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 ML sequence estimator for convolutionally codedasynchronous DS-CDMA systems

The optimal multiuser sequence estimator is formulated for an asynchronous direct-sequence code-division multiple-access (DS-CDMA) system where each user employs convolutional coding to improve its performance on a nondispersive additive white Gaussian noise (AWGN) channel. It is shown that the decoder may be implemented efficiently using a Viterbi algorithm which operates on a time-varying trellis with a number of states which is exponential in the product of the number of users in the system and the constraint length of the codes used (for the rate 1/2 code case). The asymptotic efficiency of this receiver relative to an uncoded coherent binary phase shift keying (BPSK) receiver (termed asymptotic multiuser coding gain, or AMCG) is then upper and lower bounded. The AMCG parameter unifies the asymptotic coding gain parameter and the asymptotic multiuser efficiency parameter which are traditional figure of merit parameters for single-user coded systems and multiuser uncoded systems, respectively. Finally, some simulations are presented to illustrate the performance of the maximum likelihood sequence estimator (MLSE) at moderate and low bit error rates     

Design of reduced-rank MMSE multiuser detectors using random matrix methods

Reduced-rank minimum mean-squared error (MMSE) multiuser detectors using asymptotic weights have been shown to reduce receiver complexity while maintaining good performance in long-sequence code-division multiple-access (CDMA) systems. In this paper, we consider the design of reduced-rank MMSE receivers in a general framework which includes fading, single and multiantenna receivers, as well as direct-sequence CDMA (DS-CDMA) and multicarrier CDMA (both uplink and downlink). In all these cases, random matrix results are used to obtain explicit expressions for the asymptotic eigenvalue moments of the interference autocorrelation matrix and for the asymptotic weights used in the reduced-rank receiver.     

Joint multiuser equalization and Group decoding for asynchronous trellis-coded multiple-access channels

Reduced-complexity multiuser interference equalization and group decoding (ME-GD) is an attractive way to improve performance of multiuser transmissions for narrowband additive white Gaussian noise channels. ME-GD receivers have been investigated in the past for convolutionally coded synchronous multiple-access channels (MACs). In this paper, we propose a new ME-GD for trellis-coded asynchronous MACs. The coding information of a subset of users and the multiuser interference are jointly taken into account in the branch metric computation using per-survivor processing. The novel approach leads to a family of Viterbi decoders which offers a good tradeoff between performance and complexity. As a second contribution of this paper, we derive theoretical bounds for the performance of ME-GD considering the effect of error propagation, which is critical for asynchronous MACs. Numerical results show the excellent accuracy of the proposed bounds. Finally, based on the novel theoretical analysis, we derive a new criterion to achieve good tradeoffs between performance and complexity.     

Efficient adaptive receivers for joint equalization and interference cancellation in multiuser space-time block-coded systems

This paper develops low-complexity adaptive receivers for space-time block-coded (STBC) transmissions over frequency-selective fading channels. The receivers are useful for equalization purposes for single user transmissions and for joint equalization and interference cancellation for multiuser transmissions. The receivers exploit the rich code structure of STBC codes in order to deliver recursive-least-squares (RLS) performance at least-mean-squares (LMS) complexity. Besides reduced complexity, the proposed adaptive receivers also lower system overhead requirements.     

Iterative multiuser detection for turbo-coded synchronous CDMA inGaussian and non-Gaussian impulsive noise

We develop an iterative multiuser receiver for decoding turbo-coded synchronous code-division multiple-access signals in both Gaussian and non-Gaussian noise. A soft-input soft-output nonlinear multiuser detector is combined with a set of single-user channel decoders in an iterative detection/decoding structure. The nonlinear multiuser detector utilizes the prior probabilities of each user's bits to form soft estimates used for multiple-access interference cancellation. The channel decoders perform turbo-code decoding and produce posterior probabilities which are fed back to the multiuser detector for use as prior probabilities. Simulation results show that the proposed multiuser receiver performs well in both Gaussian and non-Gaussian noise. In particular, single-user turbo-code performance can be approached within a few iterations with medium to low cross correlation (ρ⩽0.5)     

