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• The asymptotic distribution of the projector associated with the SCM is given for arbitrary distributions of the useful signal and noise with finite fourth-order moments. • The asymptotic distribution of the DOA estimate given by the MUSIC algorithm is proved for both nonparametric non-Gaussian noise and parametric CES noise models. Theoretical evaluation of the loss of performance is given for heavy-tailed distributions of the noise which is significant for weak SNR and closely spaced sources. • For CES distributed observations, the asymptotic distribution of the projector associated with any M -estimate of the covariance matrix is given. This allows us to prove that this loss of performance can be alleviated. • These theoretical results are confirmed by some simulations performed with either a complex circular Student t -distribution or a complex generalized Gaussian distribution of the noise or the observations model. This paper addresses the theoretical analysis of the robustness of subspace-based algorithms with respect to non-Gaussian noise distributions using perturbation expansions. Its purpose is twofold. It aims, first, to derive the asymptotic distribution of the estimated projector matrix obtained from the sample covariance matrix (SCM) for arbitrary distributions of the useful signal and the noise. It proves that this distribution depends only of the second-order statistics of the useful signal, but also on the second and fourth-order statistics of the noise. Second, it derives the asymptotic distribution of the estimated projector matrix obtained from any M -estimate of the covariance matrix for both real (RES) and complex elliptical symmetric (CES) distributed observations. Applied to the MUSIC algorithm for direction-of-arrival (DOA) estimation, these theoretical results allow us to theoretically evaluate the performance loss of this algorithm for heavy-tailed noise distributions when it is based on the SCM, which is significant for weak signal-to-noise ratio (SNR) or closely spaced sources. These results also make it possible to prove that this performance loss can be alleviated by replacing the SCM by an M -estimate of the covariance for CES distributed observations, which has been observed until now only by numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of testing impropriety (i.e., second-order noncircularity) of a sequence of complex-valued random variables (RVs) based on the generalized likelihood ratio test (GLRT) for Gaussian distributions is considered. Asymptotic (w.r.t. the data length) distributions of the GLR are given under the hypothesis that RVs are proper or improper, and under the true, not necessarily Gaussian distribution of the RVs. The considered RVs are independent but not necessarily identically distributed: assumption which has never been considered until now. This enables us to deal with the practical important situations of noncircular RVs disturbed by residual frequency offsets and additive circular noise. The receiver operating characteristic (ROC) of this test is derived as byproduct, an issue previously overlooked. Finally illustrative examples are presented in order to strengthen the obtained theoretical results. [Copyright &y& Elsevier]

Abstract: A performance analysis of likelihood ratio test (LRT)-based and generalized likelihood ratio test (GLRT)-based array receivers for the detection of a known real-valued signal corrupted by a potentially noncircular interference is considered in this paper. The distribution of the decision statistics associated with the LRT and GLRT is studied. This allows us to give exact closed-form expressions of the probability of detection (P D) and false alarm (P FA) for two LRT-based receivers. Then, asymptotic (with respect to the data length) closed-form expressions are given for P D and P FA for four GLRT-based receivers. Finally, in order to strengthen the obtained results, some illustrative examples are presented. [Copyright &y& Elsevier]

Abstract: In many detection applications, the main performance criterion is the signal to interference plus noise ratio (SINR). After linear filtering, the optimal SINR corresponds to the maximum value of a Rayleigh quotient, which can be interpreted as the largest generalized eigenvalue of two covariance matrices. Using an extension of Szegö''s theorem for the generalized eigenvalues of Hermitian block Toeplitz matrices, an expression of the theoretical asymptotic optimal SINR w.r.t. the number of taps is derived for arbitrary arrays with a limited but arbitrary number of sensors and arbitrary spectra. This bound is interpreted as an optimal zero-bandwidth spatial SINR in some sense. Finally, the speed of convergence of the optimal wideband SINR for a limited number of taps is analyzed for several interference scenarios. [Copyright &y& Elsevier]

• This paper derives interpretable unified closed-form expressions for the threshold ASNR along the Cox and the Sharman and Durrani criteria associated with the conventional MUSIC and NC MUSIC algorithms in the context of arbitrary circular or rectilinear distributed correlated sources and circular CES distributed noise. • Using these expressions, we investigate the impact of the non-Gaussianity of the noise, as well as of the phase and magnitude of the correlation of the sources. • In particular, we prove for the first time that the phase of the correlation, which is the non-circularity phase separation for rectilinear sources, may have a strong impact on the resolution and a zero phase may lead to overly optimistic resolution. • We quantify the resolution benefit provided when the SCM is replaced by M - estimates of the covariance matrix for CES observations. The concept of threshold array signal-to-noise ratio (ASNR) which is defined as the minimal SNR at which specific high-resolution algorithms are able to resolve two closely spaced far-field sources, allows to quantify and to compare sensors array performance in localizing remote targets. This paper generalizes and extends the expressions of the threshold ASNR given in the literature for the conventional and non-circular (NC) MUSIC direction-of-arrival (DOA) estimation algorithms in the context of uncorrelated stochastic circular or rectilinear Gaussian sources and circular complex Gaussian (C-CG) noise, in a more general stochastic framework. We assume that the sources are correlated with an arbitrary distribution, which is inherent in a context of multipath or smart jammers, and that the noise is circular complex elliptically symmetric (C-CES) distributed, which can model impulsive noise with heavy-tailed distributions. The C-CES and NC-CES distributed observations are also considered to quantify the gain in resolution provided when the sample covariance matrix (SCM) of the observations is replaced by M -estimates of this matrix. Asymptotic approaches and perturbation analysis have been performed to derive closed-form expressions of the mean null spectra of the two considered MUSIC algorithms for both observation models, which allow us to derive, for the first time, general unified explicit analytical expressions of the threshold ASNR along the Cox and the Sharman and Durrani criteria. These expressions allow us to quantify the impact of the non-Gaussianity of noise and observations, as well as of the phase and magnitude of the correlation on the resolution threshold, and to quantify the benefit provided when the SCM is replaced by M -estimates of this covariance matrix for CES observations. Finally, numerical illustrations are included to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of signal-to-interference-plus-noise ratio (SINR). The criterion used by Zatman to define a narrowband environment, i.e., the ratio between the jammer plus noise covariance matrix and the noise eigenvalue, is studied from the point of view of a loss of SINR after narrowband beamforming under non narrowband conditions. Using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by Lee, it is shown that Zatman's criterion can be interpreted as an upper bound on the SINR loss which is nearly reached under certain conditions that are specified. [ABSTRACT FROM AUTHOR]

This letter addresses the stochastic Cramer-Rao bound (CRB) pertaining to the joint estimation of the carrier frequency offset, the carrier phase and the noise and signal powers of binary phase-shift keying (BPSK), minimum shift keying (MSK), and quaternary phase-shift keying (QPSK) modulated signals corrupted by additive white circular Gaussian noise. Because the associated models are governed by simple Gaussian mixture distributions, an explicit expression of the Fisher information matrix is given and an explicit expression for the stochastic CRB of these four parameters are deduced. Specialized expressions for low and high SNR are presented as well. Finally. these expressions are related to the modified CRB and our proposed analytical expressions are numerically compared with the approximate expressions previously given in the literature. [ABSTRACT FROM AUTHOR]