基于共轭梯度法的低复杂度信道估计

考虑在大规模MIMO系统中基于导频的信道估计,基站端配置有数百根天线,传统的MMSE估计器虽然在估计精度上有着良好的性能,但是由于在利用MMSE方法进行信道估计时,存在对协方差矩阵求逆的运算,导致其计算复杂度为OM3,其中M为信道协方差矩阵的维度。在基站天线数很大的时候,这将是一个极其复杂的过程。为解决这个问题,将通过将求逆过程转化为解线性方程组的问题,利用共轭梯度法,使整个计算过程的计算复杂度降为ONM2,其中N为共轭梯度法的迭代次数,而且N<相似文献   

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.     

A competitive minimax approach to robust estimation of random parameters

We consider the problem of estimating, in the presence of model uncertainties, a random vector x that is observed through a linear transformation H and corrupted by additive noise. We first assume that both the covariance matrix of x and the transformation H are not completely specified and develop the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible covariance matrices and transformations H in the region of uncertainty. Although the minimax approach has enjoyed widespread use in the design of robust methods, we show that its performance is often unsatisfactory. To improve the performance over the minimax MSE estimator, we develop a competitive minimax approach for the case where H is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst-case regret, namely, the worst-case difference between the MSE attainable using a linear estimator, ignorant of the signal covariance, and the optimal MSE attained using a linear estimator that knows the signal covariance. The linear minimax regret estimator is shown to be equal to a minimum MSE (MMSE) estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region. We demonstrate, through examples, that the minimax regret approach can improve the performance over both the minimax MSE approach and a "plug in" approach, in which the estimator is chosen to be equal to the MMSE estimator with an estimated covariance matrix replacing the true unknown covariance. We then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly Gaussian is nonlinear, we often do not lose much by restricting attention to linear estimators.     

Large-sample performance of blind and Group-blind multiuser detectors: a perturbation perspective

In blind and group-blind multiuser detection, different detectors can be designed using either the sample data covariance matrix directly or its eigencomponents. Due to finite-sample effect in practice, their performance deviates from the corresponding optimum. A perturbation technique is developed rigorously and systematically to analyze those detectors in this work. Subject to the assumption that the first-order perturbation dominates, corresponding results can be applied to a practical system of a given sample size. In particular, performance of the following typical detectors is studied for either flat or estimated multipath channels: direct-matrix-inversion (DMI) blind minimum mean-square error (MMSE) detector, subspace blind MMSE detector, direct zero-forcing (ZF) detector, subspace ZF detector, and group-blind hybrid detector. Simulation examples further verify various analytical results.     

Minimax MSE-ratio estimation with signal covariance uncertainties

In continuation to an earlier work, we further consider the problem of robust estimation of a random vector (or signal), with an uncertain covariance matrix, that is observed through a known linear transformation and corrupted by additive noise with a known covariance matrix. While, in the earlier work, we developed and proposed a competitive minimax approach of minimizing the worst-case mean-squared error (MSE) difference regret criterion, here, we study, in the same spirit, the minimum worst-case MSE ratio regret criterion, namely, the worst-case ratio (rather than difference) between the MSE attainable using a linear estimator, ignorant of the exact signal covariance, and the minimum MSE (MMSE) attainable by optimum linear estimation with a known signal covariance. We present the optimal linear estimator, under this criterion, in two ways: The first is as a solution to a certain semidefinite programming (SDP) problem, and the second is as an expression that is of closed form up to a single parameter whose value can be found by a simple line search procedure. We then show that the linear minimax ratio regret estimator can also be interpreted as the MMSE estimator that minimizes the MSE for a certain choice of signal covariance that depends on the uncertainty region. We demonstrate that in applications, the proposed minimax MSE ratio regret approach may outperform the well-known minimax MSE approach, the minimax MSE difference regret approach, and the "plug-in" approach, where in the latter, one uses the MMSE estimator with an estimated covariance matrix replacing the true unknown covariance.     

