An adaptive CMMSE receiver for space-time block-coded CDMA systems in frequency-selective fading channels

A technique that can suppress multiple-access interference (MAI) in space-time block-coded (STBC) multiple-input-multiple-output (MIMO) code-division multiple-access (CDMA) systems is developed. The proposed scheme, called a constrained minimum mean square error (CMMSE) receiver, is an extension of the CMMSE receiver for a single-input-single-output system to MIMO systems. It is shown that the complexity of the proposed CMMSE receiver is almost independent of the number of transmitter antennas. The advantage of the proposed receiver over the existing receivers for STBC CDMA systems is demonstrated by comparing the closed-form expressions of the signal-to-interference plus noise ratio and simulated bit error rates. The results indicate that the proposed CMMSE receiver can provide a significant performance improvement over the conventional receivers and that the gain achieved by suppressing the MAI can be larger than that from increasing the transmitter or receiver diversity.     

Constrained MMSE receivers for CDMA systems in frequency-selective fading channels

A constrained minimum mean square error (CMMSE)-RAKE receiver for multipath fading channels is developed by extending the CMMSE receiver for flat fading channels. Based on the observation that interpath interference causes a bias of the channel estimator in , a receiver that can remove such a bias is proposed, plus a closed-form expression of the bit-error rate of the receiver is derived. Computer simulation is used to demonstrate that the proposed receiver can outperform existing RAKE receivers.     

On channel estimation and sequence detection of interleaved codedsignals over frequency nonselective Rayleigh fading channels

Due to the receiver complexity introduced by interleaving, the implementation of maximum likelihood (IML) decoding of interleaved coded signals transmitted over frequency nonselective Rayleigh fading channels has been shown to be practically impossible. As an alternative, a two-stage receiver structure has been proposed, where the channel estimation and sequence decoding are done separately. The channel estimation issue in a two-stage receiver is examined in detail in this paper. It is shown that although an optimum (maximum a posteriori (MAP)) channel estimation is not possible in practice, it can be approached asymptotically by joint MAP estimation of the channel and the coded data sequence. The implementation of the joint MAP estimation is shown to be an ML sequence estimator followed by an minimum mean-square error (MMSE) channel estimator. Approximate fill sequence estimation using pilot symbol interpolation is also studied, and through computer simulations, its performance is compared to receivers using hit sequence estimation. The effect of decision delay (DD), prediction order, and pilot insertion rate (PIR) on the reduced complexity ML sequence estimation is investigated as well. Finally, a practical receiver is proposed that makes the best compromise among the error performance, receiver complexity, DD, and power (or bandwidth) expansion due to pilot insertion     

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     

Properties of the single-bit single-user MMSE receiver for DS-CDMAsystems

The single-bit single-user minimum mean-squared error (MMSE) receiver for direct-sequence code-division multiple access systems is studied in great detail. It is shown that the MMSE receiver is near-far resistant and asymptotically optimum as the interference or noise disappear (i.e., in interference or noise dominated scenarios). It is experimentally shown that the popular Gaussian approximation of the error probability is reasonable for the MMSE receiver over a broad range of operating conditions-i.e., signal-to-noise ratios and interference situations-even though this may not be the case for the standard matched-filter receiver. The concept of dimension reduction is introduced to reduce the complexity of the adaptive part of the receiver and the optimum dimension reduction transform is derived. Unfortunately, the optimum transform is dependent on unknown side-information and is, therefore, of limited practical use. However, several practical schemes are proposed (one which is asymptotically optimum). The schemes are shown to outperform previously known methods     

