaptive**
**filters, a decisions-aided scheme is proposed, in which the signal**
**waveform is first reconstructed and then subtracted from the input**
**data of the adaptive filters. With signal subtraction, the proposed**
**MC-CDMA receiver can achieve nearly the performance of the**
**ideal maximum signal-to-interference-plus noise ratio receiver **
**as-suming perfect channel and frequency offset information. Finally,**
**a low-complexity partially adaptive (PA) realization of the GSC**
**adaptive filters is presented as an alternative to the conventional**
**multiuser detectors. The new PA receiver is shown to be robust**
**to multiuser channel estimation errors and offer nearly the same**
**performance of the fully adaptive receiver.**

**Index Terms—Generalized sidelobe canceller, maximum **

**signal-to-interference-plus noise ratio (MSINR) receiver, multicarrier**
**code-division multiple access (MC-CDMA), partial adaptivity**
**(PA).**

I. INTRODUCTION

**T**

HE DIRECT sequence code-division multiple-access
(CDMA) air interface has been selected to be a major
can-didate for providing multimedia services in the third-generation
(3G) mobile radio communications. This is mainly due to its
soft multiple access characteristics, robustness against fading,
and anti-interference capability. Recently, a new CDMA
tech-nology has been proposed based on the combination of CDMA
and multicarrier (MC) transmission to support high data rate
services [1]. The MC-CDMA systems can be categorized
into two major types [1]: One is a combination of orthogonal
frequency-division multiplexing (OFDM) and CDMA, and
Manuscript received August 1, 2001; revised April 8, 2002; accepted July 17, 2002. The editor coordinating the review of this paper and approving it for publication is W.-Y. Kuo. This work was supported in part by the Ministry of Education and in part by the National Science Council of R.O.C. under Contract 89-E-FA06-2-4.

The authors are with the Department of Communication Engineering and Mi-croelectronics and Information Systems Research Center, National Chiao Tung University, Hsinchu 300, Taiwan, R.O.C. (e-mail: jhdeng.cm88g@nctu.edu.tw; tslee@mail.nctu.edu.tw).

Digital Object Identifier 10.1109/TWC.2003.811188

the other is a scheme of parallel transmission of narrowband direct sequence (DS) waveforms in the frequency domain. In the former system (referred to as MC-CDMA), a spreading sequence of length is serial-to-parallel converted, and then each chip modulates a different carrier frequency. This implies that the resulting signal has a spreading sequence in the frequency domain. In the latter system (referred to as MC DS-CDMA), the available frequency spectrum is divided into equi-width frequency bands, or carriers. Each frequency band is used to transmit a narrowband DS waveform, which means that the spreading operation is done in the time domain. Both of these two types of schemes can offer frequency diver-sity and robustness to the adverse effect of frequency-selective fading. In addition to multipath effects, an MC-CDMA system is also subject to limiting factors such as multiple-access interference (MAI) and intercarrier interference (ICI) induced by frequency offset. In forward link synchronous transmission with good channel conditions, MAI can be eliminated by em-ploying orthogonal spreading codes. However, this is typically not achievable in reverse link asynchronous transmission or under poor channel conditions, where orthogonality among spreading codes no longer holds.

In order to effectively combat the MAI, a CDMA receiver
should be able to perform adaptive processing at the chip or
symbol level [2]. On the other hand, to cope with the ICI, an
OFDM receiver needs to obtain an estimate of the frequency
offset before further processing [3]. Unfortunately, the
fre-quency offset cannot be accurately estimated in the presence of
strong MAI. This dictates the development of an MC-CDMA
receiver with effective MAI suppression before frequency offset
compensation. More importantly, the suppression of MAI must
*be frequency offset independent. To this end, a novel iterative*
adaptive receiver is proposed which involves the following
implementation procedure. First, a set of adaptive filters, one
for each finger, is constructed to collect multipath signals with
different delays, assuming that an initial timing estimate is
available. The tap weights of each adaptive filter are determined
in accordance with the linearly constrained minimum variance
(LCMV) [4] criterion so that strong MAI can be effectively
suppressed. In particular, these LCMV adaptive filters are
realized in the form of generalized sidelobe canceller (GSC)
[4], and a modified blocking matrix is designed to remove the
signal with frequency offset from the received data. Second,
pilot symbols assisted frequency offset estimation, channel
es-timation and RAKE combining, together capture the resolvable