A low-complexity SISO multiuser detector for iterative decoding of asynchronous CDMA systems with convolutional codes

The optimal decoding scheme for asynchronous code-division multiple-access (CDMA) systems that employ convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. A direct implementation of the optimal SISO multiuser detector, however, has exponential computational complexity in terms of the number of users which is still prohibitive for channels with a medium to large number of users. This paper presents a low-complexity SISO multiuser detector using the decision-feedback scheme, of which tentative hard decisions are made and fed back to the SISO multiuser from the previous decoding output. In the proposed scheme, the log-likelihood ratios (LLR) as well as the tentative hard decisions of code bits are fed back from the SISO decoders. The hard decisions are used to constrain the trellis of the SISO multiuser detector and the LLRs are used to provide a priori information on the code bits. The detector provides good performance/complexity tradeoffs. The computational complexity of the detector can be set to be as low as linear in the number of users. Simulations show that the performance of the low-complexity SISO multiuser detector approaches that of the single-user system for moderate to high signal-to-noise ratios even for a large number of users.     

Multiuser square-law detection with applications to fiber optic communications

Optimal and suboptimal multiuser noncoherent detection for square-law receivers is studied in this paper. Great potential is found for the multiuser square-law detector when compared with the conventional single-user square-law detector. We study the optimal detector and two detectors with simpler structures: the asymptotically optimal detector and the pairwise linear detector. The saddle-point approximation method is used to study the error performance and its asymptotic behavior as noise reduces. Due to difficulty in optimizing the detectors at an arbitrary noise level, we propose to use the asymptotic efficiency for detector optimization. For a low-error-rate system like a fiber optic communication system, the asymptotic efficiency is found to be an efficient way to design detectors. Numerical results show that the asymptotically optimized detectors perform as well as the optimal detector, even for nonzero noise levels of practical interest. Despite their exponential complexity, these detectors are applicable to wavelength-division multiplexed systems in which only a few neighboring channels produce strong interference.     

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     

Iterative (turbo) soft interference cancellation and decoding forcoded CDMA

The presence of both multiple-access interference (MAI) and intersymbol interference (ISI) constitutes a major impediment to reliable communications in multipath code-division multiple-access (CDMA) channels. In this paper, an iterative receiver structure is proposed for decoding multiuser information data in a convolutionally coded asynchronous multipath DS-CDMA system. The receiver performs two successive soft-output decisions, achieved by a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders, through an iterative process. At each iteration, extrinsic information is extracted from detection and decoding stages and is then used as a priori information in the next iteration, just as in turbo decoding. Given the multipath CDMA channel model, a direct implementation of a sliding-window SISO multiuser detector has a prohibitive computational complexity. A low-complexity SISO multiuser detector is developed based on a novel nonlinear interference suppression technique, which makes use of both soft interference cancellation and instantaneous linear minimum mean-square error filtering. The properties of such a nonlinear interference suppressor are examined, and an efficient recursive implementation is derived. Simulation results demonstrate that the proposed low complexity iterative receiver structure for interference suppression and decoding offers significant performance gain over the traditional noniterative receiver structure. Moreover, at high signal-to-noise ratio, the detrimental effects of MAI and ISI in the channel can almost be completely overcome by iterative processing, and single-user performance can be approached     

Adaptive Multiuser Detection Based on RBF Networks in Impulsive Noise CDMA Channels

With increasing need for capacity in mobilecellular communications, code division multiple accesshas been viewed as the technique to meet this goal.However, the conventional receiver suffers frommultiuser interference and the near-far effect. Toalleviate this problem, various multiuser receivers havebeen proposed. They have been shown to enhance theperformance of the conventional receiver with respect to capacity and interference rejection. Butthese receivers, intended for Gaussian noise channels,can fail in other environments such as impulsive noiseconditions. A possible solution is to exploit the advantages of neural networks. A neuralnetwork's ability to reject non-Gaussian noise can beutilized to implement multiuser receivers that rejectboth impulsive noise and multiuser interference.Following this logic, this paper considers nonadaptivemultiuser receiver and adaptive multiuser receiver basedon radial basis function neural networks. Simulations ofthese receivers show results that are superior to previously studied multiuser receivers, withrespect to practicality and performance.     

