Robust mean-squared error estimation in the presence of model uncertainties

We consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties, where the vector x is known to satisfy a weighted norm constraint. We first assume that the model is known exactly and seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible values of x. We show that for an arbitrary choice of weighting, the optimal minimax MSE estimator can be formulated as a solution to a semidefinite programming problem (SDP), which can be solved very efficiently. We then develop a closed form expression for the minimax MSE estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of Mayer and Willke, with a specific choice of shrinkage factor that explicitly takes the prior information into account. Next, we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst-case MSE across all possible values of x and all possible values of the model matrix. As we show, the robust minimax MSE estimator can also be formulated as a solution to an SDP. Finally, we demonstrate through several examples that the minimax MSE estimator can significantly increase the performance over the conventional least-squares estimator, and when the model matrix is subject to uncertainties, the robust minimax MSE estimator can lead to a considerable improvement in performance over the minimax MSE estimator.     

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.     

Blind classification of the short-code and the long-code direct sequence spread spectrum signals

Direct sequence spread spectrum (DSSS) signals are now widely used for communications. According to the relationship between spreading factor and code length, the DSSS signals can be divided into two types: the short-code (SC) and the long-code (LC) DSSS. For the cooperative receivers, the above type information is known in advance. However, under the non-cooperative contexts, such information becomes one of the unknown parameters of interest. To extract this information, a blind algorithm that is based on the second-order statistics of the matrix norms of the signal correlation matrices is proposed in this study. A set of correlation matrices is constructed from the received signal samples following which the matrix norm of each correlation matrix is computed and normalised by the maximum. Then, by comparing the variance of the normalised matrix norms with a preset threshold, the type of the received DSSS signal can be identified. Simulation results verify the capability of the proposed method in various scenarios, such as multipath fading channel and multiple access interference.     

Blind channel estimation for long code multiuser CDMA systems

In CDMA systems with long codes, the users' signatures change in each bit period, impeding the estimation of the time-invariant multipath parameters. In this paper, correlation-matching methods are employed to blindly estimate those multipath parameters. For given code sequences, the output correlation matrix (parameterized by the unknown channel coefficients) is compared with its instantaneous approximation. By minimizing the Frobenius norm of the resulting error matrix, the channel parameters can be estimated up to a complex scalar ambiguity. Both batch and adaptive algorithms are derived. Under the assumption of i.i.d. code sequences, identifiability up to a complex scalar ambiguity for each channel is guaranteed, and the asymptotic convergence of the proposed algorithm is established. Furthermore, step-size selection for the adaptive version is investigated. When only the code sequence of the user of interest is available, a single user receiver is also derived. Simulation results verify those claims and provide comparisons with other methods     

Joint decorrelating multiuser detection and channel estimation inasynchronous CDMA mobile communications channels

The asymptotic efficiencies of two decorrelators, path-by-path and channel-matched decorrelators, are analyzed in fading multipath propagation environments, and based upon the analytical results, a new joint multiuser detection and channel estimation scheme is proposed for asynchronous code division multiple access (CDMA) mobile communications channels. In the path-by-path decorrelator, each of the received signals corresponding to one of the multiple propagation paths is regarded as an independent interference source. On the contrary, in the channel-matched decorrelator, each composite signal transmitted from an identical user is regarded as a response of the multipath channel to the corresponding user's spreading sequence. The asymptotic efficiency of the path-by-path decorrelator is shown to drop rapidly as the number of simultaneous users increases. It is shown that the asymptotic efficiency can be made independent of the number of the propagation paths by the channel-matched decorrelator at the expense of requiring knowledge about the fading complex envelopes of all the propagation paths. The proposed joint multiuser detection and channel estimation scheme uses both path-by-path and channel-matched decorrelators. The path-by-path decorrelator is used for providing the channel estimator with the (noisy) channel information path-by-path, and decisions are made on the output of the channel-matched decorrelator. The decision results are fed back to the channel estimator, and used as the reference signals. The received complex envelope of each of the propagation paths is estimated in the channel estimator. Results of a series of exhaustive computer simulations are presented in order to demonstrate the overall performance of the proposed scheme, both in non-fading and fading multipath propagation environments     