An improved blind adaptive MMSE receiver for fast fading DS-CDMAchannels

Blind adaptive minimum mean-squared errors (MMSE) receivers for multiuser direct-sequence code-division multiple access (DS-CDMA) systems that assume knowledge of the steering vector, i.e., the cross-correlation between the desired output and the input signal, are known for their robustness against channel fading as they do not attempt to explicitly track the channel of the user of interest. However, these receivers often have higher excess mean squared error and, hence, poorer performance than training-sequence based adaptive MMSE receivers. In this paper, an improved correlation matrix estimation scheme for blind adaptive MMSE receivers is provided. The new scheme takes advantage of the fact that the desired linear receiver can be expressed as a function of the interference correlation matrix only, rather than the total data correlation matrix. A theoretical analysis is performed for the flat fading case which predicts that the new estimation scheme will result in significant performance improvement. Blind adaptive MMSE receivers with the new estimation scheme appear to achieve performance comparable to the training-sequence based adaptive MMSE receivers. Detailed computer simulations for the fast multipath fading environment verify that the proposed scheme yields strong performance gains over previous methods     

Soft‐output MMSE V‐BLAST receiver with MMSE channel estimation under correlated Rician fading MIMO channels

For wireless multiple‐input multiple‐output (MIMO) communications systems, both channel estimation error and spatial channel correlation should be considered when designing an effective signal detection system. In this paper, we propose a new soft‐output MMSE based Vertical Bell Laboratories Layered Space‐Time (V‐BLAST) receiver for spatially‐correlated Rician fading MIMO channels. In this novel receiver, not only the channel estimation errors and channel correlation but also the residual interference cancellation errors are taken into consideration in the computation of the MMSE filter and the log‐likelihood ratio (LLR) of each coded bit. More importantly, our proposed receiver generalizes all existing soft‐output MMSE V‐BLAST receivers, in the sense that, previously proposed soft‐output MMSE V‐BLAST receivers can be derived as the reduced forms of our receiver when the above three considered factors are partially or fully simplified. Simulation results show that the proposed soft‐output MMSE V‐BLAST receiver outperforms the existing receivers with a considerable gain in terms of bit‐error‐rate (BER) performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance of antenna diversity multiuser receivers in CDMA channels with imperfect fading estimation

The performance of antenna diversity coherent and differentially coherent linear multiuser receivers is analyzed in frequency-nonselective Rayleigh fading CDMA channels with memory. The estimates of the complex fading processes are utilized for maximal-ratio combining and carrier recovery of the coherent multiuser receiver. To analyze the impact of channel estimation errors on the receiver performance, error probability is assessed directly in terms of the fading rate and the number of active users, showing the penalty imposed by imperfect channel estimation as well as the fading-induced error probability floor. The impact of fading dynamics on the differentially coherent decorrelating receiver with equal-gain combining is quantified. While performance of multiuser receivers at lower SNR is determined by both the fading dynamics and the number of active CDMA users, performance at higher SNR is given by an error probability floor which is due to fading only and has the same value as in a single-user case. The comparison of the two receiver structures indicates that the coherent decorrelating receiver with diversity reception may be preferable to the differentially coherent one in nonselective fading CDMA channels with memory.     

Performance of a Hybrid Receiver in the Downlink Multicell CDMA System

In this paper, we propose a novel low-complexity receiver, namely, a hybrid receiver (HR) for the downlink of a multicell code-division multiple-access (CDMA) system with a transmit delay diversity transmission scheme. The proposed receiver is designed by combining the merits of the decorrelating receiver (DR) and the conventional receiver (CR). Unlike most multiuser receivers, HR operates with the same information as CR. For a target performance metric (e.g., bit error probability (BEP)=10^-2), the reduced-complexity HR significantly outperforms CR, DR, and minimum mean-square error (MMSE) receiver with estimated channel information. We also compare the performance of the reduced-complexity HR with a reduced-complexity MMSE receiver, which slightly outperforms the former at a price of higher complexity     

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.     

