Minimum Mean Square Error Multiuser Research Articles

Performance Analysis of Sliding Window Multiuser Detectors Used in Asynchronous Ds-cdma Systems (Dept.E)

In this paper, the sliding-window method is applied on both decorrelating and linear minimum mean-squared error (LMMSE) multiuser detectors. The analytical expressions for the error probability of those multiuser detectors (MUDs) are derived. The analysis is presented for asynchronous direct sequence code-division multiple access (DS-CDMA) in additive white Gaussian noise (AWGN) and multipath fading environment. The adopted detectors divide the received signal stream into processing windows and process them window by window. The effects of expanding the processing-window length on the error probabilities are investigated. The analysis shows that the error performance of the decorrelating detector is much better than that of the LMMSE detector when the power of the interfering users is larger than the desired user power. It is also shown that the performance of the presented detectors will be significantly improved with processing-window length up to four symbols.

Redundant Residue Number System Assisted Multicarrier Direct-Sequence Code-Division Dynamic Multiple Access for Cognitive Radios

A redundant residue number system (RRNS)-assisted multicarrier direct-sequence code-division dynamic multiple-access (MC/DS-CDDMA) scheme is proposed for application in cognitive radios (CRs). Taking the advantages of both multicarrier direct-sequence code-division multiple access and RRNS, the RRNS MC/DS-CDDMA has a low complexity for implementation and a high flexibility for reconfiguration and is robust to dynamic spectrums. Associated with the RRNS MC/DS-CDDMA, in this paper, the so-called receiver multiuser diversity aided multistage minimum mean-square error multiuser detector (RMD/MS-MMSE MUD) is considered for signal detection. Specifically, three types of RMD/MS-MMSE MUDs are proposed: Type-I.1, Type-II.1, and Type-I.2 RMD/MS-MMSE MUDs. In these MUD schemes, the Type-I.1 MUD carries out the joint detection of all the subcarrier signals using both the observations and the channel state information (CSI) of all the subcarriers. In the Type-I.2 and Type-II.1 RMD/MS-MMSE MUDs, the embedded MMSE-MUDs are implemented subcarrier by subcarrier independently. Furthermore, in the Type-I.2 RMD/MS-MMSE MUD, the autocorrelation matrices used by the MMSE-MUDs are free from CSI. Explicitly, both Type-II.1 and Type-I.2 RMD/MS-MMSE MUDs are suitable for operation in dynamic spectrum environments. Furthermore, our simulation results show that the preceding three types of RMD/MS-MMSE MUDs are capable of making the RRNS MC/DS-CDDMA systems achieve similar error and throughput performance. Owing to the foregoing merits, the RRNS MC/DS-CDDMA employing either Type-I.2 or Type-II.1 RMD/MS-MMSE MUD may be considered one of the highly promising dynamic multiple-access schemes for application in CR systems.

Analysis of Asynchronous Band-Limited DS-CDMA with MMSE Multiuser Detector over Generalized-k Fading Channels

In this paper, we investigate bit-error-rate (BER) performance of a minimum mean-squared error (MMSE) multiuser receiver for asynchronous band-limited direct- sequence code-division multiple-access (DS-CDMA) systems. We focus on the BER performance in the presence of multitone jamming (MTJ) over frequency-selective multipath fading channels. We consider the generalized-K fading model in our analysis, as it can model a large spectrum of fading-channel characteristics. We also analyze the effects of band- limited pulse shape on the BER performance of the system. Multipath diversity based on the maximal-ratio combining (MRC) scheme is employed to combat fading effects. Our analytical expressions are valid for arbitrary diversity levels and fading parameters. Spectrum raised cosine (SRC) and Beaulieu---Tan---Damen (BTD) pulse shapes are employed for numerical analysis. Numerical results show that in the presence of MTJ and under various channel conditions, the MMSE based receiver gives better BER performance than the one without it. Moreover, the system with BTD pulses outperforms the one with SRC pulses.

Error probability of direct sequence-code division multiple access systems with adaptive antenna minimum mean-square error multiuser receivers in Rayleigh-lognormal fading

In direct sequence-code division multiple access (DS-CDMA) cellular systems spreading codes, fading and positions of the users can be modelled as independent random variables and the corresponding multiuser interference (MUI) experienced by the base station is non-stationary. Here we evaluate in closed form the bit error probability for space-time linear minimum mean square error (MMSE) multiuser receivers for symbol-synchronous DS-CDMA system (bounds are provided for symbol-asynchronous system) by extending the known asymptotic results for random spreading sequences to non-stationary MUI. The analysis is based on the effective interference at the decision variable that is carried out to account for the non-stationary MUI that results from the multiuser beamforming that adapts each spatial filter to the randomness of the angle of arrivals of all the users. Propagation for each user is Rayleigh-lognormal faded channels as it is fairly general to model the imperfect power-control. The numerical validation proves that a simple geometrical model is accurate to evaluate the error probability for any arbitrary system loading.