Fig. 1. Transmitter of an MC-CDMA system.

signal multipath components coherently and give the estimate
of the signal symbols. In order to enhance the convergence
behavior of the GSC adaptive filters, a decisions-aided scheme
is proposed, in which signal waveform is first reconstructed
by exploiting the frequency offset estimate, channel estimate,
symbol decisions, and signal’s signature. The reconstructed
signal waveform is subtracted from the GSCs input data sent
to the next iteration. Due to signal subtraction preprocessing,
the output signal-to-interference-plus noise ratio (SINR)
per-formance of the adaptive filters can be significantly improved
[5], leading to better frequency offset estimation, channel
estimation and RAKE combining, as iterations proceed. It is
noteworthy that the proposed receiver subtracts the estimated
signal waveform before MAI suppression. This is opposite
to conventional interference cancellers [7], which estimate
and subtract MAI instead. More specifically, adaptive MAI
*suppression is performed blindly without the signal’s channel*
and frequency offset information. This means that the proposed
receiver can be initialized and MAI can be effectively
sup-pressed without the aid of pilot symbols and frequency offset
compensation. The only information required is the timing
information for performing FFT. It is shown that the proposed
receiver can provide nearly the performance of the optimal
maximum SINR (MSINR) receiver [5] with a few iterations.
Finally, a low-complexity partially adaptive (PA) realization
[8] of the GSC adaptive filters is proposed as an alternative
to the conventional multiuser detectors. In particular, partial
adaptivity is achieved by working with a reduced size blocking
matrix obtained by projecting the estimated MAI composite
channel vectors onto the range space of the original blocking
matrix. It is shown that the low-complexity PA receiver is
insensitive to multiuser channel estimation errors, and offers
nearly the same performance of the fully adaptive receiver. In
summary, the proposed MC-CDMA receiver with PA MAI
suppression performs robust and near optimal signal reception
with tolerance to large frequency offsets and resistance to
strong MAI.

II. MC-CDMA DATAMODEL ANDMSINR RECEIVER

Suppose that there are active users in an MC-CDMA system. Each user is assigned a unique spreading code in the

Fig. 2. Structure of proposed iterative MC-CDMA receiver.

frequency domain, as shown in Fig. 1, such that the complex baseband equivalent transmitted signal of the th user over the

th data symbol can be written as [9]

(1)

where , with being the symbol

dura-tion, is the transmit power, is the spreading code with , is the th symbol assumed to be indepen-dent and iindepen-dentically distributed (i.i.d.) with zero-mean and unit variance and is the number of subcarriers. The transmis-sion channel is modeled as with resolvable Rayleigh-fading paths, and a guard time of is inserted after to cope with the intersymbol interference (ISI). After passing through the channel and removing the guard time, as shown in Fig. 2, the received complex baseband data can be expressed as

(2) where is the frequency offset associated with the th user (due to oscillator drifting), and are the complex gain and delay of the th path of the th user, respectively. is the additive white Gaussian noise (AWGN) with power . The

received data is sampled at over the th symbol

duration, where is the chip duration, yielding the discrete-time data samples [3]

(3)

for , where user 1 is assumed the desired

user

(4)

is the MAI, , and

(6) is the equivalent complex path gain with the effects of transmit power and frequency offset incorporated

(7) is the spreading code sequence premultiplied by the linear phase

due to path delay , and and are the FFT of

and , respectively. The term is the ICI at the th subcarrier induced by the frequency offset and is given by

(8)

with

(9) being the corresponding complex gains. Note that the first com-ponent on the righthand side of (5) is the th symbol pre-multiplied by an effective channel gain due to multipath fading and frequency offset.

