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.     

Large-system performance analysis of blind and group-blindmultiuser receivers

We present a large-system performance analysis of blind and group-blind multiuser detection methods. In these methods, the receivers are estimated based on the received signal samples. In particular, we assume binary random spreading, and let the spreading gain N, the number of users K, and the number of received signal samples M all go to infinity, while keeping the ratios K/N and M/N fixed. We characterize the asymptotic performance of the direct-matrix inversion (DMI) blind linear minimum mean-square error (MMSE) receiver, the subspace blind linear MMSE receiver, and the group-blind linear hybrid receiver. We first derive the asymptotic average output signal-to-interference-plus-noise ratio (SINR) for each of these receivers. Our results reveal an interesting "saturation" phenomenon: The output SINR of each of these receivers converges to a finite limit as the signal-to-noise ratio (SNR) of the desired user increases, which is in stark contrast to the fact that the output SINR achieved by the exact linear MMSE receiver can get arbitrarily large. This indicates that the capacity of a wireless system with blind or group-blind multiuser receivers is not only interference-limited, but also estimation-error limited. We then show that for both the blind and group-blind receivers, the output residual interference has an asymptotic Gaussian distribution, independent of the realizations of the spreading sequences. The Gaussianity indicates that in a large system, the bit-error rate (BER) is related to the SINR simply through the Q function     

A low complexity reduced-rank MMSE receiver for DS/CDMA communications

The minimum mean squared error (MMSE) receiver is a linear filter which can achieve optimal near-far resistance in direct-sequence code-division multiple-access communications. However, one of the main problems of this receiver is the required number of filter taps, which is typically large. This is especially true in systems with a large processing gain in which case the receiver's computation burden becomes very high. As a result, methods for reducing the complexity of the MMSE receiver have been of great interest in recent years. We propose an efficient partitioned MMSE receiver based on a classification algorithm. It is shown that the computational complexity (in terms of the filter taps) of the proposed receiver can be reduced significantly while good performance is maintained. Based on the special structure of our proposed receiver, we also propose a release-merge adaptive partition algorithm which can update the partition and the receiver's coefficients simultaneously. In particular, it is demonstrated that the proposed receiver can perform much better than previously proposed reduced-rank MMSE receivers, such as the partial despreading MMSE receiver and the cyclically shifted filter bank receiver, with even a smaller number of taps.     

Hybrid SNR-Adaptive Multiuser Detectors for SDMA-OFDM Systems

Multiuser detection (MUD) and channel estimation techniques in space-division multiple-access aided orthogonal frequency-division multiplexing systems recently has received intensive interest in receiver design technologies. The maximum likelihood (ML) MUD that provides optimal performance has the cost of a dramatically increased computational complexity. The minimum mean-squared error (MMSE) MUD exhibits poor performance, although it achieves lower computational complexity. With almost the same complexity, an MMSE with successive interference cancellation (SIC) scheme achieves a better bit error rate performance than a linear MMSE multiuser detector. In this paper, hybrid ML-MMSE with SIC adaptive multiuser detection based on the joint channel estimation method is suggested for signal detection. The simulation results show that the proposed method achieves good performance close to the optimal ML performance at low SNR values and a low computational complexity at high SNR values.     

A Blind LCMV-Based CFO Estimation for MC-CDMA Systems Over Multipath Fading Channels

This paper proposes a blind carrier frequency offset (CFO) estimation for multi-carrier code-division multiple access systems over multipath fading channels. The scheme first determines a preliminary CFO estimate by maximizing the total output power of a set of correlators, which is constructed with the linearly constrained minimum variance optimization. A fine CFO estimate is subsequently found by solving the well-developed quadratic cost function. Finally, by using the frequency-compensated data, a subspace minimum output energy (MOE) receiver is formed to provide the maximum output signal-to-interference-plus-noise ratio. Numerical results demonstrate that, with the proposed CFO estimation as a stage proceed, the subspace MOE receiver can achieve nearly the performance of the optimal minimum mean square error receiver.     