Covariance Matrix Estimation With Heterogeneous Samples

We consider the problem of estimating the covariance matrix M_p of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly M_p. More precisely, we assume that the training samples can be clustered into K groups, each one containing L_k, snapshots sharing the same covariance matrix M_k. Furthermore, a Bayesian approach is proposed in which the matrices M_k. are assumed to be random with some prior distribution. We consider two different assumptions for M_p. In a fully Bayesian framework, M_p is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of M_p which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the weighted SCM, and we determine theoretically the optimal level of loading. Finally, in order to relax the a priori assumptions about the covariance matrix M_p, the second part of the paper assumes that this matrix is deterministic and derives its maximum-likelihood estimator. Numerical simulations are presented to illustrate the performance of the different estimation schemes.     

Demodulation and code acquisition using decorrelator detectors forQS-CDMA

A linear detector for a quasisynchronous code-division multiple-access (QS-CDMA) cellular system is presented, which is designed according to a minimum mean-square error (MMSE) criterion. By using a time-averaged version of the interfering signal covariance matrix, it is shown that multiuser interference can be rejected without the need to estimate signal time-of-arrival. Furthermore, unlike previous MMSE receiver designs, estimation of the received signal covariance matrix is not required. An asymptotic form of the MMSE detector, corresponding to a decorrelator implemented using a projection operator, is also obtained. Bit-error rate (BER) results are presented which demonstrate the superiority of the MMSE receiver over the conventional matched-filter detector under strong near-far conditions. An analysis of the expected acquisition time T¯_ACQ is given for the decorrelator detector using a serial search scheme. The results obtained show that T¯_ACQ is far less for a code acquisition method using the decorrelator as opposed to a conventional matched filter     

Recursive short-data-record estimation of AV and MMSE/MVDR linear filters for DS-CDMA antenna array systems

The presence of the desired signal during estimation of the minimum mean-square error (MMSE)/minimum-variance distortionless-response (MVDR) and auxiliary-vector (AV) filters under limited data support leads to significant signal-to-interference-plus-noise ratio (SINR) performance degradation. We quantify this observation in the context of direct-sequence code-division multiple-access (DS-CDMA) communications by deriving close approximations for the mean-square filter estimation error, the probability density function of the output SINR, and the probability density function of the symbol-error rate (SER) of the sample matrix inversion (SMI) receiver evaluated using both a desired-signal-"present" and desired-signal-"absent" input covariance matrix. To avoid such performance degradation, we propose a DS-CDMA receiver that utilizes a simple pilot-assisted algorithm that estimates and then subtracts the desired signal component from the received signal prior to filter estimation. Then, to accommodate decision-directed operation, we develop two recursive algorithms for the on-line estimation of the AV and MMSE/MVDR filter and we study their convergence properties. Finally, simulation studies illustrate the SER performance of the overall receiver structures.     

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.     

Performance analysis of reduced-rank beamformers for estimating dipole source signals using EEG/MEG

We study the performance of various beamformers for estimating a current dipole source at a known location using electroencephalography (EEG) and magnetoencephalography (MEG). We present our beamformers in the form of the generalized sidelobe canceler (GSC). Under this structure, the beamformer can be solved by finding a filter that achieves the minimum mean-squared error (MMSE) between the mainbeam response and filtered observed signal. We express the MMSE as a function of the filter's rank and use it as a criterion to evaluate the performance of the beamformers. We do not make any assumptions on the rank of the interference-plus-noise covariance matrix. Instead, we treat it as low-rank and derive a general expression for the MMSE. We present numerical examples to compare the MSE performance of beamformers commonly studied in the literature: principal components (PCs), cross-spectral metrics (CSMs), and eigencanceler (EIG) beamformers. Our results show that good estimates of the dipole source signals can be achieved using reduced-rank beamformers even for low signal-to-noise ratio (SNR) values.     

一种基于矩阵重组的功率倒置改进算法

针对功率倒置(Power Inversion,PI)算法信噪比恶化问题,推导了最小均方误差准则下最优权矢量组成,提出了处理增益更高、工作范围更广的改进算法.算法通过对接收信号协方差矩阵进行特征分解,根据特征值分布特点舍去噪声特征向量,组成新的协方差矩阵,得到具有指向性的最优权值矢量.仿真结果表明,与传统PI算法相比,改...     