The post-FFT received data over the th symbol can be put

into the vector

(10) where

(11)
*is the post-FFT signature vector associated with the th path of*
user 1

(12)

is the ICI vector,

, is the

(15) is the “frequency shifted” symbol varying with time index , and is the signal vector. With the data model in (13), it is clear that a receiver for user 1 is one that identifies and removes to retrieve . Frequency offset compensation then recovers from . For example, a linear receiver combines the entries of into an estimate of , i.e.,

(16) where is the weight vector, and denotes the conjugate transpose. The weight vector can be chosen in accordance with the popular minimum mean-square error (MMSE) or MSINR criterion [5]. For the MMSE receiver, we have

(17) where

(18) is the post-FFT data correlation matrix, with

(19) being the post-FFT interference-plus-noise correlation matrix. For the MSINR receiver, we have

(20) Since the channel vector is obtained with the frequency shifted training symbols, the receivers in (17) and (20) are referred to as the frequency shifted (FS) MMSE and MSINR receivers, respectively.

Finally, from (13) and (16), with the frequency offset esti-mated as , the symbol decision can be obtained by

dec (21)

Popular frequency offset estimators are readily found in the lit-erature [3] and [10]. For example, the maximum-likelihood es-timator (MLE) [3] is the optimum eses-timator under AWGN

where is the number of pilot symbols . Most existing frequency offset estimators are developed based on the assump-tion of no or little interference (i.e., AWGN). With the presence of strong MAI, these estimators often degrade seriously. It is, thus, necessary to perform interference suppression before fre-quency offset estimation. In the next section, an iterative adap-tive receiver will be proposed which initializes without the aid of channel and frequency offset estimation, and approaches the optimal MSINR receiver in an successive fashion via signal re-construction and subtraction.

III. DEVELOPMENT OFPROPOSEDMC-CDMA RECEIVER

An iterative MC-CDMA receiver is developed whose overall schematic diagram is depicted in Fig. 2. The receiver consists of an upper branch and a lower branch. The upper branch consists of the “slave” adaptive filter bank, frequency offset estimator, composite channel vector estimator, and RAKE combiner. The lower branch involves the “master” adaptive filter bank and signal reconstruction. At the th iteration, the master adaptive filters process the “signal subtracted” data and compute an adaptive weight vector for each finger, which provides effective signal (including multipath and intercarrier interference) reception and MAI suppression. The weight vectors of the master adaptive filters are then copied to the slave adaptive filters, which operate on the original data to yield signal symbol decisions. In summary, the design of the receiver involves the following procedure. First, a slave adaptive filter for each finger transforms from the chip domain to symbol domain and performs MAI suppression. Second, frequency offset estimation ( ), path gain estimation ( s), and a RAKE combiner give the signal symbol decisions ( ). Finally, composite channel vector estimation ( ) and waveform reconstruction ( ) is done by exploiting the frequency offset estimate, path gain estimate, signal symbol decisions, and signal’s signature vectors. The reconstructed signal waveform is then subtracted from the data sent to the next iteration to obtain an estimate of for the master adaptive filter bank. It is noteworthy that the master and slave adaptive filters use different input data.

*A. Construction of GSC-Based Master Adaptive Filters*

The following development considers the design of the master adaptive filter bank in the lower branch. Suppose that at the th iteration, the RAKE combiner consists of fingers, with each finger equipped with an adaptive filter. The adaptive filter at the th finger is a linear combiner matched to the post-FFT signature vector whose output is given by

(23)

where is the weight vector, and is the post-FFT

data vector. Note that, as depicted in Fig. 2, . To ensure an effective suppression of MAI, adaptive cancellation is performed for each of the filters. A popular criterion for

Fig. 3. Structure of GSC for master adaptive filters.

interference cancellation is the LCMV criterion [4] which de-termines the weight vectors according to

subject to: (24)

for , where

(25) is the post-FFT data correlation matrix at the th iteration.