Performance Analysis of Blind Adaptive MOE Multiuser Receivers Using Inverse QRD-RLS Algorithm

The inverse QR (IQRD) recursive least-squares (RLS) algorithm (IQRD-RLS) is very popular because it has good numerical stability and can be mapped onto COordinate Rotation DIgital Computer (CORDIC) processor-based systolic arrays, which are suitable for very large-scale integrated circuits (VLSI) architecture and real-time applications. In this paper, the blind optimal minimum output energy (MOE) detector which is developed for multiuser detection (MUD) in direct-sequence code-division multiple-access (DS-CDMA) systems is implemented using the linearly constrained IQRD-RLS algorithm. Specifically, the max/min approach is combined with subspace tracking for producing the optimal MOE multiuser detector. A new fast subspace tracking algorithm based on Lagrange multiplier methodology and the IQRD-RLS algorithm is developed. A comparative analysis among the recently emerged channel-estimation techniques is conducted using the IQRD-RLS algorithm. The corresponding robust MOE receivers at low SNR are implemented using the IQRD method, and their performances are assessed in terms of SINR, BER, and computational complexity. A robust multiuser receiver is developed by adding a quadratic inequality constraint to the optimal max/min MOE detector. The feasibility of systolic array implementation of the IQRD-based optimal MOE detector is explored. Several simulation experiments are conducted in a severe near–far environment to analyze the IQRD-based receivers and the subspace tracking algorithms.      

Asymptotic Performance Analysis of Blind Minimum Output Energy Receivers for Large DS-CDMA Systems

The random matrix theory is used to analyze the asymptotic performance of the blind minimum output energy (MOE) receiver in direct-sequence code division multiple-access (DS-CDMA) systems in the presence of unknown multipath channel under the condition that the spreading factor and the number of users go to infinity with the same rate. As a special case, the asymptotic properties of the blind Capon receiver are also studied and the conditions of convergence of the signal-to-interference-plus-noise ratio (SINR) of this receiver to that of the optimal minimum-mean-square error (MMSE) receiver are discussed. In particular, it is shown that the SINR performances of the Capon and MMSE receivers are nearly identical in the uplink scenario, while the performance of the Capon receiver may be considerably inferior to that of the MMSE receiver in the downlink transmission case. As the performance of the Capon receiver is closely related to the performance of the Capon channel estimator, the asymptotic properties of the latter estimator are also studied and the conditions of convergence of the Capon channel estimate to a scaled version of the channel vector of the user-of-interest are obtained.     

A Fuzzy MOE Receiver for Uplink MC-CDMA Systems with Carrier Frequency Offset over Multipath Fading Channels

A novel fuzzy minimum output energy (MOE) detector is proposed for uplink multicarrier CDMA (MC-CDMA) systems with carrier frequency offset (CFO) over multipath fading channels. The proposed receiver involves the following stages. First, the fuzzy CFO constrained MOE detector after coarse CFO estimation is proposed to suppress multiple access interference and combat the degradation problem of the conventional MOE detector caused by the CFO effect. Next, using the signal subspace projection technique, the proposed detector can further reduce the enhanced noise due to the fuzzy CFO constrained detector. Finally, the output data obtained from these detectors are coherently combined to offer multipath diversity gain in accordance with the maximum ratio combining criterion. Furthermore, the proposed single input single output (SISO) robust detector can be easily extended for a multiple input multiple output (MIMO) MC-CDMA system with a high rate of performance. Simulation results show that the proposed SISO detector, which offers a similar performance as the optimal detector, can provide robustness against CFO and outperform the conventional detectors. The proposed MIMO detector with spatial multiplexing gain also exhibits excellent performance.     

A subspace approach to adaptive narrow-band interferencesuppression in DSSS

We address the problem of suppression of a digital narrow-band interferer in direct-sequence spread spectrum (DSSS) communications. We focus on the adaptive suppression method proposed by Honig, Madhow and Verdti (see IEEE Trans. Inform. Theory, vol.41, p.944-960, 1995) for wide-band interference, applying it to a narrow-band interferer. We identify the eigenspaces of the system dynamics to analyze the convergence of the adaptive version of the minimum mean square error (MMSE) algorithm for this application. Using this subspace approach we are able to: (1) significantly decrease the convergence times via a new constraint on the step size in adaptation; (2) introduce a simple parameterization of the mean output energy (MOE) and signal-to-interference ratio (SIR) to compare performance of various receivers; and (3) identify modes of operation where the algorithm will cease to effectively cancel interference. We propose a new adaptive receiver that avoids the convergence anomalies identified, while capitalizing on the new step size for faster convergence. Simulation results to support theoretical results are presented     

A constrained MMSE receiver for DS/CDMA systems in fading channels

The convergence problem of minimum mean square-error (MMSE) receivers is discussed, and to overcome the problem, a constrained MMSE receiver is proposed. In addition, we propose the orthogonal decomposition-based least mean square algorithm to implement the constrained MMSE receiver adaptively. Through computer simulations, it is shown that the proposed receiver provides significant performance improvement in the bit-error rate over the conventional matched filter receiver and currently available MMSE receivers.     

