Performance of linear reduced-rank multistage receivers for DS-CDMA in frequency-selective fading channels

The performance of a set of linear reduced-rank multistage filter banks is studied in the context of multiuser detection for direct-sequence (DS) code-division multiple-access (CDMA) systems. The set of filter banks under consideration is comprised of the minimum mean-square error (MMSE), the minimum output energy (MOE), the best linear unbiased estimator (BLUE), and the maximum-likelihood (ML) detector. Based on a common framework for the multistage implementations of the aforementioned filter banks, the signal-to-interference plus noise ratios (SINRs) and bit-error rates (BERs) of these reduced-rank filter banks are studied for multipath Rayleigh-fading channels. A generic BER formula is provided for coherent detection and noncoherent differential detection schemes constructed under this common framework. Analysis shows that all of these performance measures are characterized by a kernel matrix K/sub mmse/ whose trace forms the output SINR of the MMSE filter bank. Through investigating the recursive structure of K/sub mmse/, the output SINRs are proven to be monotonically increasing with the number of stages and upper-bounded by a number equal to the paths of the desired user's channel. The condition for asymptotically achieving this upper bound is also provided, which leads to the notion of effective user capacity of linear reduced-rank multiuser detection as well as serves as a test for the existence of a BER floor for coherent detection. In addition, the channel mismatch due to differential detection is also shown to yield a BER floor for noncoherent detection. Based on this analysis, a simple yet effective rule for choosing the number of stages is provided for both coherent and noncoherent linear multistage multiuser detection.     

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.     

Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals

In this paper, we study the performance of multiple-input multiple-output channel estimation methods using training sequences. We consider the popular linear least squares (LS) and minimum mean-square-error (MMSE) approaches and propose new scaled LS (SLS) and relaxed MMSE techniques which require less knowledge of the channel second-order statistics and/or have better performance than the conventional LS and MMSE channel estimators. The optimal choice of training signals is investigated for the aforementioned techniques. In the case of multiple LS channel estimates, the best linear unbiased estimation (BLUE) scheme for their linear combining is developed and studied.     

Improved ML Channel Estimation for Uplink MC-CDMA Systems in Closely Spaced Multipath Channels

In order to attain near-single user performance in uplink multicarrier code- division multiple-access (MC-CDMA) systems, multiuser detection (MUD) methods may be employed which rely on simultaneous estimation of the channel frequency responses of multiple users. Pilot symbol assisted (PSA) channel estimation is needed in fast fading channels and it can be performed either by applying maximum likelihood (ML) criterion or minimum mean-squared error (MMSE) criterion. The performance of ML estimation technique degrades significantly in the case of fractionally spaced (FS) multipath channels where dominant paths are closely spaced with respect to the time resolution of the system. In such situation, the number of effective paths (which contribute more towards signal power) becomes considerably less than the actual number of multipaths at low and moderate SNR values. We propose an improved ML estimation method which considers only effective paths during the estimation process. The proposed method performs nearly identical to the MMSE estimation method and it can also provide significant reduction in the computational complexity when a large number of users are accommodated in the system.     

一种新的最小均方误差线性合并算法

针对未编码的多输入多输出系统,将基于训练序列的最小均方误差(MMSE)信道估计算法与最优线性无偏估计结构(BLUE)相结合对已估计的信道参数进行估计.仿真结果表明,使用线性合并的MMSE算法比传统的MMSE算法具有较小的参数估计误差,比使用线性合并的LS算法性能更好.     

基于NLMS的CDMA盲自适应多用户检测算法研究

多用户检测是抑制DS-CDMA系统多址干扰最有效的技术之一。由于所需的先验知识仪有期望用户的地址码,盲多用户检测技术的研究尤受重视。最小输出能量(MOE)准则被广泛用于盲线性多用户检测。目前已提出的该类检测器多采用LMS或RLS算法。本文则研究基于NLMS算法的盲自适应检测技术,并进一步提出盲自适应变步长NLMS检测器和参数可变的盲自适应变步长NLMS检测器。它们具备很好的收敛速度和跟踪能力,以及较高的输出信干比,同时计算复杂度仅为O(3N)或O(4N),非常适合硬件实现。     

BLUE‐Based Channel Estimation Technique for Amplify and Forward Wireless Relay Networks

The best linear unbiased estimator (BLUE) is most suitable for practical application and can be determined with knowledge of only the first and second moments of the probability density function. Although the BLUE is an existing algorithm, it is still largely unexplored and has not yet been applied to channel estimation in amplify and forward (AF)‐based wireless relay networks (WRNs). In this paper, a BLUE‐based algorithm is proposed to estimate the overall channel impulse response between the source and destination of AF strategy‐based WRNs. Theoretical mean square error (MSE) performance for the BLUE is derived to show the accuracy of the proposed channel estimation algorithm. In addition, the Cramér‐Rao lower bound (CRLB) is derived to validate the MSE performance. The proposed BLUE channel estimation algorithm approaches the CRLB as the length of the training sequence and number of relays increases. Further, the BLUE performs better than the linear minimum MSE estimator due to the minimum variance characteristic exhibited by the BLUE, which happens to be a function of signal‐to‐noise ratio.     

