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This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in [7], a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of unsupervised Bayesian hidden Markov chain restoration. When the hidden chain is stationary, the classical "Hidden Markov Chain" (HMC) model is quite efficient, and associated unsupervised Bayesian restoration methods using the "Expectation-Maximization" (EM) algorithm work well. When the hidden chain is non stationary, on the other hand, the unsupervised restoration results using the HMC model can be poor, due to a bad match between the real and estimated models. The novelty of this paper is to offer a more appropriate model for hidden nonstationary Markov chains, via the theory of evidence. Using recent results relating to Triplet Markov Chains (TMCs), we show, via simulations, that the classical restoration results can be improved by the use of the theory of evidence and Dempster-Shafer fusion. The latter improvement is performed in an entirely unsupervised way using an original parameter estimation method. Some application examples to unsupervised image segmentation are also provided. [ABSTRACT FROM AUTHOR]

Target tracking algorithms usually treat the probability of detection as independent of the target state. In most cases, this assumption is not true, with subsequent degradation in the target tracking performance from both expected and optimal levels. One typical example is the Doppler frequency based clutter rejection, the other is obfuscation (shadowing) of ground based targets, and the third is antijamming notch filtering. This dependence of the probability of target detection on the target trajectory state modulates the measurement likelihood, which, in turn, introduces measurement nonlinearity. In this paper, we first present a general algorithm for target tracking in clutter when the probability of detection is target state dependent, and then proceed to an algorithm where both target state estimate and the probability of detection are modeled by Gaussian mixtures. The probability of target existence is recursively updated as the track quality measure used for false track discrimination. A two-sensor-based ground maneuvering target tracking in clutter simulation validates this approach. [ABSTRACT FROM AUTHOR]

The most popular algorithms for blind equalization are the constant-modulus algorithm (CMA) and the Shalvi-Wein- stein algorithm (SWA). It is well-known that SWA presents a higher convergence rate than CMA, at the expense of higher computational complexity. If the forgetting factor is not sufficiently close to one, if the initialization is distant from the optimal solution, or if the signal-to-noise ratio is low, SWA can converge to undesirable local minima or even diverge. In this paper, we show that divergence can be caused by an inconsistency in the nonlinear estimate of the transmitted signal, or (when the algorithm is implemented in finite precision) by the loss of positiveness of the estimate of the autocorrelation matrix, or by a combination of both. In order to avoid the first cause of divergence, we propose a dual-mode SWA. In the first mode of operation, the new algorithm works as SWA; in the second mode, it rejects inconsistent estimates of the transmitted signal. Assuming the persistence of excitation condition, we present a deterministic stability analysis of the new algorithm. To avoid the second cause of divergence, we propose a dual-mode lattice SWA, which is stable even in finite-precision arithmetic, and has a computational complexity that increases linearly with the number of adjustable equalizer coefficients. The good performance of the proposed algorithms is confirmed through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to a statistical performance analysis of blind estimation of bit error rates (BER5) of a bank of detectors, using empirical estimation algorithms that have appeared in the literature (by Dixit et al.). In particular, we prove that these blind estimators asymptotically (in the number of observed bits) achieve the accuracy obtained with perfect knowledge of the transmitted bits. We propose a maximum-likelihood solution which follows from the standard expectation-maximization (EM) algorithm, considered to be a reference algorithm. Finally, the optimal fusion rule is revisited and our theoretical results are compared to Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

While the theory of estimation of monocomponent polynomial phase signals is well established, the theoretical and methodical treatment of multicomponent polynomial phase signals (mc-PPSs) is limited. In this paper, we investigate several aspects of parameter estimation for mc-PPSs and derive the Cramér-Rao bound. We show the limits of existing techniques and then propose a nonlinear least squares (NLS) approach. We also motivate the use the Nelder-Mead simplex algorithm for minimizing the nonlinear cost function. The slight increase in computational complexity is a tradeoff for improved mean square error performance, which is evidenced by simulation results. [ABSTRACT FROM AUTHOR]

In array signal processing, high-resolution direction-of-arrival (DOA) estimation algorithms are known to be sensitive to system errors. In practice, the system should be properly calibrated before DOA estimation. In this paper, a calibration method of gain and phase errors of linear equispaced arrays (LEAs) is considered. A class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed. The statistical performance analyses of the calibration algorithms due to finite data perturbations are presented. Expressions for average bias (Abias) and square root of average variance (SRAV) of the calibration algorithms are derived using first-order approximation. These statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations, the more inferior performance that may be obtained. Based on this conclusion, the simple and optimal gain and phase error calibration algorithms for such model are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel joint algorithm to estimate the symbol timing and carrier frequency offsets of wireless orthogonal frequency division multiplexing (OFDM) signals. To jointly estimate synchronization parameters using the maximum likelihood (ML) criterion, researchers have derived conventional models only from additive white Gaussian noise (AWGN) or single-path fading channels. We develop a general ML estimation algorithm that can accurately calculate symbol timing and carrier frequency offsets over a fast time-varying multipath channel. To reduce overall estimation complexity, the proposed scheme consists of two estimation stages: coarse and fine synchro nizations. A low complexity coarse synchronization based on the least-squares (LS) method can rapidly estimate the rough symbol timing and carrier frequency offsets over a fast time-varying multipath channel. The subsequent ML fine synchronization can then obtain accurate final results based on the previous coarse synchronization. Simulations demonstrate that the coarse-to-fine method provides a good tradeoff between estimation accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

In some practical applications of array processing, the directions of the incident signals should be estimated adaptively, and/or the time-varying directions should be tracked promptly. In this paper, an adaptive bearing estimation and tracking (ABEST) algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow-band signals impinging on a uniform linear array (ULA) based on the subspace-based method without eigendecomposition (SUMWE), where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property. Specifically, the null space is estimated using the least-mean-square (LMS) or normalized LMS (NLMS) algorithm, and the directions are updated using the approximate Newton method. The transient analyses of the LMS and NLMS algorithms are studied, where the "weight" (i.e., the linear operator) is in the form of a matrix and there is a correlation between the "additive noise" and "input data" that involve the instantaneous correlations of the received array data in the updating equation, and the step-size stability conditions are derived explicitly. In addition, the analytical expressions for the mean-square error (MSE) and mean-square deviation (MSD) learning curves of the LMS algorithm are clarified. The effectiveness of the ABEST algorithm is verified, and the theoretical analyses are corroborated through numerical examples. Simulation results show that the ABEST algorithm is computationally simple and has good adaptation and tracking abilities. [ABSTRACT FROM AUTHOR]

In this paper, a new computationally simple approach to blind decoding of orthogonal space-time block codes (OSTBCs) is proposed. Using specific properties of OSTBCs, the authors' approach estimates the channel matrix in a closed form and in a fully blind fashion. This channel estimate is then used in the maximum-likelihood (ML) receiver to decode the information symbols. The proposed estimation technique provides consistent channel estimates, and, as a result, the performance of the authors' blind ML receiver approaches that of the coherent ML receiver, which exploits the exact channel state information (CSI). Simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space-time modulation scheme. [ABSTRACT FROM AUTHOR]