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

The capacity of multiple-input multiple-output (MIMO) wireless channels is limited by both the spatial fading correlation and rank deficiency of the channel. While spatial fading correlation reduces the diversity gains, rank deficiency due to double scattering or keyhole effects decreases the spatial multiplexing gains of multiple-antenna channels. In this paper, taking into account realistic propagation environments in the presence of spatial fading correlation, double scattering, and keyhole effects, we analyze the ergodic (or mean) MIMO capacity for an arbitrary finite number of transmit and receive antennas. We assume that the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is allocated to each of the transmit antennas. Using some statistical properties of complex random matrices such as Gaussian matrices, Wishart (1928) matrices, and quadratic forms in the Gaussian matrix, we present a closed-form expression for the ergodic capacity of independent Rayleigh-fading MIMO channels and a tight upper bound for spatially correlated/double scattering MIMO channels. We also derive a closed-form capacity formula for keyhole MIMO channels. This analytic formula explicitly shows that the use of multiple antennas in keyhole channels only offers the diversity advantage, but provides no spatial multiplexing gains. Numerical results demonstrate the accuracy of our analytical expressions and the tightness of upper bounds.     

Asymptotic analysis of blind cyclic correlation-based symbol-rate estimators

This paper considers the problem of blind symbol rate estimation of signals linearly modulated by a sequence of unknown symbols. Oversampling the received signal generates cyclostationary statistics that are exploited to devise symbol-rate estimators by maximizing in the cyclic domain a (possibly weighted) sum of modulus squares of cyclic correlation estimates. Although quite natural, the asymptotic (large sample) performance of this estimator has not been studied rigorously. The consistency and asymptotic normality of this symbol-rate estimator is established when the number of samples N converges to infinity. It is shown that this estimator exhibits a fast convergence rate (proportional to N/sup -3/2/), and it admits a simple closed-form expression for its asymptotic variance. This asymptotic expression enables performance analysis of the rate estimator as a function of the number of estimated cyclic correlation coefficients and the weighting matrix. A justification for the high performance of the unweighted estimator in high signal-to-noise scenarios is also provided.     

Range Estimation in a Time Varying Multipath Channel

In this paper, range estimation in a time varying multipath channel is investigated, on the basis of which a multicarrier (MC) signal is compared with its pseudo-random (PN) counterpart in terms of the Cramer-Rao lower bound (CRLB) and the maximum likelihood estimator (MLE). The CRLB for range estimation in a time varying multipath channel is derived for three cases: (1) known channel state information (CSI); (2) unknown CSI; and (3) a special case of unknown CSI where the channel is modeled via Doppler shift. Furthermore, the MLE is developed for range estimation for each one of the above three cases and is investigated for a multipath Doppler channel with respect to the separability of its multipath components. Besides, the condition for a multipath Doppler channel to be separable is explored for a PN signal as well as for a MC signal. Simulation results show that range estimation with a MC signal outperforms its PN counterpart in a time varying channel, similar as that in a time invariant channel.     

Lower bound on training-based channel estimation error for frequency-selective block-fading Rayleigh MIMO channels

A lower bound on the error correlation matrix of training-based channel estimators is derived for multiple-input multiple-output (MIMO) systems over block-fading frequency-selective channels with symbol-spaced receivers. The bound is obtained in a constructive way by evaluating the asymptotic performance of an estimator that fully exploits the algebraic structure of the multipath channel. In particular, the estimator is assumed to be able to estimate the long-term features of the channel consistently (e.g., second order statistics of fading, delays, angles) while tracking the fast-varying fading fluctuations by Wiener filtering. Known estimators that are able to attain the bound under simplified settings are referred to, and general guidelines for designing novel estimators are discussed. Based on the simple analytical expression of the bound, the impact of channel estimation error on the link capacity is investigated for different system parameters and channel characteristics (e.g., Doppler shift, spatial correlation of fading). Numerical results are provided to corroborate the analysis.     