In LCMV combining, the adverse phenomenon of signal can-cellation usually occurs due to the mismatch of signature vec-tors [11]. With such mismatch present, the signal can be treated as interference and receive a very small gain. An effective so-lution proposed herein is to employ the scheme of GSC [4], which is essentially an indirect but simpler implementation of the LCMV algorithm. The concept of GSC, as depicted in Fig. 3, is to decompose the weight vector into two branches:

. In the upper branch, is the fixed matched filter. In the lower branch, is a predesigned “blocking” matrix which removes the signal component (including multipath and inter-carrier interference) in . Thus, the upper branch contains both the signal and MAI, and the lower branch contains only the MAI. The goal is then to choose the adaptive weight vector to cancel the MAI in the upper branch output. To apply the GSC in constructing the adaptive filter bank, two modifications should be made. First, instead of blocking signals for a specific path, must remove signals from the entire delay spread so as to avoid signal cancellation. Second, since is required to re-move all multipath signals, it is natural to share the same for all fingers, instead of using a different matrix for each adap-tive filter. Following the procedure of GSC, is determined by the following MMSE problem:

(26)

Solving for and substituting in gives

(27)

for . Since the upper branch contains both

the signal and MAI, and the lower branch contains the MAI only, minimizing the error between the two branches leads naturally to an adaptive weight vector that cancels the MAI. The solution in (27) involves the inversion of whose size depends on the number of columns of . In the following sections, methods for choosing and efficient realization will be discussed.

To this end, a method is proposed in which a dense set of

frequencies , , is chosen to

accom-modate an offset range , and is chosen to

be an matrix whose columns are orthogonal to

, ,

where

FFT IFFT

(28) is the distorted post-FFT signature vector of the th path due to frequency offset , with denoting the Hadamard (element-wise) product. Depending on the width of , the above signature vectors will span an effective rank of . In other words, a set of vectors can be found well representing these signature vectors. A simple method for finding these rep-resenting vectors is via the eigenvalue decomposition of the fol-lowing matrix:

(29)

where and are the eigenvalues and eigenvectors of in descending order. Depending on the width of , there will be dominant modes (with large eigenvalues) in (29). The blocking matrix can then be chosen to consist of the remaining eigenvectors associated with the smaller eigen-values

(30) Due to the orthogonality among s, the so constructed should

satisfy , , .

By blocking all possible distorted signature vectors due to dif-ferent frequency offset values, can effectively remove the

signal component in that . The choosing of is a

tradeoff between the blocking effect and degree of freedom for
adaptive nulling. With a fixed and , a small leads to
*better blocking but poor interference suppression and vice versa.*
A heuristic choice which has been confirmed by numerical
re-sults is , i.e., two degrees of freedom are used
for blocking each finger. By removing both the signal and ICI
components before adaptive filtering, the GSC adaptive filters
can put all their efforts suppressing the MAI as desired. As a
final remark, the blocking matrix in (30) can be computed in
advance given a predetermined and .

the beamformer weight vector, which in turn causes a drop in output SINR. With the increase of data sample size, this cross correlation gradually vanishes and the LCMV beamformer approaches the optimal MSINR beamformer. The same state-ments apply to GSC adaptive filters. First, the data correlation matrix in (27) is replaced by its sample average version under finite data samples

(31)

where , , and are the sample signal correlation ma-trix, interference-plus-noise correlation mama-trix, and cross corre-lation matrix between signal and interference-plus-noise. Using

the fact , we have

(32) Note that the first term on the righthand side of (32) represents the “optimal” MSINR weight vector in (20) [12], and the second term represents the perturbation leading to poor convergence [6]. A natural way to remedy this is then by removing the per-turbation term, which can be achieved by removing the signal

component in such that . This suggests an

it-erative procedure in which the signal is estimated, reconstructed at the th iteration, and subtracted from at the th iteration.

*1) Frequency Offset Estimation and RAKE Combining: At*

the th iteration, the slave adaptive filters in the upper branch are used to despread the original post-FFT data

(33)

for . After despreading, the MAI is suppressed

to a certain extent, and the frequency offset estimate can be obtained. Methods such as the MLE described in (22) can be employed, but found to yield a large estimation variance due to residual MAI. As a more robust alternative approach, the Fourier method can be employed which starts with the -point FFT of the sequence

FFT (34)

where denote either the pilot symbols only (for ) or pilot symbols plus data decisions from the previous

TABLE I

ALGORITHMSUMMARY OFPROPOSEDRECEIVER

to different fingers are then incoherently summed to acquire the initial frequency offset estimate

(35) For , a coherent estimator can be constructed as

(36)

where s are the path gain estimates from the previous it-eration. Alternatively, since the MAI has been sufficiently sup-pressed, the MLE can be readily applied using the formula in (22), with replaced by the tentative RAKE combiner

output and replaced by .