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.     

Asymptotic Performance of Linear Receivers in MIMO Fading Channels

Linear receivers are an attractive low-complexity alternative to optimal processing for multiple-antenna multiple-input multiple-output (MIMO) communications. In this paper, we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-signal-to noise-ratio (SNR) regime in terms of the diversity-multiplexing tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas.As far as the DMT is concerned, we report a negative result: we show that both linear zero-forcing (ZF) and linear minimum mean- square error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and deAcircnot coding is performed across the antennas. We also provide an apAcircnot proximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and nonasymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of an MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear reAcircnot ceiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.     

Performance analysis of an over-sampling multi-channel equalization for a multi-band uwb system

This paper proposes an over-sampling multi-channel equalizer per sub-band for multi-band ultra-wideband (UWB) system and compares its performance with conventional RAKE receiver when operating in practical UWB channel models. Three transmission modes have been considered, and inter-symbol interference (ISI) is found to be inherent to certain transmission modes due to the large UWB channel delay spreads. Through detailed analytical and simulation studies, the proposed over-sampled minimum mean square error (MMSE) equalizer is shown to be able to handle ISI under any channel conditions or transmission modes, with an acceptable BER. In addition, the rich multipath diversity of the UWB channels is harnessed by the over-sampling scheme, for output SNR improvement. Over-sampling is done in the expense of an increase in system complexity     

Equalization for discrete multitone transceivers to maximize bitrate

In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces the intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Current TEQ design methods such as the minimum mean-squared error (MMSE), maximum shortening SNR (MSSNR), and maximum geometric SNR (MGSNR) do not directly maximize bit rate. We develop two TEQ design methods to maximize the bit rate. First, we partition an equalized multicarrier channel into its equivalent signal, noise, and ISI paths to develop a new subchannel SNR definition. Then, we derive a nonlinear function of TEQ taps that measures the bit rate, which the proposed maximum bit rate (MBR) method optimizes. We also propose a minimum-ISI method that generalizes the MSSNR method by weighting the ISI in the frequency domain to obtain higher performance. The minimum-ISI method is amenable to real-time implementation on a fixed-point digital signal processor. Based on simulations using eight different carrier-serving-area loop channels, (1) the proposed methods yield higher bit rates than MMSE, MGSNR, and MSSNR methods; (2) the proposed methods give three-tap TEQs with higher bit rates than 17-tap MMSE, MGSNR, and MSSNR TEQs; (3) the proposed MBR method achieves the channel capacity (as computed by the matched filter bound using the proposed subchannel SNR model) with a five-tap TEQ; and (4) the proposed minimum-ISI method achieves the bit rate of the optimal MBR method     

异步垂直空时结构中的功率扩展技术

在平坦衰落信道中,针对异步垂直贝尔实验室空时结构(V-BLAST)信号模型下,现有线性最佳检测算法误码率性能随信噪比提高改善缓慢的问题,提出一种基于功率扩展的迭代检测方法:发射端用功率扩展将发射信号扩展到整个空时信号块上,接收端进行基于功率扩展的迭代检测。同时,分析了所提方法在每次迭代检测后的误码率性能。分析和仿真验证了误码率性能的改进。在4发4收场景下,误码率为10-5时,相比于线性最优最小均方误差(MMSE)方法,获得了约6dB信噪比增益。     

Pilot-based estimation of time-varying multipath channels forcoherent CDMA receivers

Reliable coherent wireless communication requires accurate estimation of the time-varying multipath channel. This paper addresses two issues in the context of direct-sequence code-division multiple access (CDMA) systems: (i) linear minimum-mean-squared-error (MMSE) channel estimation based on a pilot transmission and (ii) impact of channel estimation errors on coherent receiver performance. A simple characterization of the MMSE estimator in terms of a bank of filters is derived. A key channel characteristic controlling system performance is the normalized coherence time, which is approximately the number of symbols over which the channel remains strongly correlated. It is shown that the estimator performance is characterized by an effective signal-to-noise ratio (SNR)-the product of the pilot SNR and the normalized coherence time. A simple uniform averaging estimator is also proposed that is easy to implement and delivers near-optimal performance if properly designed. The receivers analyzed in this paper are based on a time-frequency RAKE structure that exploits joint multipath-Doppler diversity. It is shown that the overall receiver performance is controlled by two competing effects: shorter coherence times lead to degraded channel estimation but improved inherent receiver performance due to Doppler diversity, with opposite effects for longer coherence times. Our results demonstrate that exploiting Doppler diversity can significantly mitigate the error probability floors that plague conventional CDMA receivers under fast fading due to errors in channel estimation     

