Performance of the MMSE multiuser detector with equicorrelated signatures

In this letter, we analyze the performance of the minimum mean-square error (MMSE) detector for a code-division multiple-access system employing binary phase-shift keying. The performance is measured in terms of the probability distribution and the average number of correctly decoded users. We consider the case of equipower users having equicorrelated signature waveforms. The distribution of the number of correctly decoded users is expressed as an integral over sum of products of Gaussian Q-functions. From it, a closed-form expression for the average number of correctly decoded users is derived.     

Blind multiuser MMSE detector for CDMA signals in ISI channels

A technique is introduced that allows the blind and direct estimation of an optimal, in the minimum mean-squared error sense, linear multiuser receiver for direct-sequence code-division multiple-access signals. We consider the case of an asynchronous multiple access channel in the presence of possibly large intersymbol-interference. Our approach does not require channel estimation and uses the knowledge of the code for the user of interest only, Unlike other comparable techniques, this method converges to the true optimum receiver as the sample size increases, regardless of signal-to-noise ratio     

非线性调制下MMSE盲自适应多用户接收机

主要介绍三种面向非正交多脉冲调制(NMM)系统的非相干最小均方误差(MMSE)多用户检测器,它们均采用MMSE预滤波器(per-filter),但分别满足三种不同的非相干判决准则。其中最简单的判决准则是最大(MM)准则,另外两种则需要考虑MMSE滤波后的残余多用户干扰(MAI)的二阶统计量。然后介绍一种基于随机估计方法的盲自适应算法。最后对这三种判决准则进行性能分析。     

Performance analysis of MC-CDMA cellular systems employing MMSE multiuser detector in presence of own-cell and co-cell interference

In this work, it is analyzed the uplink performance of MC-CDMA cellular systems in order to show that a MMSE multiuser detector can mitigate not only the own-cell interference, but also the co-cell interference. For the analysis, it is also considered a linear antenna array at the base station. The channel includes additive white Gaussian noise, exponential path-loss and slow frequency-selective Rayleigh fading. First, the interference in the cellular system is analyzed. Then, approximate expressions to evaluate the signal-to-interference ratio (SIR) are derived. Also, expressions to evaluate the bit error rate (BER) both for BPSK and M-QAM modulations are obtained. Monte Carlo simulations verify the tightness of the expressions. The results show that when we include the co-cell interference statistics in the MMSE detector design, the effects of this interference can be mitigated. Also, it is observed that the system can be overloaded when the number of antennas in the array is increased while the mean BER maintains reasonable values. Finally, with an asymptotic analysis of the BER expressions, the BER reduction with the MMSE multiuser detector when compared with the zero-forcing multiuser detector is obtained. This BER reduction has not been previously obtained in the literature.     

A novel iterative multiuser detector for complex modulation schemes

A novel multiuser detector for direct sequence code division multiple access is proposed. The receiver performs iterated soft decision interference cancellation (ISDIC) based on multiuser interference suppression filters designed for minimization of the mean-square error. Assuming a complex modulation format, we show that the multiuser interference becomes rotationally variant in the course of the iterations. Regarding this rotational variance in the design of the multiuser interference suppression filter, the presented iterative multiuser detector achieves significant performance gains compared with conventional ISDIC employing a standard minimum mean-squared error filter which is optimum only for rotationally invariant multiuser interference     

Performance analysis of an improved MMSE multiuser receiver formismatched delay channels

Motivated by the fact that time delays in a practical direct-sequence code-division multiple-access (DS-CDMA) system can never be perfectly estimated, an improved minimum-mean squared-error (MMSE)-based receiver is proposed and analyzed. Via the simple assumption of a probability distribution for the delay estimation errors, the proposed receiver can achieve a performance superior to that of the conventional MMSE (CMMSE) receiver. The performances of this improved receiver and the CMMSE receiver are compared in terms of the mean squared error (MSE), probability of error, and asymptotic multiuser efficiency (AME). As the original definition of AME does not consider mismatched channels, the behavior of three single-user receivers bearing imperfect delay estimation is also investigated. These single-user receivers are employed to define a more appropriate AME. Finally, an efficient update mechanism to accommodate dynamic channel statistics, and thus practical implementation, is proposed     

