Asymptotic analysis of the MMSE multiuser detector fornonorthogonal multipulse modulation

We develop the minimum mean-squared-error (MMSE) multiuser detector for nonorthogonal multipulse modulation over the noncoherent additive white Gaussian noise channel. We analyze the asymptotic performance of the detector and show that, unlike the case of linear modulation, the MMSE detector does not generally approach the generalized maximum-likelihood (GML) detection rule as the noise power vanishes. It does, however, approach a detector which nulls out the multiaccess interference. This detector is termed the multipulse decorrelating detector due to its similarity to the linear decorrelating detector. The probability of error for this detector is derived and used to find the asymptotic multiuser efficiencies of both the multipulse decorrelating detector and the MMSE detector. It is shown that for noncoherent binary signaling, in which the multipulse modulation is two-dimensional, the multipulse decorrelating detector is superior to the GML detector asymptotically. This result does not generalize to larger dimensionality signal sets     

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     

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.     

Performance of linear MMSE multiuser detection combined with a standard IS-95 uplink

Current implementation of IS-95 based systems is performance limited due to the use of a “conventional” detection scheme, which is susceptive to inter-user interference. We focus on the uplink, and try to examine the performance enhancement achieved by a suboptimal linear multiuser MMSE pre-filter, applied in front of the “standard” detection mechanism. We demonstrate the limitations of this relatively simple approach, and the constellations in which it may show improved performance. This revised version was published online in July 2006 with corrections to the Cover Date.     

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     

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.     

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     

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.     

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     

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。     

An adaptive multiuser detector with joint amplitude and delayestimation

A multiuser detector is developed in which the delays and amplitudes of the incoming waveforms are estimated recursively. The algorithm is an extension of the symbol-by-symbol detector of Abend and Fritchman, originally derived for intersymbol interference (ISI) channels, to the multiuser application. In order to make the multiuser detector adaptive, the likelihoods in the symbol-by-symbol metric update are approximated using a set of extended Kalman filter (EKF) innovations. The EKF's provide, in addition to the likelihoods, joint estimates of the signal delays and amplitudes. The resulting algorithm is quite complex, due to the large number of possible composite symbols corresponding to the multiple users. However, it is shown that the likelihood computations and EKF updates can be expressed it terms of a set of cross-correlation functions, which need only be computed for a subset of the possible symbols. The cross-correlator outputs are updated at the bit rate, and thus the EKF and metric update computations need be performed only at a function of the spread-spectrum chip rate. A metric pruning technique is proposed that further reduces the number of EKF delay/amplitude estimators required. Finally, an important sampling simulation strategy is used to obtain bit-error rate estimates for the adaptive multiuser detector     

结合功率控制的时-空多用户检测器

针对CDMA系统中抗干扰技术,提出一种结合多用户检测、波束成形和功率控制的算法,对接收信号在时域和空间上进行联合处理,能大大抑制干扰,提高系统容量。     

Decorrelator-based neighbour-searching multiuser detector in CDMAsystems

A new decorrelator-based neighbour-searching (DENS) multiuser detector is proposed for synchronous CDMA systems. It is shown that the DENS multiuser detector with neighbour-searching radius r=2 can achieve good bit-error-rate performance close to that of an optimum multiuser-detector     

Suboptimal resource allocation with MMSE detector for grouped MC-CDMA systems

This article puts forward two novel user-grouping algorithms for grouped multi-carrier （MC）-code division multiple access （CDMA） systems. As is well known, the adaptive assignment for user-grouping plays an important role for link quality of multi-access transmissions. In the study, the capacity-maximizing problem of user-grouping is formulated. By using the Kuhn-Tucker condition, the optimal criterion is deduced and found to have a similar form with signal to noise plus interference （SINR）. However SINR includes the signal power that can only be determined after user-grouping. Therefore the optimal criterion will lead to an impractical application. To deal with it, the user＇s equivalent SINR for minimum mean square error （MMSE） detector is proposed and served as a suboptimal assignment criterion, based on which two kinds of user-grouping algorithms are proposed. In the algorithms, only partial channel information is needed at the base station, which saves a large part of the bandwidth occupied by feedback information. Computer simulations have evaluated an excellent performance of the proposed algorithms at both link quality and data rate. Meanwhile, the proposed algorithms have lower implementation complexity for practical reality.     

Blind adaptive multiuser detection based on a constrained MMSE criterion

The proposed blind adaptive multiuser detector utilizes the signature waveform and time information of the desired user. With each received sample vector, the proposed algorithm updates the detector and gives the symbol estimate in the current time slot. Such property facilitates it to track time-varying channels.     

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。