MMSE based joint Tomlinson-Harashima source and linear relay precoder design in non-regenerative MIMO relay system

This paper proposes a joint nonlinear transceiver design scheme based on minimum mean square error(MMSE) criterion for non-regenerative multiple input multiple output(MIMO) relay system.The proposed scheme decomposes the error covariance matrix,reformulates the original joint design problem as two separate optimization problems,and then provides a closed-form solution with only local channel state information(CSI) available at the source and destination.Performance evaluation shows that the proposed scheme significantly outperforms linear schemes,and has a competitive performance compared with existing global CSI based nonlinear schemes,both iterative and non-iterative.     

大规模MIMO系统中基于二对角矩阵分解的低复杂度检测算法

在大规模多输入多输出(MIMO)系统的上行链路检测算法中,最小均方误差(MMSE)算法是接近最优的,但算法涉及到大矩阵求逆运算,计算复杂度仍然较高。近年提出的基于诺依曼级数近似的检测算法降低了复杂度但性能有一定的损失。为了降低复杂度的同时逼近MMSE算法性能,该文提出基于二对角矩阵分解的诺依曼级数(Neumann Series)近似,即将大矩阵分解为以两条主对角线上元素组成的矩阵与空心矩阵之和。理论分析与仿真结果表明所提算法检测性能逼近MMSE检测算法,且其复杂度从O(K3)降低到O(K2),这里K是用户的数目。     

An MMSE Decoding Algorithm without Matrix Inversion in QSTBC

The matrix inversion operation is needed in the MMSE decoding algorithm of orthogonal space-time block coding （OSTBC） proposed by Papadias and Foschini. In this paper, an minimum mean square error （MMSE） decoding algorithm without matrix inversion is proposed, by which the computational complexity can be reduced directly but the decoding performance is not affected.     

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     

Demodulation with a Multichannel Estimation Method Using a Reduced Rank Constraint

This paper deals with the Maximum Likelihood Estimation of the multichannel impulse response in a mobile communication system whose base stations are equipped with antennas arrays. The following problem is solved: using the training sequence, find the maximum likelihood multichannel impulse response from one mobile to the base station under a reduced rank constraint in the presence of gaussian noise and jammers with unknown covariance matrix. This method finds applications in demodulation (the reduced rank channel estimate can be used in a Viterbi Algorithm), and experimental results using real signals demonstrate its high performance compared with the standard Minimum Mean Square Error (MMSE) multichannel estimate.     

多径衰落下多天线CDMA系统信道容量研究

该文对准静态Rayleigh衰落下MIMO-CDMA系统信道容量进行了研究,分析了扩频码为Walsh函数,基于多码检测的极大似然检测器(MLD)和解相关检测器的性能,并和MMSE多用户检测器(MUD)进行了比较;分析了对不同检测器在一定的信噪比下系统天线数目和信道容量的关系。仿真结果表明:在相同的情况下,基于Walsh码CDMA系统容量按MUD、干扰方差已知的MLD,干扰方差未知的MLD和解相关检测器递减,并且后面的3种检测器在大信噪比的时候均有渐进的平台效应;在信噪比较大且一定时,CDMA系统信道容量与天线数目呈线性关系。     

High-resolution direction finding: the missing data case

This paper considers the problem of estimating the direction-of-arrival (DOA) of one or more signals using an array of sensors, where some of the sensors fail to work before the measurement is completed. Methods for estimating the array output covariance matrix are discussed. In particular, the maximum-likelihood (ML) estimate of this covariance matrix and its asymptotic accuracy are derived and discussed. Different covariance matrix estimates are used for DOA estimation together with the MUSIC algorithm and with a covariance matching technique. In contrast to MUSIC, the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix, and it is demonstrated that this yields a significant performance gain     

Diversity-assisted channel estimation and multiuser detection for downlink CDMA with long spreading codes

In downlink communication of a direct-sequence (DS) code-division multiple-access (CDMA) system, each user's short spreading codes are superimposed by base station's common long codes. This situation creates much difficulty in blind signal detection when multipath propagation occurs. However, when spatial/temporal diversity is available at the receiver, it is shown in this paper that subspace technique can be directly applied to estimate the common downlink multipath channel. Then, typical linear receivers, such as zero-forcing (ZF), minimum mean-square-error (MMSE) and RAKE receivers can be designed to detect the desired signal. Since the data covariance matrix is used but estimated from finite data samples, performance of both channel estimator and receivers gets perturbed. It is thus thoroughly and jointly analyzed by perturbation analysis. Justification of analysis and comparison of different receivers are also made through simulations.