A full-rank regularization technique for MMSE detection in multiuser CDMA systems

In multiuser code-division multiple-access (CDMA) environments, the ill-conditioning of the covariance matrix of the received signal may degrade the performance of minimum mean-squared error (MMSE) detectors, especially when few samples are available for the covariance matrix estimation. In order to mitigate this performance degradation, we propose a full-rank regularized MMSE detector based on the covariance matrix tapering (CMT) technique. Simulation results show the effectiveness of the proposed technique at high signal-to-noise ratio (SNR).     

Performance of coded DS‐CDMA system using reduced rank MMSE receiver in Rayleigh fading channels

This paper examines the performance of a reduced rank minimum mean square error (MMSE) receiver‐based direct sequence code division multiple access (DS‐CDMA) system. For such system, when a large processing gain is employed, substantial time is consumed in computing the filter tap weights. Many schemes for reducing the complexity of the MMSE have been proposed in recent years. In this paper, computational complexity reduction of the MMSE receiver is achieved by using the K‐mean classification algorithm. The performance of the uncoded and coded systems are investigated for the full rank MMSE receiver and reduced rank MMSE receiver and results are compared in terms of bit error rate at different loading levels in both AWGN and fading channels. A system with the matched filter (MF) receiver is also presented for the purpose of comparison and an analytical pair‐wise error bound for the coded system is derived. In the adaptive implementation of the receivers, results show that good performance is achieved for the reduced rank receiver when compared to the full rank receiver in both coded and uncoded systems, while in the optimum implementation of the tap weights, the reduced dimension receiver performance experiences degradation when compared to the full rank scheme. Over the band‐limited channels considered, results for the reduced rank receiver also reiterate the fact that higher code rates tend to yield lower BER than that of low rate codes. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance of MMSE Receiver Based CDMA System with Higher Order Modulation Formats in a Fading Channel

This paper studies the effect of using higher order modulation formats on the performance of minimum mean-squared error (MMSE) receiver based direct-sequence (DS) code-division multiple access (CDMA) systems at different loading levels in additive white Gaussian noise (AWGN) and slow fading channels. The performance of BPSK, QPSK, and 16QAM modulation formats are compared and analytical and simulation results are presented in terms of the bit error rates (BER) for these different modulation formats. A comparison of the rejection of the near-far effects for each modulation scheme is also presented. The main contribution of this paper is in showing that user capacity may be increased by using higher order modulation schemes to cause the MMSE receiver to operate away from the interference limiting region. In particular it is shown that under high loading levels, 16QAM outperforms QPSK and BPSK for identical bandwidth and information rate, while at moderate loading levels, QPSK represents the best option. A combination of pilot symbol assisted modulation (PSAM) and linear prediction are used to estimate the fading process. A general structure of the MMSE receiver capable of demodulating a wide range of digital modulation formats in this type of environment is presented.     

Minimum mean squared error impulse noise estimation andcancellation

Impulses are infrequent bursts of high amplitude noise. A wide-band communications or data acquisition receiver has a fast sampling rate, so it can capture many samples of each impulse waveform. The arrival of an impulse can be identified by its distinct waveform and amplitude. The paper models impulse waveforms as a vector subspace of low dimension. Formulas are derived for the minimum mean squared error (MMSE) estimation of the arrival time and amplitudes of impulses, given that a set of vectors that spans the subspace is known. Formulas are also derived for the adaptive MMSE estimation of a set of vectors that spans the subspace. The values of the mean squared error (MSE) of the amplitude estimates are determined. It is shown how the theory can be used to cancel impulse noise. Correlated impulse noise arriving at a reference input can be used to estimate and cancel the primary input impulse noise. The MMSE coefficients for impulse noise cancellation are derived and presented. Simulations are presented that use the equations and methods derived in the paper for modeling and canceling impulse noise measured on copper telephone loops for asymmetric digital subscriber lines (ADSL)