Adaptive MAP receiver via the EM algorithm and message passings for MIMO-OFDM mobile communications

This paper proposes two new types of maximum a posteriori probability (MAP) receivers for multiple-input-multiple-output and orthogonal frequency-division multiplexing mobile communications with a channel coding such as the low-density parity-check code. One proposed receiver employs the expectation-maximization algorithm so as to improve performance of approximated MAP detection. Differently from a conventional receiver employing the minimum mean-square estimation (MMSE) algorithm, it applies the recursive least squares (RLS) algorithm to the channel estimation in order to track a fast fading channel. For the purpose of further improvement, the other proposed receiver applies a new adaptive algorithm that can be derived from the message passing on factor graphs. The algorithm exploits all detected signals but one of targeted time, and can gain a considerable advantage over the MMSE and RLS. Computer simulations show that the first proposed receiver is superior in channel-tracking ability to the conventional receiver employing the MMSE. Furthermore, it is demonstrated that the second proposed receiver remarkably outperforms both the conventional and the first proposed ones.     

Optimal diversity combining based on linear estimation of rician fading channels

Optimal receiver diversity combining employing linear channel estimation is examined. Based on the statistical properties of least-squares (LS) and minimum mean square error (MMSE) channel estimation, an optimal diversity receiver for wireless systems employing practical linear channel estimation on Rician fading channels is proposed. The new receiver structure includes the conventional maximal ratio combining receiver as a special case. Exact analytical expressions for the symbol error rates (SERs) of LS and MMSE channel estimation aided optimal diversity combining are derived. It is shown that, if an optimal detector is used, an MPSK wireless system with MMSE channel estimation has the same SER when the MMSE channel estimation is replaced by LS estimation. This is an interesting counterexample to the common perception that channel estimation with smaller mean square error leads to smaller SER. Extensive simulation results validate the theoretical results.     

An Adaptive Multiuser Detection Algorithm for CDMA Systems Using Antenna Diversity

Based on the minimum mean squared error (MMSE) between the data stream and the linear combiner output, a new multiuser detection (MUD) algorithm that combines space–time (ST) processing and antenna array on direct-sequence CDMA signals is proposed. The proposed ST-MUD algorithm is proved to be equivalent to two existing MMSE-based ST-MUD algorithms, and the theoretical BER performances for all the three algorithms are the same. The most attractive feature of the new ST-MUD algorithm is based on the fact that the new method does not require explicit estimation of channel and signaling information. This avoids any channel estimation error, and the method is thus more robust and more accurate than the other two ST-MUD algorithms in practical implementation. Adaptation of the proposed ST-MUD algorithm is implemented by using training sequences. Performance of this new multiuser detector is compared with that of two existing MMSE multiuser detectors and the conventional single-user space–time rake receiver through simulations. The proposed ST-MUD algorithm provides a performance better than existing algorithms and is especially suitable for practical CDMA systems.     

Blind multiuser detection in uplink CDMA with multipath fading: a sequential EM approach

We consider joint channel estimation and data detection in uplink asynchronous code-division multiple-access systems employing aperiodic (long) spreading sequences in the presence of unknown multipath fading. Since maximum-likelihood (ML) sequence estimation is too complex to perform, multiuser receivers are proposed based on the sequential expectation-maximization (EM) algorithm. With the prior knowledge of only the signature waveforms, the delays and the second-order statistics of the fading channel, the receivers sequentially estimate the channel using the sequential EM algorithm. Moreover, the snapshot estimates of each path are tracked by linear minimum mean-squared error filters. The user data are detected by a ML sequence detector, given the channel estimates. The proposed receivers that use the exact expressions have a computational complexity O(2/sup K/) per bit, where K is the number of users. Using the EM algorithm, we derive low-complexity approximations which have a computational complexity of O(K/sup 2/) per bit. Simulation results demonstrate that the proposed receivers offer substantial performance gains over conventional pilot-symbol-assisted techniques and achieve a performance close to the known channel bounds. Furthermore, the proposed receivers even outperform the single-user RAKE receiver with Nyquist pilot-insertion rate in a single-user environment.     

