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     

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.     

Blind multiuser detection: from MOE to subspace methods

The minimum output energy (MOE) multiuser receiver has been shown to approach the minimum mean-square-error (MMSE) receiver at high signal-to-noise ratio (SNR). However, performance degradation is incurred by noise induced channel estimation error. In this paper, we propose a Power of R (POR) technique to significantly improve the performance of the MOE receiver. It is shown that the new receiver asymptotically converges to the MMSE receiver without performance penalty. The convergence is established either under high SNR, with large exponent raised in the power of the covariance matrix, or with sufficiently large number of data samples. Connection between our POR method and a widely studied subspace method is investigated from the respective optimization criteria. Asymptotic equivalence between these two methods is also established. Extensive simulations based on finite data samples show that the proposed method significantly outperforms the subspace method in systems with medium to heavy loading, severe multipath distortion, or smaller processing gain. Moreover, adaptive implementation of the proposed method exhibits very robust performance in a dynamic loading environment.     

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.     

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.     

Asymptotic normality of linear multiuser receiver outputs

This paper proves large-system asymptotic normality of the output of a family of linear multiuser receivers that can be arbitrarily well approximated by polynomial receivers. This family of receivers encompasses the single-user matched filter, the decorrelator, the minimum mean square error (MMSE) receiver, the parallel interference cancelers, and many other linear receivers of interest. Both with and without the assumption of perfect power control, we show that the output decision statistic for each user converges to a Gaussian random variable in distribution as the number of users and the spreading factor both tend to infinity with their ratio fixed. Analysis reveals that the distribution conditioned on almost all spreading sequences converges to the same distribution, which is also the unconditional distribution. This normality principle allows the system performance, e.g., the multiuser efficiency, to be completely determined by the output signal-to-interference ratio (SIR) for large linear systems.     

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。     

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     

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.     

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.     

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.     

Continuous Phase Chirp (CPC) Signals for Binary Data Communication--Part II: Noncoherent Detection

Previous work has shown that coherent multiple bit observation of binary continuous phase chirp (CPC) signals gives improved error rate performance compared to the conventional bit-by-bit detection scheme. This paper determines bounds on the error rate improvement made possible by multiple bit observation for optimum and suboptimum [average matched filter (AMF)] noncoherent detection of binary CPC signals in additive white Gaussian noise (AWGN). For the same observation interval, it is shown that noncoherent CPC receivers provide higher signal-to-noise (SNR) gain than coherent receivers compared to the respective optimum single bit schemes. In particular, the three-bit noncoherent AMF receiver is shown to yield 3 dB SNR gain over a wide range of signal parameters.     

Continuous Phase Chirp (CPC) Signals for Binary Data Communication-Part I: Coherent Detection

Chirp (linear FM) signals provide an attractive wideband digital modulation scheme in applications where interference rejection is important. This paper evaluates the error rate (performance) of coherent binary continuous phase chirp (CPC) receivers operating on the additive white Gaussian noise (AWGN) channel and determines the improvement in performance made possible by multiple bit observation. In particular, it is shown that a receiver with two bit observation, giving up to 1.75 dB signal-to-noise ratio (SNR) improvement over the optimum single bit chirp receiver, provides a good compromise between SNR gain and system complexity. Furthermore, a simple, suboptimum, average matched filter (AMF) receiver is analyzed, and it is shown that a two-bit observation is optimum, giving a performance equivalent to that of antipodal phaseshift keying (PSK). An implementation of this receiver in the form of in-phase and quadrature demodulators is also derived.     

Asymptotic analysis of improved linear receivers for BPSK-CDMAsubject to fading

In this paper, we design and analyze a new class of linear multiuser detectors, which can be applied when the users employ BPSK modulation and the fading coefficients of the active users are known at the receiver (such as base-station demodulation). The tools of asymptotic distribution of the spectrum of large random matrices are used to show that relative to the classical minimum mean-square-error (MMSE) receiver, the output signal-to-noise ratio (SNR) improves by halving the number of effective interferers and adding 3 dB to the input SNR. We also propose sensible approximations to the proposed linear receivers so as to facilitate their use in CDMA systems that employ long codes     

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     

Near-ML multiuser detection with linear filters and reliability-based processing

The prohibitive - exponential in the number of users - computational complexity of the maximum-likelihood multiuser detector for direct-sequence code-division multiple-access communications has fueled an extensive research effort for the development of low-complexity multiuser detection alternatives. We show that we can efficiently and effectively approach the error rate performance of the optimum multiuser detector as follows. We utilize a multiuser zero-forcing or minimum mean-square error (MMSE) linear filter as a preprocessor and we establish that the output magnitudes, when properly scaled, provide a reliability measure for each user bit decision. Then, we prepare an ordered, reliability-based error search sequence of length linear in the number of users; it returns the most likely user bit vector among all visited options. Numerical and simulation studies for moderately loaded systems that permit exact implementation of the optimum detector indicate that the error rate performance of the optimum and the proposed detector are nearly indistinguishable over the whole predetection. signal-to-noise ratio range of practical interest. Similar studies for higher user loads (that prohibit comparisons with the optimum detector) demonstrate error rate performance gains of orders of magnitude in comparison with straight decorrelating or MMSE multiuser detection.     

Group-Based Space-Time Multiuser Detection with User Sharing

To reduce the complexity of space-time multiuser detection, it has been proposed recently to exploit the spatial dimension by forming groups of users and apply the detection individually to each group. In this work we propose a new space-time receiver structure based on the group-optimal MMSE linear detector along with a new grouping algorithm that respects practical hardware limitations. Furthermore, an extension of the proposed structure which allows non-mutually exclusive grouping is presented. The simulation results show that the proposed reduced-complexity receiver structure provides a bit error rate (BER) performance close to the full linear MMSE multiuser detector.     

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.     

A DS-CDMA tracking mode receiver with joint channel/delayestimation and MMSE detection

A tracking mode receiver for asynchronous direct-sequence CDMA is presented based on the extended Kalman filter (EKF). The EKF jointly estimates the delays and multipath coefficients of the received CDMA waveform, and provides a modified minimum mean-square error (MMSE) estimate of the user data (MMSE-EKF). In order to obtain a practical algorithm, each user signal is tracked individually, with the remaining users modeled as colored Gaussian noise. However, the EKFs are coupled through the multiple access interference (MAI) covariance estimates. In order to obtain meaningful performance measures, approximate worst-case undesired user delays that minimize the desired user SNR and delay estimation Cramer-Rao bound are obtained. It is shown that such worst-case delays can be efficiently computed using the alternating maximization (A-M) algorithm. The resulting bit error rate (BER) performance of the MMSE-EKF tracking receiver is evaluated through a combination of simulation and analysis. The mean-time to lose lock (MTTLL) for a genie-aided EKF delay estimator is also obtained using the A-M computed delays