Next, with , , and , the path gains can be

estimated at the th iteration as

(37)

for . Based on these estimates, coherent RAKE

combining is achieved by

(38) which is then sent to the data decision device

(39) It is suggested that hard decisions be used at the initialization of the iterations to avoid large errors in signal reconstruction [see (41)] due to MAI. With MAI suppressed after the first iteration, it is shown that both soft and hard decisions give similar results.

*2) Channel Estimation, Signal Reconstruction, and *
*Subtrac-tion: As an analogy to (14), the composite channel vector *

es-timation is accomplished by exploiting , , and signal’s signature vector ( s)

(40)

where is the estimated ICI vector obtained based on ,

s, and (9) and (12). Next, with , , and

available, signal reconstruction can be done by

(41)

Finally, the reconstructed signal is subtracted from the data sent to the next iteration. This leads to the residual data given by

(42) By using as the new input of the GSC adaptive fil-ters in (23), the adverse poor convergence can be effectively improved. This above described procedure can be iterated sev-eral times (three to four iterations for typical scenarios) to gain further improvement and approach the performance of the ideal MSINR receiver.

IV. IMPLEMENTATION ANDPERFORMANCEISSUES

*A. MSINR Receiver and Algorithm Summary*

With signal subtraction, the proposed receiver will act like the optimal MSINR receiver operating on . In particular, as iterations proceed, will contain only the interference and noise such that , and will approach the true composite channel vector in (14). It is, thus, natural to replace the adaptive filter bank at the final iteration [with superscript omitted] by a single receiver with the weight vector [12]

(43)

where is a full rank matrix satisfying

. It is noteworthy that the above alternative is nearly identical to the MSINR receiver and provides better MAI suppression in a heavily loaded system due to its larger degree of freedom for nulling. Nevertheless, (32) and (43) offer nearly the same performance under moderately loaded scenarios. The complete algorithm of the proposed receiver is summarized in Table I.

*B. PA Implementation for Multiuser Scenario*

In the direct matrix inversion (DMI) implementation, the computation of adaptive weight vector in (27) involves the

inversion of , which is . With a large

, this would lead to a high computational load and poor convergence for real-time implementation. To alleviate this, partial adaptivity can be incorporated to reduce the size of s by working with a reduced size . Here, a technique suitable for multiuser scenarios is developed. In a multiuser scenario, the MAIs composite channel vectors can be obtained by pilot symbols assisted path gain and frequency offset estimation in the same way as that described in Section II. In particular, the composite channel vector of user can be obtained by

jecting onto the column space of these set of vectors (45) where we have assumed that the columns of form an or-thonormal set. PA realization via (45) is simple and proves ro-bust to errors in MAIs channel estimates. In particular, errors in s tend to decrease the cross correlation between the two branches, and results in only slight performance degradation. When viewed as a multiuser detector, the proposed PA receiver is much more robust than the conventional ones, which detect and subtract the MAI [7]. In conventional multiuser detectors, a phase error in MAIs channel estimate can result in an enhanced MAI power and possible error propagation.

*C. Recursive Computation of Weight Vectors*

For a more efficient implementation, the GSC weight vector and path gain estimation can be done in a time-recursive fashion using stochastic gradient algorithms such as LMS [14]. For the computation of GSC weight vector in (27), we have the recur-sive formulation

(46) for . On the other hand, a recursive algorithm for the estimation of path gain in (37) is given by [15]

(47) In the above, and are the adaptation stepsizes.

V. COMPUTERSIMULATIONS

Simulation results are demonstrated to confirm the perfor-mance of the proposed receiver in a time-multiplexed pilot symbols assisted system. For all users, independent Rayleigh-fading paths were generated with the delays s

chosen from , which was smaller than the guard

interval . The path gains s were assumed

i.i.d. unit variance complex Gaussian random variables. The

number of subcarriers was chosen to be equal to

the processing gain. All MC-CDMA signals were generated

Fig. 4. Output SINR versus input SNR, with MSR= 10 dB, N = 300,

K = 10, and = 0:2.

with binary phase-shift keying (BPSK) data modulation and orthogonal gold codes were used as the spreading codes. Also, the frequency offsets of all users were assumed to be in the

range such that . The

blocking matrix was constructed by the eigenvector method

described in Section III-B, with and .