A multiuser approach to narrowband cellular communications

We compare three receivers for coded narrowband transmission affected by fading and co-channel interference. The baseline receiver is based on conventional diversity reception with maximal-ratio combining. A multiuser approach allows us to derive a maximum-likelihood multiuser receiver and its reduced-complexity suboptimal version. Finally, a decorrelating diversity receiver, which seeks a tradeoff between performance and complexity, is studied. Closed-form performance parameters are derived for all the proposed receivers in the case of coded coherent PSK and independent frequency nonselective Rayleigh fading     

Iterative space-time processing for multiuser detection in multipath CDMA channels

Space-time processing and multiuser detection are two promising techniques for combating multipath distortion and multiple-access interference in code division multiple access (CDMA) systems. To overcome the computational burden that rises very quickly with increasing numbers of users and receive antennas in applying such techniques, iterative implementations of several space-time multiuser detection algorithms are considered here. These algorithms include iterative linear space-time multiuser detection, Cholesky iterative decorrelating decision-feedback space-time multiuser detection, multistage interference canceling space-time multiuser detection, and expectation-maximization (EM)-based iterative space-time multiuser detection. A new space-time multiuser receiver structure that allows for efficient implementation of iterative processing is also introduced. Fully exploiting various types of diversity through joint space-time processing and multiuser detection brings substantial gain over single-receiver-antenna or single-user-based methods. It is shown that iterative implementation of linear and nonlinear space-time multiuser detection schemes discussed in this paper realizes this substantial gain and approaches the optimum performance with reasonable complexity. Among the iterative space-time multiuser receivers considered in this paper, the EM-based (SAGE) iterative space-time multiuser receiver introduced here achieves the best performance with excellent convergence properties.     

A covariance shaping framework for linear multiuser detection

A new class of linear multiuser receivers, referred to as the covariance shaping multiuser (CSMU) receiver, is proposed, for suppression of interference in multiuser wireless communication systems. This class of receivers is based on the recently proposed covariance shaping least-squares estimator, and is designed to minimize the total variance of the weighted error between the receiver output and the observed signal, subject to the constraint that the covariance of the noise component in the receiver output is proportional to a given covariance matrix, so that we control the dynamic range and spectral shape of the output noise. Some of the well-known linear multiuser receivers are shown to be special cases of the CSMU receiver. This allows us to interpret these receivers as the receivers that minimize the total error variance in the observations, among all linear receivers with the same output noise covariance, and to analyze their performance in a unified way. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio in the large system limit. We also characterize the spectral efficiency versus energy-per-information bit of the CSMU receiver in the wideband regime. Finally, we consider a special case of the CSMU receiver, equivalent to a mismatched minimum mean-squared error (MMSE) receiver, in which the channel signal-to-noise ratio (SNR) is not known precisely. Using our general performance analysis results, we characterize the performance of the mismatched MMSE receiver. We then treat the case in which the SNR is known to lie in a given uncertainty range, and develop a robust mismatched MMSE receiver whose performance is very close to that of the MMSE receiver over the entire uncertainty range.     

Decision-feedback soft-input/soft-output multiuser detector foriterative decoding of coded CDMA

The optimal decoding scheme for a code-division multiple-access (CDMA) system that employs convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input/soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. However, a direct implementation of the full-complexity SISO multiuser detector also has the exponential computational complexity in terms of the number of users. This paper proposes a low-complexity SISO multiuser detector based on tentative hard decisions that are made and fed back from the channel decoders in the previous iteration. The computational complexity of the proposed detector is linear in terms of the number of users and can be adjusted according to the complexity/performance tradeoff. Simulation results show that even with this simple feedback scheme, the performance of the coded multiuser system approaches that of the single-user system for moderate to high signal-to-noise ratios (SNRs)     