Probability of error in MMSE multiuser detection

The performance analysis of the minimum-mean-square-error (MMSE) linear multiuser detector is considered in an environment of nonorthogonal signaling and additive white Gaussian noise. In particular, the behavior of the multiple-access interference (MAI) at the output of the MMSE detector is examined under various asymptotic conditions, including: large signal-to-noise ratio; large near-far ratios; and large numbers of users. These results suggest that the MAI-plus-noise contending with the demodulation of a desired user is approximately Gaussian in many cases of interest. For the particular case of two users, it is shown that the maximum divergence between the output MAI-plus-noise and a Gaussian distribution having the same mean and variance is quite small in most cases of interest. It is further proved in this two-user case that the probability of error of the MMSE detector is better than that of the decorrelating linear detector for all values of normalized crosscorrelations not greater than ½√(2+√3)≅0.9659     

Adaptive MMSE maximum likelihood CDMA multiuser detection

The well-known code division multiple access maximum likelihood receiver (MF-ML) uses a bank of matched filters as a generator of sufficient statistics for maximum likelihood detection of users transmitted symbols. In this paper, the bank of matched filters is replaced by a bank of adaptive minimum mean squared error (MMSE) filters as the generator of sufficient statistics. This formal replacement of the MF bank by the adaptive MMSE filter bank has significant conceptual consequences and provides improvement by several performance measures. The adaptive MMSE-ML receiver's digital implementation is significantly computationally simplified. The advantages of the proposed adaptive MMSE-ML receiver over the MF-ML receiver are: (1) ability to perform joint synchronization, channel parameter estimation, and signal detection where the signal is sent over an unknown, slowly time-varying, frequency-selective multipath fading channel; (2) increased information capacity in a multicellular environment; and (3) significantly improved bit error rate (BER) performance in a multicellular mobile communications environment. The information capacity and the BER of the proposed MMSE-ML receiver are analyzed. Numerical results showing the BER performance of the MMSE-ML receiver in a multipath channel environment are presented     

Asymptotic analysis of optimum and suboptimum CDMA downlink MMSE receivers

In this paper, we investigate the performance of two linear receivers for code-division multiple-access (CDMA) downlink transmissions over frequency-selective channels, the users having possibly different powers. The optimum minimum mean-square error (MMSE) receiver is first considered. Because this receiver requires the knowledge of the code vectors attributed to all the users within the cell when these vectors are time varying, its use may be unrealistic in the forward link. A classical suboptimum receiver, consisting in a chip rate equalizer followed by a despreading with the code of the user of interest, is therefore studied and compared to the optimum MMSE receiver. Performance of both receivers is assessed through the signal-to-interference-plus-noise ratio (SINR) at their outputs. The analytical expressions of these SINRs depend in a rather nonexplicit way on the codes allocated to the users of the cell, and are therefore not informative. This difficulty is dealt with by modeling the users code matrix by a random matrix. Because the code matrices used in the forward link are usually isometric, the code matrix is assumed to be extracted from a Haar-distributed random unitary matrix. The behavior of the SINRs is studied when the spreading factor and the number of users converge to /spl infin/ at the same rate. Using certain results of the free probability theory, we establish the fact that the SINRs converge almost surely toward quantities that depend only on the complex amplitudes of propagation channel paths. We then use the expressions of these SINR limits to discuss the influence of the various parameters on the performance of the receivers.     