Capacity and Error Performance of Reduced-Rank Transmitter Multiuser Preprocessing Based on Minimum Power Distortionless Response

In this contribution we first derive a transmitter multiuser preprocessing (TMP) scheme for a general multiuser multiple-input-multiple-output (MIMO) system based on the minimum power distortionless response (MPDR) criterion, which minimizes the power in the context of a given downlink mobile terminal (MT) under the distortionless condition. This optimization problem results in a solution, which has the same form as the minimum mean-square error (MMSE) multiuser detection (MUD). Hence, we then extend the well-known rank-reduction techniques in MMSE-MUD to the MPDR-TMP in order to mitigate the possible implementation problems of the MPDRTMP. In our study three classes of rank-reduction algorithms are considered, which are derived, respectively, based on the eigen-analysis methods of principal components (PC) and crossspectral metrics (CSMs) as well as on the Taylor polynomial approximation (TPA) approach, which does not depend on the eigen-analysis. In this contribution both the capacity and error performance of a downlink space-division multiple-access (SDMA) system is investigated, when either the full-rank or reduced-rank MPDR-TMP is invoked. From our study and simulation results, it can be shown that the MPDR-TMP scheme is highly efficient for achieving the capacity and for suppressing the multiuser interference (MUI). The reduced-rank techniques can be employed by the MPDR-TMP, so as to reduce its implementation complexity while achieving the near full-rank performance of the full-rank MPDR-TMP.

Low-Complexity MIMO Multiuser Receiver: A Joint Antenna Detection Scheme for Time-Varying Channels

This paper deals with the uplink of a wireless multiple-input multiple-output (MIMO) communication system based on multicarrier (MC) code division multiple access (CDMA). We focus on time-varying channels for users moving at vehicular speeds. The optimal maximum a posteriori (MAP) receiver for such a system is prohibitively complex and can be approximated using iterative linear minimum mean-square error (LMMSE) multiuser detection and parallel interference cancellation (PIC). For time-varying channels, two LMMSE filters for channel estimation and multiuser detection need to be computed at every time instant, making implementation in a real-time system difficult. We develop a novel low-complexity receiver that exploits the multiple antenna structure of the system and performs joint iterative multiuser detection and channel estimation. Our receiver algorithms are based on the Krylov subspace method, which solves a linear system with low complexity, trading accuracy for efficiency. The computational complexity of the channel estimator can be reduced by one order of magnitude. For multiuser detection, a PIC scheme in the user space, i.e., after the matched filter, allows simultaneous detection of all users as well as drastic computational complexity reduction by more than one order of magnitude.

MMSE Multiuser Receiver for Uniformly Quantized Synchronous CDMA Signals in AWGN Channels

We analyze and design the minimum mean-square error (MMSE) multiuser receiver for uniformly quantized synchronous code division multiple access (CDMA) signals in additive white Gaussian noise (AWGN) channels. The input-output relationship of the quantizer is represented by the gain-plus-additive-noise model. Based on this model, we derive the weight vector and the output signal-to-interference ratio (SIR) of the MMSE receiver. The effects of quantization on the MMSE receiver performance is characterized in a single parameter named equivalent noise variance which is a function of the sum of each active user's signal-to-noise ratio (SNR), processing gain, and the number of quantization levels. The optimal quantizer stepsize which maximizes the MMSE receiver output SNR is also determined. Simulation results validate the accuracy of our analysis.

Performance Analysis of Multiuser Detectors for Uplink Quasi-synchronous MC-CDMA Systems

This paper analyses and compares the average bit error rate (BER) of different multiuser detectors (MUD) in the uplink of a multicarrier code- division multiple access (MC-CDMA) system. In particular, maximum likelihood, zero-forcing, minimum mean-square error and interference cancellation-based multiuser detectors have been analysed for the special case of uncorrelated subcarriers. The derived BER expressions are based upon previous results on diversity combining and also on recent findings on multiple input multiple output (MIMO) architectures. The subcarrier correlation is considered in the context of physical parameters currently under discussion for future wireless systems to give an indication up to what extent the assumption of uncorrelated subcarrier fading is plausible.

