Multiuser detection in asynchronous CDMA frequency-selective fading channels

Multipath fading severely limits the performances of conventional code division multiple-access (CDMA) systems. Since every signal passes through an independent frequency-selective fading channel, even modest cross-correlations among signature sequences may induce severe near-far effects in a central multiuser receiver. This paper presents a systematic approach to the detection problem in CDMA frequency-selective fading channels and proposes a low complexity linear multiuser receiver, which eliminates fading induced near-far problem.We initially analyze an optimal multiuser detector, consisting of a bank of RAKE filters followed by a dynamic programming algorithm and evaluate its performance through error probability bounds. The concepts of error sequence decomposition and asymptotic multiuser efficiency, used to characterize the optimal receiver performance, are extended to multipath fading channels.The complexity of the optimal detector motivates the work on a near-far resistant, low complexity decorrelating multiuser detector, which exploits multipath diversity by using a multipath decorrelating filter followed by maximal-ratio combining. Analytic expressions for error probability and asymptotic multiuser efficiency of the suboptimal receiver are derived that include the effects of multipath fading, multiple-access interference and signature sequences correlation on the receiver's performance.The results indicate that multiuser detectors not only alleviate the near-far problem but approach single-user RAKE performance, while preserving the multipath diversity gain. In interference-limited scenarios multiuser receivers significantly outperform the RAKE receiver.This paper was presented in part at the Twenty-Sixth Annual Conference on Information Sciences and Systems, Princeton, NJ, March 1992 and MILCOM'92, San Diego, CA, October 1992. This work was performed while author was with the Department of Electrical and Computer Engineering, Northeastern University, Boston, USA.     

Multiuser receivers for randomly spread signals: fundamental limitswith and without decision-feedback

Synchronous code-division multiple-access (CDMA) communication systems with randomly chosen spreading sequences and capacity-achieving forward error correction coding are analyzed in terms of spectral efficiency. Emphasis is on the penalties paid by applying single-user coding in conjunction with suboptimal multiuser receivers as opposed to optimal joint decoding which involves complexity that is exponential in the number of users times the code word length. The conventional, the decorrelating, and the (re-encoded) decorrelating decision-feedback detectors are analyzed in the nonasymptotic case for spherical random sequences. The re-encoded minimum mean-squared error (MMSE) decision-feedback receiver achieving the same performance as joint multiuser decoding for equal power users is shown to be suboptimal in the case of equal rates     

Improved Robust Techniques for Multiuser Detection in Non-Gaussian Channels

In many physical channels where multiuser detection techniques are to be applied, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulsive phenomena. This is due to the impulsive nature of man-made electromagnetic interference and a great deal of natural noise. This paper presents a robust multiuser detector for combating multiple access interference and impulsive noise in code division multiple access (CDMA) communication systems. A new M-estimator is proposed for "robustifying" the detector. The approach is corroborated with simulation results to evaluate the performance of the proposed robust multiuser detector compared with that of the linear decorrelating detector, and the Huber and the Hampel M-estimator based detectors. Simulation results show that the proposed detector with significant performance gain outperforms the linear decorrelating detector, and the Huber and the Hampel M-estimator based detectors. This paper also presents an improved robust blind multiuser detection technique based on a subspace approach, which requires only the signature waveform and the timing of the desired user to demodulate that user's signal. Finally, we show that the robust multiuser detection technique and its blind adaptive version can be applied to both synchronous and asynchronous CDMA channels.     

A flexible receiver for CDMA multiuser communications

Code division multiple access (CDMA) capacity is limited by interference amongst users. The effect of this interference on receiver outputs depends on the users' signatures and the actual detector used in the receiver. A matched filter receiver is particularly sensitive to interference, whereas an optimum multiuser receiver is less sensitive but infeasible due to its exponential complexity. We propose a receiver structure that trades detection performance for reduced complexity. It can interpolate between the performances and complexities of these two receivers. Our detector uses a tree structure, and some of its special cases are the decision feedback detector, the decorrelating detector, and the optimal linear detector. We show that at equal complexity levels, a particular implementation of our detector outperforms these detectors. We also show that our approach can be used with a minimum-mean-square-error design criterion and coded CDMA transmission     

Optimally near-far resistant multiuser detection in differentiallycoherent synchronous channels

The noncoherent demodulation of differentially phase-shift keyed signals transmitted simultaneously via a synchronous code-division multiple-access (CDMA) channel is studied under the assumption of white Gaussian background noise. A class of noncoherent linear detectors is defined with the objective of obtaining the optimal one. The performance criterion considered is near-far resistance that denotes worst-case multiuser asymptotic efficiency over near-far environments. It is shown that the optimal linear detector is a noncoherent decorrelating detector. The commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established. In particular, it is shown that no other differential phase-shift keying (DPSK), multiuser detector achieves a higher near-far resistance than does the noncoherent decorrelator     