A new family of MMSE multiuser receivers for interferencesuppression in DS/CDMA systems employing BPSK modulation

We deal with interference suppression in asynchronous direct-sequence code-division multiple-access (CDMA) systems employing binary phase-shift keying modulation. Such an interference may arise from other users of the network, from external low-rate systems, as well as from a CDMA network coexisting with the primary network to form a dual-rate network. We derive, for all of these cases, a new family of minimum mean-square-error detectors, which differ from their conventional counterparts in that they minimize a modified cost function. Since the resulting structure is not implementable with acceptable complexity, we also propose some suboptimum systems. The statistical analysis reveals that both the optimum and the suboptimum receivers are near-far resistant, not only with respect to the other users, but also with respect to the external interference. We also present a blind and a recursive least squares-based, decision-directed implementation of the receivers wherein only the signature and the timing of the user to be decoded and the signaling time and the frequency offset of the external interferer are assumed known. Finally, computer simulations show that the proposed adaptive algorithm outperforms the classical decision-directed RLS algorithm     

Noncoherent MMSE multiuser receivers and their blind adaptiveimplementations

Three noncoherent minimum mean-squared error (NMSE)-based multiuser receivers are proposed for multipulse modulation. These receivers have a common MMSE prefilter and are followed by one of three phase-independent decision rules. The simplest decision rule selects the maximum magnitude of the MMSE filter outputs, and the other two account for the second-order statistics of the residual multiple-access interference that remains after MMSE filtering. Blind adaptive algorithms are then proposed for the three noncoherent MMSE receivers. The common adaptive algorithm for the MMSE prefilter, which is based on the stochastic approximation method, is shown to converge in the mean-squared error sense to the nonblind NMSE prefilter. Our convergence analysis yields new insight into the tradeoff between the rate of convergence and the residual mean-squared error. The noncoherent blind receivers obtained here do not require the knowledge of the received signals of any of the interfering users, and are hence well-suited for distributed implementation in cellular wireless networks or in communication systems that must operate in noncooperative environments     

Asymptotic analysis of blind multiuser detection with blind channel estimation

The analytical performance of the subspace-based blind linear minimum mean-square error (MMSE) multiuser detection algorithm in general multipath multi-antenna code-division multiple-access (CDMA) systems is investigated. In blind multiuser detection, the linear MMSE detector of a given user is estimated from the received signals, based on the knowledge of only the spreading sequence of that user. Typically, the channel of that user must be estimated first, based on the orthogonality between the signal and noise subspaces. An asymptotic limit theorem for the estimate of the blind linear detector (when the received signal sample size is large) is obtained, based on which approximate expressions of the average output signal-to-inference plus noise ratios (SINRs) and bit error rates (BERs) for both binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulations are given. Corresponding results for group-blind multiuser detectors are also obtained. Examples are provided to demonstrate the excellent match between the theory developed in this paper and the simulation results.     

Robust blind adaptive multiuser detector

A modified version of the constrained mean output energy (CMOE) detector, called a multiuser detector (MUD), is presented. With estimation of the channel noise variance, a significant reduction in performance can be avoided when signature mismatch exits, which is one of main problems of the CMOE detector. Numerical results are presented which confirm the validity of the method     

MMSE multiuser downlink multiple antenna transmission for CDMA systems

In this paper, we propose a new downlink transmit antenna processing (TAP) technique for code division multiple access (CDMA) equipped with multiple transmit antennas. In order to find the weight vectors for downlink signals, a minimum mean square error (MMSE) performance criterion is used. Since the multiuser interference is taken into account in the calculation of the weighting vectors for TAP, the proposed method is a multiuser downlink TAP method. It is assumed that the downlink channels are known by the downlink TAP. For given channel conditions, the optimal weight vectors are found with a closed-form expression under both flat and frequency-selective fading channel assumptions.     