On the performance optimization in multiuser MIMO systems

AbstractWe maximize the performance of multiple‐input multiple‐output (MIMO) multiple access channels (MAC) and broadcast channels (BC) under individual and sum power constraints. We observe that the performance metrics sum capacity and sum mean‐square error (MSE) belong to a general class of functions which are the trace of a matrix‐monotone function. The sum capacity if successive interference cancellation (SIC) is applied in the uplink or if Costa Precoding is applied in the downlink, or the normalised sum MSE if a multi‐user minimum mean‐square error (MMSE) receiver is applied at the base, belong to that class of performance functions. We use Löwner's representation of matrix monotone functions in order to characterise the optimum transmission strategies. Using the Karush‐Kuhn‐Tucker optimality conditions, we show that the mutual covariance matrix optimisation can be decomposed into power allocation and covariance matrix optimisation under individual power constraints. The covariance matrix optimisation under individual power constraints in turn can be decomposed into a kind of modified single‐user covariance matrix optimisation treating the other users as noise. The concrete structure of the single‐user program depends on the performance metric used. The proposed algorithms efficiently solve the multi‐user MIMO performance optimisation problem. These results generalise the results regarding the performance capacity optimisation recently reported for sum capacity optimisation and the results regarding the sum MSE optimisation. The optimal transmit strategy deconstructs into two independent parts: the coding and the signal processing part. The second part is adapted to the channel and performs multi‐user power control and transmit covariance matrix optimisation. Copyright © 2006 AEIT

An Adaptive MMOE-PIC Detector for Asynchronous DS-CDMA Communications

We propose a modified linear parallel interference cancelation (PIC) structure using the adaptive minimum mean output-energy (MMOE) algorithm for direct-sequence code-division multiple-access (DS-CDMA) systems. The complexity of the proposed receiver structure is shown to be linear in the number of users and hence, lower complexity than the centralized minimum mean-squared error (MMSE) multiuser detector. It is demonstrated that the proposed receiver structure can significantly reduce the long training period required by the standard adaptive MMOE receiver in near-far environments. Both numerical and theoretical results show that the proposed receiver performs close to the optimum MMSE receiver whereas the conventional adaptive MMOE detector suffers from high BER's due to the imperfect filter coefficients. Also our results show a three fold increase in the number of users when the MMOE-PIC is used relative to the conventional MMOE receiver. Furthermore, the transient behavior of the proposed MMOE-PIC receiver due to abrupt changes in the interference level is examined. It is shown that the proposed adaptive receiver offers much faster self recovery, with less signal-to-interference ratio (SIR) degradation, than the standard MMOE in sever near-far scenarios.

Asymptotically optimal nonlinear MMSE multiuser detection based on multivariate Gaussian approximation

In this paper, a class of nonlinear minimum mean-squared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multiple-access interference for large systems. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interference-cancellation scheme. Corresponding multiuser soft-input, soft-output detectors delivering extrinsic log-likelihood ratios are derived for application in iterative multiuser decoders. Finally, a large-system performance analysis is conducted for the simplified PDA, showing that the bit-error rate (BER) performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative large-system prediction. Numerical results demonstrate that for large systems, the BER is accurately predicted by the analysis and found to be close to optimal performance

Proportional Fair Space–Time Scheduling for Wireless Communications

We extend the proportional fair (PF) scheduling algorithm to systems with multiple antennas. There are K client users (each with a single antenna) and one base station (with n/sub R/ antennas). We focus on the reverse link of the system, and assume a slow-fading channel where clients are moving with pedestrian speed. Qualcomm's original PF scheduling algorithm satisfies the PF criteria only when the communication is constrained to one user at a time with no power waterfilling. However, the original PF algorithm does not generalize easily when we have n/sub R/ receive antennas at the base station. In this paper, we shall formulate the PF scheduling design as a convex optimization problem. One challenge is in the optimal power allocation over the multiantenna multiaccess capacity region, which is still an open problem. For practical consideration, we consider multiuser minimum mean-square error processing at the base station. To obtain first-order insight, we propose an asymptotically optimal PF scheduling solution. Using the proposed PF solution for a multiantenna base station, the system capacity is enhanced by exploiting the multiuser selection diversity, as well as the distributed multiple-input multiple-output configuration. It is found that the PF scheduler achieves a good balance between fairness and system capacity gain.