Finite-length MIMO equalization using canonical correlationanalysis

We propose finite-length multi-input multi-output (MIMO) equalization methods for "smart" antenna arrays using the statistical theory of canonical correlations. We show that the proposed methods are related to maximum likelihood (ML) reduced-rank channel and noise estimation algorithms in unknown spatially correlated noise as well as to several previously developed equalization schemes     

Reduced-rank adaptive multiuser detection in hybrid direct-sequence time-hopping ultrawide bandwidth systems

In this paper a range of reduced-rank adaptive multiuser detectors (MUDs) are proposed and investigated for the hybrid direct-sequence time-hopping ultrawide bandwidth (DS-TH UWB) systems. The adaptive MUDs are operated based on the recursive least square (RLS) principles. Three types of reduced-rank techniques are investigated, which are the principal component (PC), cross-spectral metric (CSM) and Taylor polynomial approximation (TPA). These reduced-rank adaptive techniques are beneficial to achieving low-complexity, high spectral-efficiency and robust detection in hybrid DSTH UWB systems. In this contribution bit error rate (BER) performance of the hybrid DS-TH UWB systems using proposed reduced-rank adaptive MUDs is investigated by simulations, when communicating over UWB channels modelled by the Saleh-Valenzuela (S-V) channel model. Our simulation results show that, given a sufficiently high rank of the detection subspace, the reduced-rank adaptive MUDs are capable of achieving a similar BER performance as that of the full-rank ideal minimum meansquare error MUD (MMSE-MUD) but with significantly lower detection complexity. Furthermore, the TPA-based reduced-rank adaptive MUD is capable of yielding a better BER performance than the PC- or CSM-based reduced-rank adaptive MUD, when the same but relatively low rank detection subspace is assumed.     

MBER Space-Time Decision Feedback Equalization Assisted Multiuser Detection for Multiple Antenna Aided SDMA Systems

This paper proposes a space-time decision feedback equalization (ST-DFE) assisted multiuser detection (MUD) scheme for multiple receiver antenna aided space division multiple access systems. A minimum bit error rate (MBER) design is invoked for the MUD, which is shown to be capable of improving the achievable bit error rate performance and enhancing the attainable system capacity over that of the standard minimum mean square error (MMSE) design. An adaptive implementation of the MBER ST-DFE assisted MUD is proposed using a stochastic gradient-based least bit error rate algorithm, which is demonstrated to consistently outperform the classical least mean square (LMS) algorithm, while achieving a lower computational complexity than the LMS algorithm for the binary signalling scheme. Our simulation results demonstrate that the MBER ST-DFE assisted MUD is more robust to channel estimation errors as well as to potential error propagation imposed by decision feedback errors, compared to the MMSE ST-DFE assisted MUD.     

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.     

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.     

Symbol rate timing recovery for higher order partial responsechannels

This paper provides a framework for analyzing and comparing timing recovery schemes for higher order partial response (PR) channels. Several classes of timing recovery schemes are analyzed. Timing recovery loops employing timing gradients or phase detectors derived from the minimum mean-square error (MMSE) criterion, the maximum likelihood (ML) criterion, and the timing function approach of Mueller and Muller (1976) (MRI) are analyzed and compared. The paper formulates and analyzes MMSE timing recovery in the context of a slope look-up table (SLT), which is amenable for an efficient implementation. The properties and performance of the SLT-based timing loop are compared with the ML and MM loops. Analysis and time step simulations for a practical 16-state PR magnetic recording channel show that the output noise jitter of the ML phase detector is worse than that of the SLT-based phase detector. This is primarily due to the presence of self-noise in the ML detector. Consequently, the SLT-based phase detector is to be preferred. In comparing the SLT and MM based timing loops, it is found that both schemes have similar jitter performance     

Performance of multiuser detectors based on EM-like method for ultra-wideband communications systems in multipath fading channel

An adaptive multiuser detector (MUD) is proposed for direct-sequence ultra-wideband (DS-UWB) multiple access communication systems to suppress both multiple access interference (MAI) and inter-symbol interference (ISI). In this contribution, considering the MUD from a combination viewpoint, we proposed a MUD based on electromagnetism-like (EM) method, which applied the concept of EM search to Hopfield neural network (EMHNN) for solving optimization problems. We analyze the performance of the EMHNN MUD in multipath fading channel, and compare it with the optimum detector and several suboptimum schemes such as conventional, decorrelator detector (DD), minimum-mean-squared error (MMSE) and HNN MUD. Simulation results will demonstrate that the proposed EMHNN MUD, which alleviates the detrimental effects of the MAI problem, can significantly improve the system performance.     