The length of FFT in (34) was chosen to be , with zero padding applied. As a performance index, the output SINR is defined to be the ratio of the signal power ( )

to MAI-plus-noise power ( )

at the receiver output. Also, the input SNR was defined as

SNR , and the MAI-to-signal ratio (MSR) was

defined as MSR , , where we assumed

equal power MAI. For each simulation trial, symbols (including data and pilot) were used to obtain the sample estimate of , and pilot symbols were used to obtain and s at the first iteration. A total of 500 Monte Carlo trials were executed to obtain one output SINR value, with each trial using a different set of s and data/noise sequence. For performance comparison, the results obtained with the ideal FS-MSINR receiver and FS-MMSE receiver were also included. The ideal FS-MSINR receiver was implemented by artificially removing the signal component in the data, and using the true composite channel vector to obtain (20). On the other hand, the FS-MMSE receiver was implemented by first estimating the frequency offset using (35) with directly de-spread data, followed by composite channel vector estimation to obtain (17). Finally, the following “standard” parameters will be used throughout the section unless otherwise mentioned:

SNR dB, MSR 10 dB, , , ,

. Except for one case, the true MAI channel

vectors were assumed in (45), i.e., , .

In the first set of simulations, the output SINR performance is evaluated as a function of input SNR for both the fully adap-tive (FA) and PA versions of the proposed receiver. The results shown in Fig. 4 indicate that the proposed receiver successively approaches the ideal MSINR receiver, with a degradation of only about 0.2 dB in three iterations. The FS-MMSE receiver performs poorly due to poor frequency offset estimation prior

Fig. 5. Output SINR versus received symbol sizeN , with SNR = 0 dB, MSR= 10 dB, K = 10, and = 0:2.

Fig. 6. Output SINR versus relative channel estimation error = , with SNR = 0 dB, MSR = 10 dB, N = 300, K = 10, and = 0:2.

to MAI cancellation. On the other hand, the PA receiver has almost the same performance of the FA receiver, confirming the assertion in Section IV-B. In the second set of simulations, the output SINR performance is evaluated as a function of re-ceived symbol size . The results given in Fig. 5 show that the proposed receiver successively improves as iterations pro-ceed, approaching the ideal MSINR receiver within about 300 symbols. These results confirm that the MAIs were indeed suc-cessfully suppressed by the proposed receiver, and PA imple-mentation can retain the performance of the FA receiver. In the following, only the proposed PA and FS-MMSE receivers will be evaluated.

In the third set of simulations, the robustness of the proposed PA receiver against MAI channel estimation errors is

demon-strated. In this case, in (45), where is

a random vector with the entries being i.i.d. complex Gaussian random variables with the same variance of 3. Note that the en-tries of are i.i.d. complex Gaussian random variables with

variance . Fig. 6 shows the output SINR versus

Fig. 7. Output SINR versus normalized frequency offset , with SNR = 0 dB, MSR= 10 dB, N = 300, and K = 10.

Fig. 8. Output SINR versus user numberK, with SNR = 0 dB, MSR

= 10 dB, N = 300, and = 0:2.

. The results confirm that the proposed PA receiver can perform quite reliably for up to a 20% relative error in MAI channel estimation. In the fourth set of simulations, the toler-ance of the proposed PA receiver against different frequency off-sets is evaluated. The resulting output SINR curves as a function of are plotted in Fig. 7, which shows that within the entire

range , the output SINR is almost constant.

The results indicate that the modified blocking matrix effec-tively removes the signal and ICI together so as to avoid possible signal cancellation in the GSC adaptive filters. With successful signal reception and MAI suppression by the adaptive filters, an accurate frequency offset estimate can then be obtained to guar-antee a high output SINR.

In the fifth set of simulations, the system capacity is evaluated with different values of . As shown in Fig. 8, the proposed re-ceiver again successively approaches the MSINR rere-ceiver, with a degradation of about 2 dB in output SINR with . The simulation results confirm that the proposed receiver is able to offer the performance of the optimal MSINR receiver with a

Fig. 9. Output SINR versus MSR, with SNR = 0 dB, N = 300, K = 10, and = 0:2.