Asymptotic multiuser efficiencies for decision-directed multiuserdetectors

The asymptotic multiuser efficiencies (AMEs) are derived for various classes of decision-directed multiuser detectors, including multistage detectors, and decision-feedback detectors. Novel classes of soft-decision multistage detectors are proposed and analyzed. Each class is specified in part by a soft-decision nonlinearity, such as a symmetric quantizer or a linear clipper. Closed-form expressions for two-user AMEs are derived for soft-decision two-stage detectors and can be used as a design criterion to optimize the soft-decision nonlinearities. For a special case of two synchronous users, the soft-decision two-stage detector using an optimized linear clipper with either conventional or decorrelated tentative decisions is shown to achieve optimum AME. Upper and lower bounds on the AME are obtained for decision-feedback detectors using either conventional or decorrelated tentative decisions. It is demonstrated that decision-directed multiuser detectors with conventional tentative decisions have low near-far resistance compared to those with decorrelated tentative decisions     

Output MAI distributions of linear MMSE multiuser receivers inDS-CDMA systems

Multiple-access interference (MAI) in a code-division multiple-access (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. We study the behavior of the output MAI of the minimum mean-square error (MMSE) receiver employed in the uplink of a direct-sequence (DS)-CDMA system. We focus on imperfect power-controlled systems with random spreading, and establish that in a synchronous system (1) the output MAI of the MMSE receiver is asymptotically Gaussian, and (2) for almost every realization of the signatures and received powers, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the output interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE receiver is robust to the randomness of the signatures and received powers. The Gaussianity justifies the use of single-user Gaussian codes for CDMA systems with linear MMSE receivers, and implies that from the viewpoints of detection and channel capacity, signal-to-interference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA system     

Performance analysis of space-time MMSE multiuser detection for coded DS-CDMA systems in multipath fading channels

This paper investigates the use of convolutional coding in space-time minimum mean-square-error (MMSE) multiuser-based receivers over asynchronous multipath Rayleigh fading channels. We focus on the performance gain attained through error control coding when used with binary-phase-shift-keyed modulation (BPSK) and multiuser access based on direct sequence-code-division multiple access (DS-CDMA). In our analysis, we derive an approximation for the uncoded probability of bit-error in multipath fading channels. This bit-error rate (BER) approximation is shown to be very accurate when compared to the exact performance. For a convolutionally coded system, we obtain a closed form expression for the bit-error rate upper bound. This error bound is noted to be tight as the number of quantization levels increased beyond eight. Using our theoretical results, we obtain an estimate for the achieved user-capacity that accrues due to error control coding. It is found that using convolutional coding with 3-bit soft-decision decoding, a user-capacity gain as much as 300% can easily be achieved when complete fading state information plus ideal channel interleaving are assumed.     

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.     

基于干扰空间的盲自适应多用户检测器

在现有盲自适应多用户检测技术基础上，本文提出一种更具有实际应用价值的基于干扰空间线性MMSE盲自适应多用户检测器及其相应的基于干扰自相关矩阵C1跟踪算法。数学分析和仿真结果表明：与现有盲自适应多用户检测器相比，该检测器具有更低的实现复杂度、更快的跟踪速度和更强的健壮性。     

Adaptive multiuser CDMA detector for asynchronous AWGNchannels-steady state and transient analysis

A two-stage adaptive multiuser detector in an additive white Gaussian noise code-division multiple-access channel is proposed and analyzed. Its first stage is an asynchronous one-shot decorrelator which in terms of computational complexity only requires inversion of K symmetric K×K matrices for all K users. In addition, the K inversions can be done in parallel, and the computed results for one user can be reused by all other users as well, resulting in a latency of only one bit, same as its synchronous counterpart. The decorrelated tentative decisions are utilized to estimate and subtract multiple-access interference in the second stage. Another novel feature of the detector is the adaptive manner in which the multiple-access interference estimates are formed, which renders prior estimation of the received signal amplitudes and the use of training sequences unnecessary. Adaptation algorithms considered include steepest descent (as well as its stochastic version), and a recursive least squares-type algorithm that offers a faster transient response and better error performance. Sufficient conditions for the receiver to achieve convergence are derived. The detector is near-far resistant, and is shown to provide substantial steady-state error performance improvement over the conventional and decorrelating detector, particularly in the presence of strong interfering signals