Robust blind multiuser detection based on the worst-case performance optimization of the MMSE receiver

The conventional minimum mean-square error (MMSE) multiuser receiver requires that each particular user transmits a sequence of training symbols known to the receiver and the receiver estimates the user signatures using this knowledge. However, in the presence of multiaccess interference (MAI) during the training period and/or in scenarios with short training sequence length, the signature estimates can be erroneous, and the performance of the MMSE multiuser receiver can degrade substantially. In this paper, we propose a new blind multiuser receiver that is robust against the effects of erroneously presumed desired user signature and short data length. Our approach is based on the explicit modeling of possible mismatches in the mean-square error cost function and worst-case performance optimization. We show that this approach leads to a multiuser receiver which uses the data covariance matrix with an adaptive diagonal loading . The proposed method has simple implementation with a computational complexity comparable with that of the fixed diagonal loading-based multiuser receiver. Simulation results show performance improvements achieved by our approach relative to existing techniques.

Subspace-Based Blind Multiuser Detection for Quasi-Synchronous MC-CDMA Systems

A subspace-based linear minimum mean-square error (MMSE) multiuser detector is proposed for quasi-synchronous multicarrier code-division multiple-access (MC-CDMA) systems. The proposed receiver is totally blind, i.e., it is both channel- and delay-independent and, unlike many subspace-based algorithms, requires only an upper bound (rather than the exact knowledge) of the channel order, without needing explicit delay estimation. The effectiveness of the proposed blind approach is tested by computer simulation results, which show that it assures satisfactory performances in severe near-far scenarios, while exhibiting a lower computational complexity in comparison with existing subspace-based methods.

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.

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.

Spectral Efficiency and Cutoff Rate of Random Spreading BICM-Based CDMA Signals With MMSE Multiuser Receivers

We analyze the spectral efficiency and cutoff rate of random spreading bit-interleaved coded-modulation based synchronous code-division multiple-access signals with minimum mean-square error multiuser receivers. Both additive white Gaussian noise and frequency nonselective Rayleigh fading channels are considered. The spectral efficiency and cutoff rate are characterized as functions of the system load, modulation schemes, and signal-to-noise ratio.

Transmission strategies for the MIMO mac with MMSE receiver: average MSE optimization and achievable individual MSE region

In this work, we study the multiuser multiple-input multiple-output (MIMO) multiple access channel (MAC) under the assumption that the base station performs linear multiuser minimum mean-square error (MMSE) detection. We derive the average normalized MSE and the individual MSEs of users. At first, we optimize the average normalized MSE with respect to the transmit covariance matrices of the users. Next, adaptive power allocation is applied to further minimize the average normalized MSE. This leads to the general average normalized MSE optimization under a sum power constraint. We analyze the optimization problems and their connections by their Karush-Kuhn-Tucker conditions. The covariance matrix optimization is solved by iteratively single-user average MSE optimization in which the interference is treated as noise. We develop an iterative algorithm that performs power allocation and covariance matrix optimization. In addition to this, we study the achievable MSE region. We show that the MSE region is convex for the two-user MIMO case. Furthermore, we characterize the optimum power allocation among the users with regard to the single-user range. We show that the user with the maximum singular value of its channel matrix is the first supported user. For low SNR values, the optimal strategy is to have the best user transmitting only. In addition, we derive the individual MSE using single-user MMSE detectors and study the fulfillment of MSE requirements.

A two-layer spreading code scheme for dual-rate ds-cdma systems

This letter considers multiuser detection in variable-spreading-length multi-rate direct-sequence code-division multiple-access systems. A two-layer spreading (TLS) code scheme is proposed which facilitates the low-complexity adaptive implementation of linear minimum mean-square error multiuser receivers in a dual-rate system. It is demonstrated via large system analysis and simulation that imposing a TLS structure does not incur loss in terms of the output signal-to-interference ratio performance.

Space-Time Coded MC-CDMA: Blind Channel Estimation, Identifiability, and Receiver Design

Integrating the strengths of multicarrier (MC) modulation and code division multiple access (CDMA), MC-CDMA systems are of great interest for future broadband transmissions. This paper considers the problem of channel identification and signal combining/detection schemes for MC-CDMA systems equipped with multiple transmit antennas and space-time (ST) coding. In particular, a subspace-based blind channel identification algorithm is presented. Identifiability conditions are examined and specified which guarantee unique and perfect (up to a scalar) channel estimation when knowledge of the noise subspace is available. Several popular single-user based signal combining schemes, namely the maximum ratio combining (MRC) and the equal gain combining (EGC), which are often utilized in conventional single-transmit-antenna-based MC-CDMA systems, are extended to the current ST-coded MC-CDMA (STC-MC-CDMA) system to perform joint combining and decoding. In addition, a linear multiuser minimum mean square error (MMSE) detection scheme is also presented, which is shown to outperform the MRC and EGC at some increased computational complexity. Numerical examples are presented to evaluate and compare the proposed channel identification and signal detection/combining techniques.