Linear receivers for the multiple-input multiple-output multiple-access channel

We consider a multiuser multiple-input multiple-output (MIMO) communication system using code-division multiple access (CDMA) and multiuser detection to discriminate the different users. Our focus is on the CDMA uplink of a frequency-nonselective Rayleigh fading channel. We study two types of receivers: joint receivers, which address simultaneously both spatial and multiple-access interference; and separate receivers, addressing the two types of interference individually. This approach allows assessing the benefits of adding MIMO processing capabilities to existing multiuser single-input single-output systems. For both receiver types, we analyze solutions based on linear (matched filter, decorrelator, minimum mean-square error) and maximum-likelihood receivers. For all the receivers considered, we provide closed-form expressions (as expectations of given functions) of the resulting pairwise error probabilities. Performance results are obtained in terms of frame-error rate versus E/sub b//N/sub 0/, following two different approaches. An analytic approach using large-system asymptotic methods, whereby the system parameters (number of users and antennas, spreading gain) are assumed to grow to infinity with finite limiting ratios. A computer-simulation approach is used to illustrate the differences between asymptotic and simulation results.     

Turbo equalization: principles and new results

We study the turbo equalization approach to coded data transmission over channels with intersymbol interference. In the original system invented by Douillard et al. (1995), the data are protected by a convolutional code and the receiver consists of two trellis-based detectors, one for the channel (the equalizer) and one for the code (the decoder). It has been shown that iterating equalization and decoding tasks can yield tremendous improvements in bit error rate. We introduce new approaches to combining equalization based on linear filtering, with decoding.. Through simulation and analytical results, we show that the performance of the new approaches is similar to the trellis-based receiver, while providing large savings in computational complexity. Moreover, this paper provides an overview of the design alternatives for turbo equalization with given system parameters, such as the channel response or the signal-to-noise ratio     

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     

A simulation comparison of multiuser receivers for cellular CDMA

Multiuser detection has gained significant notoriety as a potential advanced enabling technology for the next generation of CDMA systems. Due to the limitations of the conventional correlation receiver, the capacity of a single cell using CDMA is limited by self-interference and is subject to the near-far problem. To overcome these drawbacks, several advanced receiver structures have been proposed. Unlike the conventional receiver which treats multiple access interference (MAI) as if it were AWGN, multiuser receivers treat MAI as additional information to aid in detection. Although each of the multiuser types have been the subject of much literature, there is little published work comparing all structures on the basis of common assumptions. We present a comparison of five of the most discussed receiver structures: the decorrelator, the minimum mean square error (MMSE) receiver, the multistage parallel interference cancellation receiver, the successive interference cancellation receiver, and the decorrelating decision feedback receiver. Comparisons are based on both theoretical analysis and simulation results, examining bit error rate (BER) performance in AWGN, Rayleigh fading, and near/far channels. Additionally, receiver structures are compared on the basis of computational complexity as well as robustness to code phase misalignment. Finally, we present simulation results for noncoherent architectures of the aforementioned receivers     

Analysis and design of interleavers for iterative multiuser receivers in coded CDMA systems

We deal with the design of interleavers in a coded code-division multiple-access (CDMA) scenario, where at the receiver an iterative turbo-like structure to perform multiuser detection is employed. The choice of the interleavers affects both the maximum-likelihood (ML) performance and the impact of the suboptimality of the iterative receiver. First, heuristic criteria of goodness for a set of interleavers, each assigned to a given active user, are introduced and motivated. One of these criteria is based on the intersection between the equivalent codes seen after the interleavers for each user pair. The design rules are valid for any kind of channel code. In particular, when the channel code used by every user is a terminated convolutional code, a very simple design rule, in the subset of congruential interleavers, is specified. The suitability of an interleaver set to iterative decoding is also treated. The analysis leads to a design rule which is shown to have great importance on the performance of a turbo-like receiver. Numerical results assess the validity of the derived design rules by showing that, for iterative multiuser receivers and reasonable block lengths, the suitability to iterative decoding is more important than the performance optimization.