Multiuser Detection in SDMA–OFDM Wireless Communication System Using Complex Multilayer Perceptron Neural Network

The space division multiple access–orthogonal frequency division multiplexing (SDMA–OFDM) wireless system has become very popular owing high spectral efficiency and high load capability. The optimal maximum likelihood multiuser detection (MUD) technique suffers from high computational complexity. On the other hand the linear minimum mean square error (MMSE) MUD techniques yields poor performance and also fails to detect users in overload scenario, where the number of users are more than that of number of receiving antennas. By contrast, the differential evolution algorithm (DEA) aided minimum symbol error rate (MSER) MUD can sustain in overload scenario as it can directly minimizes probability of error rather than mean square error. However, all these classical techniques are still complex as these do channel estimation and multiuser detection sequentially. In this paper, complex multi layer perceptron (CMLP) neural network model is suggested for MUD in SDMA–OFDM system as it do both channel approximation and MUD simultaneously. Simulation results prove that the CMLP aided MUD performs better than the MMSE and MSER techniques in terms of enhanced bit error rate performance with low computational complexity.     

Soft-Output MMSE V-BLAST Detector under ML Channel Estimation and Channel Correlation

Channel estimation errors have not been taken into account by existing soft-output minimum mean square error (MMSE) vertical Bell Lab Space Time (V-BLAST) detectors. As a result, the system performance will be degraded under practical channel estimation. In this letter, we propose a novel soft-output MMSE V-BLAST detector, which takes the estimation error of maximum likelihood (ML) multiple-input multiple-output (MIMO) channel estimation and receiver spatially correlation into account in the computation of the MMSE filter and loglikelihood ratio (LLR) of each coded bit. When compared with existing MMSE V-BLAST detectors, simulation results show that the proposed novel detector can obtain sizable performance gain.     

DS-CDMA系统中基于信号子空间的盲降秩多用户检测

 本文提出了一种基于可变阈值的降秩子空间选择算法及改进维数估计的盲降秩多用户检测技术.采用可变阈值的降秩子空间选择算法,能较快地得到合适的降秩子空间,且计算结果具有可重用性.在子空间追踪中用一种改进的AIC准则进行维数估计,在不提高误差概率的基础上,降低了维数估计的计算量.在维数过高估计时,分析了采用降秩算法的检测性能.仿真结果表明,该算法能用较低的计算复杂度满足系统要求的检测性能.     

Reduced-rank technique for joint channel estimation in TD-SCDMA systems

In time division-synchronous code division multiple access systems, increasing the system capacity by exploiting the inserting of the largest number of users in one time slot (TS) requires adding more estimation processes to estimate the joint channel matrix for the whole system. The increase in the number of channel parameters due the increase in the number of users in one TS directly affects the precision of the estimator's performance. This article presents a novel channel estimation with low complexity, which relies on reducing the rank order of the total channel matrix H. The proposed method exploits the rank deficiency of H to reduce the number of parameters that characterise this matrix. The adopted reduced-rank technique is based on truncated singular value decomposition algorithm. The algorithms for reduced-rank joint channel estimation (JCE) are derived and compared against traditional full-rank JCEs: least squares (LS) or Steiner and enhanced (LS or MMSE) algorithms. Simulation results of the normalised mean square error showed the superiority of reduced-rank estimators. In addition, the channel impulse responses founded by reduced-rank estimator for all active users offers considerable performance improvement over the conventional estimator along the channel window length.     

Performance Improvement by Microdiversity for Wideband Signals in Frequency Selective Fading Indoor Channels with Co-Channel Interference

A comprehensive analytical bit-error-rate (BER) model is presented to analyse the performance of antenna-microdiversity for wideband BPSK modulated signals in the frequency selective fading multipath channel, specified by its complex impulse response. The model includes the disturbance by intersymbol interference (ISI) and co-channel interference (CCI), as well as the channels' impact on the carrier phase- and clock recovery in the receiver. The channel impulse responses at the antenna elements are determined by taking into account the direction of arrival of the individual paths. Computational BER- and SNIR-gain results (SNIR = signal-to-noise+interference-ratio) show that a substantial performance improvement is achieved with antenna combining for wideband signals which suffer ISI and/or CCI. For the indoor multipath channel with exponentially decaying power delay profile, the performance enhancement is compared for several antenna combining schemes. Quasi-coherent equal gain combining (QCEGC) is proposed as an novel EGC scheme based on a less accurate phase estimation technique. For wideband signals, QCEGC shows a slight performance degradation when compared to maximal ratio combining or minimum mean square error combining (MMSEC), but has a much lower implementation complexity. In the channel with CCI, where the best performance is achieved with MMSEC, QCEGC performs very poor.