Optimum diversity combiner based multiuser detection fortime-dispersive Rician fading CDMA channels

Multiuser detection for asynchronous code division multiple access (CDMA) data transmission over the time-dispersive two-path Rician fading channel is considered. The multiuser maximum likelihood sequence detector (MLSD) is derived, and an equivalence of the fading channel to an asynchronous Gaussian intersymbol interference (AGISI) CDMA channel is established. However, the MLSD is found to be implementationally infeasible and this motivates the derivation of the optimum linear detector with near/far resistance as the performance criterion. The optimally near/far resistant linear time-invariant K-user detector is shown to consist of a cascade of a 2 K input/K output linear multiuser diversity combining filter followed by a K input/K output decorrelator that is designed for the equivalent AGISI/CDMA channel. This detector solves the near/far problem and also supports significantly higher bandwidth efficiencies for CDMA communication over the fading channel than does the conventional near/far limited single-user diversity combiner. The performance penalties incurred by multiuser detectors designed for the Gaussian channel when used over the Rician fading channel are also analytically characterized. It is shown that these penalties can be significant, making the case for the use of multiuser detectors optimized for this fading channel, particularly the optimum linear detector due to its relative implementational simplicity     

Adaptive joint multiuser detection and channel estimation in multipath fading CDMA channels

The problem of joint multiuser detection and channel estimation in frequency-selective Rayleigh fading CDMA channels is considered. First the optimal multiuser detector for such channels is derived, which is seen to have a computational complexity exponential in the product of the number of users and the length of the transmitted data sequence. Two suboptimal detectors are then developed and analyzed, both of which employ decorrelating filters at the front-ends to eliminate the multiple-access interference and the multipath interference. The symbol-by-symbol detector uses a Kalman filter and decision feedback to track the fading channel for diversity combining. The per-survivor sequence detector is in the form of the Viterbi algorithm with the trellis updates being computed by a bank of Kalman filters in the per-survivor fashion. Both suboptimal detectors require the knowledge of all waveforms of all users in the channel and the channel fading model parameters. Adaptive versions of these suboptimal detectors that require only the knowledge of the waveform of the user of interest are then developed. The adaptive receivers employ recursive-least-squares (RLS) minimum-mean-square-error (MMSE) filters at the front-end to mitigate the interference, and use a bank of linear predictors to track the fading channels. It is shown that the front-end RLS-MMSE filters can be implemented using systolic arrays to exploit massively parallel signal processing computation, and to achieve energy efficiency. Finally, the performance of the suboptimal detectors and their adaptive versions are assessed by simulations. This revised version was published online in July 2006 with corrections to the Cover Date.     

A New Multiuser Detector for Synchronous DS/CDMA System

1IntroductionInaCode-DivisionMultiple-Access(CDMA)system,severalindependentusersaccesssimulboeouslyacommonchannelbymodulatingpreassignedsignatUrewaveforms.Inthemobileradiochannels,MultipleAccessinterference(MAI)arises.Therefore,muchattelltionhasbeend...     

Noncoherent detection in asynchronous multiuser channels

The noncoherent demodulation of multiple differentially phase-shift-keyed signals transmitted simultaneously over an asynchronous code-division multiple-access (CDMA) channel with white Gaussian background noise is considered. A class of bilinear detectors is defined with the objective of obtaining the optimal bilinear detector. The optimality criterion considered is near-far resistance that denotes worst-case asymptotic efficiency over the signal energies and phases which are unknown at the receiver. The optimal bilinear detector is therefore obtained by solving a minimax optimization problem. In the finite packet length case, this detector is shown to be a time-varying multiinput multioutput linear decorrelating filter followed by differential decision logic. In the limit as packet lengths go to infinity, the time-varying decorrelating detector is replaced by a time-invariant multiinput multioutput decorrelating filter. Several properties of the optimally near-far resistant detector are established     

一种自适应分布式多用户检测算法

本文针对移动CDMA加性白高斯噪声和衰落信道 ,提出了一种自适应分布式多用户检测算法 .它由空间分集和解相关检测复合组成 .解相关检测器的性能近似最佳多用户检测器 ,且不依赖于其它用户的信号能量及衰落特性 .基于随机梯度技术的盲自适应分集合并方案由最佳似然比检验准则构成 .对其性能做了理论分析和数值估计 ,并与传统的选择法、等增益法及最大比值法做了比较 .所提出的方法易于实时实现 ,可以较大地提高接收机性能和系统容量增益     