Two EM-type channel estimation algorithms for OFDM with transmitter diversity

We study channel estimation for orthogonal frequency-division multiplexing (OFDM) systems utilizing transmitter diversity and operating over multipath fading channels. Two expectation-maximization (EM)-type algorithms are introduced and compared with each other in terms of convergence rate. At each iteration and for every OFDM link, the EM-type algorithms partition the problem of estimating a multi-input channel into independent channel estimations for each transmit-receive antenna pair, therefore avoiding the matrix inversion encountered in the joint least-square estimation. The EM-type algorithms can also be used to efficiently implement a recently proposed algorithm, termed the significant-tap-catching estimator, so that the system performance is more robust to different multipath channel delay profiles.     

Analysis and design of short block OFDM spreading matrices for use on multipath fading channels

We consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels. The main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver. We pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized. This formulation allows us to find explicit solutions for the optimal spreading matrices. The performance is validated for the uncoded channel as well as for the coded channel employing turbo-iterative decoding. We further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing (OFDM) do not gain any diversity advantage over traditional diagonal OFDM.     

Robust Channel Estimation Under Impulsive Noise for Multipath Fading CDMA Systems

This paper proposes a novel fuzzy channel estimator for direct-sequence code-division multiple-access systems with time-varying multipath fading channels under impulsive noise. The proposed estimator combines a least-squares channel estimator with a fuzzy median filter which is based on fuzzy rank ordering of samples. Simulation results clearly show the superior channel estimation success of the proposed estimator under highly impulsive noise.     

Channel estimation for OFDM transmission in multipath fadingchannels based on parametric channel modeling

We present an improved channel estimation algorithm for orthogonal frequency-division multiplexing mobile communication systems using pilot subcarriers. This algorithm is based on a parametric channel model where the channel frequency response is estimated using an L-path channel model. In the algorithm, we employ the ESPRIT (estimation of signal parameters by rotational invariance techniques) method to do the initial multipath time delays acquisition and propose an interpath interference cancellation delay locked loop to track the channel multipath time delays. With the multipath time delays information, a minimum mean square error estimator is derived to estimate the channel frequency response. It is demonstrated that the use of the parametric channel model can effectively reduce the signal subspace dimension of the channel correlation matrix for the sparse multipath fading channels and, consequently, improve the channel estimation performance     

OFDM channel estimation in the presence of interference

We develop a frequency-domain channel estimation algorithm for single-user multiantenna orthogonal frequency division multiplexing (OFDM) wireless systems in the presence of synchronous interference. In this case, the synchronous interferer's signal on each OFDM subcarrier is correlated in space with a rank one spatial covariance matrix. In addition, the interferer's spatial covariance matrix is correlated in frequency based on the delay spread of the interferer's channel. To reduce the number of unknown parameters we develop a structured covariance model that accounts for the structure resulting from the synchronous interference. To further reduce the number of unknown parameters, we model the covariance matrix using a priori known set of frequency-dependent functions of joint (global) parameters. We estimate the interference covariance parameters using a residual method of moments (RMM) estimator and the channel parameters by maximum likelihood (ML) estimation. Since our RMM estimates are invariant to the mean, this approach yields simple noniterative estimates of the covariance parameters while having optimal statistical efficiency. Hence, our algorithm outperforms existing channel estimators that do not account for the interference, and at the same time requires smaller number of pilots than the MANOVA method and thus has smaller overhead. Numerical results illustrate the applicability of the proposed algorithm.     

MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation

Multiple-input–multiple-output (MIMO) precoder design for frequency-selective fading channels using partial channel information based on the spatial and path correlation matrices is presented. By representing a frequency-selective fading channel as a multipath model with $L$ effective paths, a general precoding structure is proposed and used to derive optimum precoding designs that maximize Jensen's upper bound on the channel ergodic capacity under the transmitted power constraint for two cases, i.e., uncorrelated and correlated channel paths. Analytical results show that, in the uncorrelated case, the precoder structure consists of a number of parallel precoders for frequency-flat fading channels. The power assignment to each precoder and the power allocation over the eigenmodes of each precoder are calculated based on the power of channel paths and the eigenvalues of the transmit correlation matrix. In the correlated case, the precoder structure is an eigenbeamformer with the beams referred to a function of eigenvectors of the Kronecker product of path and transmit correlation matrices. Furthermore, the power allocated to each eigenmode can be obtained from a statistical water-pouring policy that is specified by the product of eigenvalues of the transmit antenna and path correlation matrices. Simulation results for different scenarios indicate that the proposed precoder can increase the ergodic capacity of MIMO systems in a frequency-selective fading environment with spatial and path correlations, and its offered capacity gain is increased with the level of correlation and numbers of antennas and channel paths.      

一种适用于多径信道下DSSS信号检测新方法

针对多径信道下直接序列扩频信号检测的难题,在基于自相关二阶矩的检测算法基础上提出了新的检测参数,从而将加性高斯白噪声信道下的直接序列扩频信号检测算法推广到多径信道。本文算法首先分析了由多径信道导致的能量峰值和由直扩信号的伪码特性导致的自相关峰值的特点,并根据此特点定义了新的检测参数——多径因子,最后将该参数应用到基于自相关二阶矩的直接序列扩频信号检测算法中,实现了对多径信道下的直接序列扩频信号的检测。理论分析和仿真实验表明,本文提出的检测新参数能真实的反映多径信道对信号自相关函数的影响;当信噪比大于-14dB时,本文提出的多径信道下直扩信号检测算法性能与加性高斯白噪声信道下的检测性能相当。      

空时分组码MC-CDMA系统盲干扰抑制

该文考虑空时分组码多载波码分多址(MC-CDMA)系统的盲干扰抑制。通过研究多径信号频域码空间和数据矢量空间,采用噪声子空间技术进行盲信道估计。使用一种修改的ULV更新算法进行噪声子空间跟踪,该算法不需要相关矩阵的秩估计,直接估计噪声子空间。为了抑制多址干扰(MAI),提出一种基于投影的辅助矢量(PAV)算法,用前一级滤波矢量的输出重构最大比合并(MRC)滤波矢量,将重构滤波矢量到由基本滤波矢量和前几级辅助矢量张成子空间上的正交投影作为辅助矢量,将前一级滤波矢量和新产生辅助矢量线性合并得到新的滤波矢量。仿真结果验证了该文算法的有效性。     

Performance analysis of blind carrier frequency offset estimatorsfor noncircular transmissions through frequency-selective channels

This paper deals with the problem of blind estimation of the carrier frequency offset of a linearly modulated noncircular transmission through an unknown frequency-selective channel. A frequency estimator is developed based on the unique conjugate cyclic frequency of the received signal, which is equal to twice the frequency offset. Consistency and asymptotic normality of the frequency estimator together with a closed-form expression for its asymptotic variance are also established. The closed-form expression of the asymptotic variance enables analysis of the performance of the proposed frequency offset estimator as a function of the number of estimated cyclic correlation coefficients used. It is shown that optimum is obtained if the number of correlation coefficients taken into account coincides with the degree of the channel. Numerical simulations are provided and confirm the conclusion of the theoretical asymptotic analysis     

Analysis of LMS-adaptive MLSE equalization on multipath fadingchannels

We consider a practical maximum-likelihood sequence estimation (MLSE) equalizer on multipath fading channels in conjunction with an adaptive channel estimator consisting of a least mean square (LMS) estimator and a linear channel predictor, instead of assuming perfect channel estimates. A new LMS estimator model is proposed which can accurately characterize the statistical behavior of the LMS estimator over multipath fading channels. Based on this model, a new upper-bound on block error rate is derived under the consideration of imperfect channel estimates. Computer simulations verify that our analytical results can correctly predict the real system performance and are applicable over a wide range of the step size parameter of the LMS estimator