Fig. 10. Evaluation of recursive algorithms with SNR = 0 dB, MSR

= 10 dB, K = 5, and = 0:2. Multipath gains changed at 500th symbol.

moderate symbol size in a heavily loaded system. In the sixth set of simulations, the near–far resistance of the proposed receiver is evaluated with different MSR values. Fig. 9 shows the output SINR curves. It is observed that the proposed receiver achieves its excellent near–far resistance by successfully cancelling the strong MAI using the temporal degree of freedom offered by the predespread data.

Finally, to demonstrate the effectiveness of the recursive al-gorithms for weight vector adaptation, we replaced the direct weight vector computation in (27) and path gain estimation in (37) by the formulae given in (46) and (47), respectively. In this case, the FA receiver was used, with and

adapta-tion stepsizes chosen as and ,

respec-tively. In order to demonstrate the tracking capability of these algorithms, the multipath fading gains of all users were delib-erately changed at the 500th symbol. The resulting learning curves shown in Fig. 10 show that the proposed receiver

con-order to enhance the convergence behavior of the GSC, a decisions-aided scheme is proposed, in which the signal wave-form is first reconstructed and then subtracted from the input data sent to the next iteration. In the upper branch, a “slave” adaptive filter bank, copied from the lower branch, performs despreading and MAI suppression, and pilot symbols assisted frequency offset estimation, channel vector estimation and RAKE combining give the desired signal symbols. With signal subtraction in the lower branch, the proposed MC-CDMA re-ceiver can achieve nearly the performance of the ideal MSINR receiver within a few iterations. Finally, a low-complexity PA realization of the GSC adaptive filters is presented for a multiuser scenario. The new PA receiver is shown to be robust to multiuser channel errors, and offer nearly the same perfor-mance of the fully adaptive receiver. In summary, the proposed MC-CDMA receiver with PA MAI suppression performs near optimal signal detection with tolerance to large frequency offsets and resistance to strong MAI. More importantly, it can be initialized in the blind mode without the aid of channel estimation and frequency offset compensation.

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**Juinn-Horng Deng (S’01) was born in Miaoli,**

Taiwan, R.O.C., in 1965. He received the B.S.E.E. degree from Chung Cheng Institute of Technology, Taiwan, R.O.C., in 1988, and the M.S.E.E. degree from Yuan Ze University, Taiwan, R.O.C., in 1993. Currently, he is working toward the Ph.D. degree in the Department of Communication Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.

From 1988 to 1991, and 1993 to 1999, he was in the Phase Array Radar Department, Chung Shan In-stitute of Science and Technology, Taiwan, R.O.C. His research interests include multiuser detection, communication signal processing, and smart antennas.

**Ta-Sung Lee (S’88–M’89) was born in Taipei,**

Taiwan, R.O.C., in 1960. He received the B.S. degree from National Taiwan University, Taipei, Taiwan, R.O.C., the M.S. degree from the University of Wis-consin, Madison, and the Ph.D. degree from Purdue University, West Lafayette, IN, in 1983, 1987, and 1989, respectively, all in electrical engineering.

In 1990, he joined the Faculty of National Chiao Tung University (NCTU), Taipei, Taiwan, where he holds a position as Professor in the Department of Communication Engineering. From 1999 to 2001, he was Director of the Communications and Computer Training Program at NCTU. He is active in research and development in advanced techniques for wireless communications, such as smart antennas for mobile cellular, BWA and WLAN systems, space–time and MIMO transceivers for high data rate transmission, OFDM based broadband wireless access systems, and interference rejection for co-existing systems. He has been involved in several National Research Pro-grams, such as the “Program for Promoting Academic Excellence of Univer-sities” supported jointly by the Ministry of Education and National Science Council (NSC) of R.O.C., and the program of “Advanced B3G Radio Access Technologies” supported by the National Telecommunications Program Office. Dr. Lee is a Member of Phi Tau Phi Society of R.O.C., and recipient of the 1999 Young Electrical Engineer Award of the Chinese Institute of Electrical Engineers and the 2001 NCTU Teaching Award.