Decision-feedback blind adaptive multiuser detector for synchronousCDMA system

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 ambiguities. To further improve the symbol error probability performance, we introduce decision feedback in our detector similar to the decorrelating derision-feedback detector (DDFD), thus forming the decision-feedback blind adaptive multiuser detector (DFBD). Simulations indicate that the performance of the DFBD is very close to that of the DDFD in additive white Gaussian noise (AWGN) channels. In Rician fading channels, the DFBD can track the slowly varying channels well and has a symbol error probability performance approaching that of the DDFD, which requires the knowledge of users' energies. The blind adaptive and decision-feedback blind adaptive multiuser detectors proposed here do not, however, require that knowledge     

A blind adaptive decorrelating detector for CDMA systems

The decorrelating detector is known to eliminate multiaccess interference when the signature sequences of the users are linearly independent, at the cost of enhancing the Gaussian receiver noise. We present a blind adaptive decorrelating detector which is based on the observation of readily available statistics. The algorithm recursively updates the filter coefficients of a desired user by using the output of the current filter. Due to the randomness of the information bits transmitted and the ambient Gaussian channel noise, the filter coefficients evolve stochastically. We prove the convergence of the filter coefficients to a decorrelating detector in the mean squared error (MSE) sense. We develop lower and upper bounds on the MSE of the receiver filter from the convergence point and show that with a fixed step size sequence, the MSE can be made arbitrarily small by choosing a small enough step size. With a time-varying step size sequence, the MSE converges to zero implying an exact convergence. The proposed algorithm is distributed, in the sense that no information about the interfering users such as their signature sequences or power levels is needed. The algorithm requires the knowledge of only two parameters for the construction of the receiver filter of a desired user: the desired user's signature sequence and the variance of the additive white Gaussian (AWG) receiver noise. This detector, for an asynchronous code division multiple access (CDMA) channel, converges to the one-shot decorrelating detector     

An adaptive multiuser receiver for CDMA systems

A new real-time, digital adaptive multiuser receiver structure is proposed for the uplink in a mobile communications system employing code division multiple access (CDMA). The receiver efficiently implements the decorrelating detector of Lupas and Verdu (1989) and can be adapted to incorporate decision feedback to further improve the detector performance. While the basic receiver design is presented for synchronous CDMA over AWGN channels, experimental evaluation of the receiver for the asynchronous case verifies its robustness for cases when the relative user delays are small compared to the symbol duration as in microcellular scenarios. An efficient decorrelating RAKE combiner for frequency-selective multipath channels is also proposed and analyzed. Performance evaluation of the detector via computer simulation scenarios is conducted in support of analytical results to substantiate its potential for real-time operation     

An asynchronous multiuser CDMA detector based on the Kalman filter

We introduce a multiuser receiver based on the Kalman filter, which can be used for joint symbol detection and channel estimation. The proposed algorithm has the advantage of working even when the spreading codes used have a period larger than one symbol interval (“long codes”), unlike adaptive equalizer-type detectors. Simulation results which demonstrate the performance advantage of the proposed receiver over the conventional detector, the minimum mean squared error (MMSE) detector and a recursive least squares (RLS) multiuser detector are presented. A thorough comparison of the MMSE detector and the proposed detector is attempted because the Kalman filter also solves the MMSE parameter estimation problem, and it is concluded that, because the state space model assumed by the Kalman filter fits the code division multiple access (CDMA) system exactly, a multiuser detector based on the Kalman filter must necessarily perform better than a nonrecursive, finite-length MMSE detector. The computational complexity of the detector and its use in channel estimation are also studied     

A near ideal noise whitening filter for an asynchronoustime-varying CDMA system

A near ideal noise whitening filter for a time-varying code-division multiple-access (CDMA) system is examined. First, the structure of the ideal noise whitening filter is determined. The ideal noise whitening filter for a time-varying CDMA system is dependent on unknown future system parameters and is, therefore, impractical. A near ideal, realizable whitening filter is introduced as a solution. The convergence of the factorization method for a time-varying CDMA system is considered. The truncation of the number of taps of the ideal noise whitening filter is studied and a metric function based on the near ideal noise whitening filter for a tree search detection algorithm is formulated. Simulation results are obtained for five and ten-user time-varying CDMA systems with binary random signature sequences of length 10 and a rectangular chip waveform. The results show that the near ideal noise whitening filter can accurately approximate the ideal noise whitening filter at a low complexity level. The performance degradation of a suboptimal tree search detector for a time-varying, asynchronous CDMA system using a typical near ideal noise whitening filter is minimal compared to an identical system using the ideal noise whitening filter     