Sparse Bayesian Learning Approach to Adaptive Beamforming Assisted Receivers

In this letter, a new adaptive beamforming assisted receiver based on sparse Bayesian learning is proposed. We consider a general probabilistic Bayesian learning framework for obtaining sparse solutions to adaptive beamforming assisted receivers to improve the performance of an adaptive beamforming assisted receiver based on the minimum mean squared error (MMSE) scheme. Simulation experiments show that the bit error rate (BER) performance of the sparse Bayesian beamforming receiver shows an outstanding BER performance compared to MMSE beamforming receivers     

Partial sampling MMSE interference suppression in asynchronousmulticarrier CDMA system

Linear minimum mean square error (LMMSE) receivers for asynchronous multicarrier code division multiple access (MC-CDMA) system under frequency-selective Rayleigh fading channel is studied. The performance of this LMMSE receiver is evaluated and shown to be superior to that of the other two schemes, equal-gain combining (EQC) and maximum-ratio combining (MRC). However, a perfect timing estimation of the desired user is needed for these receivers, as a misaligned sampling interval of these receivers results in severely self intersymbol interference (ISI) and intercarrier interference (ICI) for the desired signal at the output. In order to remove the timing acquisition requirement of a receiver for an asynchronous MC-CDMA system, we proposed a novel partial sampling MMSE (PS-MMSE) receiver. Numerical result shows that the PS-MMSE receiver without timing knowledge provides significantly stronger interference suppression capability than the LMMSE receiver with known timing. Moreover, a so-called reduced complexity partial sampling MMSE (RPS-MMSE) receiver is proposed to make the number of the receiver's taps independent of the number of subcarriers. Results show that with a proper grouping parameter, a much less complicated RPS-MMSE receiver achieves almost the same performance as the PS-MMSE receiver. Thus, one is able to implement an MMSE receiver without a prior timing requirement to perform multiuser detection for the MC-CDMA system in an asynchronous scenario at the expense of a slight complexity increase     

The impact of frequency-flat fading on the spectral efficiency ofCDMA

The capacity of the randomly spread synchronous code-division multiple-access (CDMA) channel subject to frequency-flat fading is studied in the wide-band limit of large number of users. We find the spectral efficiency as a function of the number of users per chip, the distribution of the flat fading, and the signal-to-noise ratio (SNR), for the optimum receiver as well as linear receivers (single-user matched filter, decorrelator, and minimum mean-square error (MMSE)). The potential improvements due to both decentralized transmitter power control and multi-antenna receivers are also analyzed     

STBC MIMO CDMA系统CMVDR接收机研究

提出了STBC MIMO CDMA系统中一种新的基于多用户ML估计的带制约的最小方差无失真响应(CMVDR)接收机，能有效抑制多址干扰(MAD和符号间干扰(ISI)。给出了多用户、多径的STBC MIMO CDMA系统信道模型及ML参数估计，并给出了分部加权和整体加权两种CMVDR接收机，本接收机也适用于SIMO CDMA系统。进行了系统模拟，并对分部加权和整体加权两种CMVDR接收机的性能以及自适应CMMSE接收机的性能进行了比较分析。     

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.     

An optimal whitening approach to linear multiuser detection

We propose a new linear multiuser receiver for synchronous code-division multiple-access (CDMA) systems, referred to as the orthogonal multiuser (OMU) receiver. Unlike the linear minimum mean-squared error (MMSE) receiver, the OMU receiver depends only on the signature vectors and does not require knowledge of the received amplitudes or the channel signal-to-noise ratio (SNR). Several equivalent representations of the receiver are developed with different implications in terms of implementation. In the first, the receiver consists of a decorrelator demodulator followed by an optimal whitening transformation on a space formed by the signatures. In the second, the receiver consists of a bank of correlators with correlating vectors that are projections of a set of orthogonal vectors, and are closest in a least squares sense to the decorrelator vectors and also closest in a least squares sense to the signature vectors. In the third, the receiver consists of a single-user matched filter (MF) followed by an optimal whitening transformation on a space formed by the signatures. We derive exact and approximate expressions for the probability of bit error, as well as the asymptotic signal-to-interference+noise ratio (SINR) in the large system limit. The analysis suggests that over a wide range of channel parameters the OMU receiver can outperform both the decorrelator and the single-user MF and perform similarly to the linear MMSE receiver, despite not knowing the channel parameters.