Analysis of an adaptive decorrelating detector for synchronous CDMAchannels

Multiuser detection allows for the efficient use of bandwidth in code-division multiple-access (CDMA) channels through mitigation of near-far effects and multiple-access noise limitations. The decorrelating detector, developed by Lupas and Verdu (1989), is a linear multiuser detector that is asymptotically optimal in terms of near-far resistance when certain communication parameters are completely known to the detector. In this paper, a simple adaptive decorrelating detector is developed by placing constraints on the set of spreading codes to be used by the active users. This adaptive detector has two modules: it first decorrelates the existing users, and then it determines the spreading code of a new user entering the network with or without the use of a training sequence. Maximum likelihood detection is proposed for determining the new user's spreading code. The performance of this algorithm is studied by investigating the probability of making an error in determining the new user's spreading code as a function of the number of samples used to make the determination, the number of users transmitting, and the signal to noise ratio of the new user with respect to the ambient Gaussian noise     

Recursive structures and finite impulse response implementations oflinear multiuser detectors for an asynchronous CDMA system

We present order-recursive structures for implementing the linear decorrelating and linear minimum mean square error (MMSE) detectors in a computationally efficient manner. These infinite memory length, linear time invariant, noncausal systems can be approximated by implementing them as K-input K-output finite impulse response (FIR) filters. We developed a linear multiuser receiver architecture called a recursive linear multiuser detector which has lower computational and memory requirements then an equivalent tap delay line FIR filter implementation. We establish the tradeoff between window length and bit error rate and find that relatively small window size yields performance indistinguishable from the ideal decorrelating detector and the ideal MMSE detector     

Achieving near-optimum asymptotic efficiency and fading resistanceover the time-varying Rayleigh-faded CDMA channel

We study multiuser receiver design and analysis for synchronous code-division multiple-access (CDMA) channels with time-varying Rayleigh fading. Starting from an error probability criterion, we first derive a near-optimum receiver for this channel that admits a detector-estimator decomposition, has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval. The performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time-invariant (or static) CDMA Rayleigh-fading channel when it is implemented over the time-varying channel. Notable among our conclusions is the fact that, unlike the static channel multiuser detector, the time-varying channel detector is able to withstand not only the estimated interference from the other system users, but also, the residual interference (that cannot be estimated) arising out of imperfect estimation of the interferer fading parameters. Using estimation error covariance information, this detector shows flexibility in accommodating a wide range of interferer fading conditions     

Low Complexity Polynomial Expansion Multiuser Detector for CDMA Systems

The polynomial expansion (PE) multiuser detector can iteratively approximate the linear decorrelating and MMSE multiuser detectors. This is a very promising approach since the complexity of the PE detector is considerably less than that of the decorrelating and MMSE detectors. The concept of the PE multiuser detector is a weighted matrix polynomial for which optimal weighting has been suggested in the literature. Unfortunately, the optimal weights apply only to a specific correlation matrix. As soon as the correlation between the users changes (and hence also the correlation matrix), a new set of optimal weights has to be calculated. The calculation of these weights is computationally very intense. In this paper, an approach is presented where the weights are predefined and apply for all matrices. Furthermore, a normalization factor is needed to ensure convergence. It will be shown how this factor has to be chosen to obtain the optimal convergence speed. For the optimal normalization factor the minimum and maximum eigenvalues are needed. A low complexity and accurate method to estimate these eigenvalues is derived which can be applied to all correlation matrices and therefore to any code division multiple access (CDMA) scenario. Hence, the matrix-dependent optimal normalization factor can easily be calculated and ensures a good bit error rate (BER) performance, even if the correlation between the users changes quickly (e.g., in time-variant channels). Furthermore, it will be shown how to enhance the PE detector such that it has a high near-far resistance. Additionally, for the first time it can be proven that the approximation error of the proposed detector diminishes exponentially with the number of iterations. Finally, simulations verify the fast convergence of the proposed PE detector and its flexible usage in a variety of scenarios.     

Blind turbo multiuser detection for long-code multipath CDMA

We consider the problem of demodulating and decoding multiuser information symbols in an uplink asynchronous coded code-division multiple-access (CDMA) system employing long (aperiodic) spreading sequences, in the presence of unknown multipath channels, out-cell multiple-access interference (OMAI), and narrow-band interference (NBI). A blind turbo multiuser receiver, consisting of a novel blind Bayesian multiuser detector and a bank of MAP decoders, is developed for such a system. The effect of OMAI and NBI is modeled as colored Gaussian noise with some unknown covariance matrix. The main contribution of this paper is to develop blind Bayesian multiuser detectors for long-code multipath CDMA systems under both white and colored Gaussian noise. Such detectors are based on the Bayesian inference of all unknown quantities. The Gibbs sampler, a Markov chain Monte Carlo procedure, is then used to calculate the Bayesian estimates of the unknowns. The blind Bayesian multiuser detector computes the a posteriori probabilities of the channel coded symbols, which are differentially encoded before being sent to the channel. Being soft-input soft-output in nature, the proposed blind Bayesian multiuser detectors and the MAP decoders can iteratively exchange the extrinsic information to successively refine the performance, leading to the so-called blind turbo multiuser receiver