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Abstract: This paper addresses asymptotically minimum variance (AMV) of parameter estimators within the class of algorithms based on second-order statistics for estimating parameter of strict-sense stationary complex circular processes. As an application, the estimation of the frequencies of cisoids for mixed spectra time series containing a sum of cisoids and an MA process is considered. [Copyright &y& Elsevier]

The purpose of this paper is to determine the domain of validity of spatial covariance-based narrowband DOA algorithms when processing non-narrowband data. By focusing on the case of one source and two equipowered uncorrelated sources of the same bandwidth, we examine order detection and asymptotic bias and covariance w.r.t. the bandwidth and the number of snapshots given by any narrowband algorithm. An order detector scheme, based on numerical analysis arguments introduced in channel order detection, is proposed. Closed-form expressions are given for the asymptotic bias and covariance of the DOA''s estimated by the MUSIC algorithm, for which we show the key role that bandwidth plays w.r.t. the demodulation frequency. Furthermore, a common closed-form expression of the Cramer–Rao bound is given for the DOA parameter of a narrowband or wideband source, whose spectrum is symmetric w.r.t. the demodulation frequency, in the case of an arbitrary array. This allows us to prove that the MUSIC algorithm retains its efficiency over a large bandwidth range under these conditions. [Copyright &y& Elsevier]

• This paper has shown that all the NC subspace-based algorithms built from the SCM designed for uncorrelated rectilinear sources embedded in spatially white CCG noise can be also applied for correlated rectilinear sources in the contexts of SCM estimate with C-CES noise and M-estimate with NC-CES observations. • A perturbation analysis has been performed to derive closed-form expressions for the asymptotic covariance matrices of DOA estimates for three NC MUSIC-like algorithms in two CES data models. • Interpretable closed-form expressions of the asymptotic variance of the estimated DOA of two equi-power correlated sources has been derived for the first time. • A number of properties that highlight how the asymptotic variances of NC MUSIClike DOA estimation algorithms depend on key parameters such as SNR, DOA and phase separations, correlation factor and C-CES noise parameters were derived. • Analytical robustness results were illustrated proving that the use of robust Mestimators enhances the robustness of the subspace-based DOA estimation algorithms against heavy-tailed C-CES observations model deviations, with negligibleloss in performance for C-CG distributed observations. This paper focuses on a theoretical performance analysis of subspace-based algorithms for the localization of spatially correlated rectilinear sources embedded in circular complex elliptically symmetric (C-CES) distributed noise model and also when the observations are non-circular CES (NC-CES) distributed with dependent scatter matrices on the direction of arrival (DOA) parameters. A perturbation analysis has been performed to derive closed-form expressions for the asymptotic covariance matrices of DOA estimates for non-circular subspace-based algorithms in two CES data models. Robustness of subspace-based algorithms is theoretical evaluated using robust covariance matrix estimators (instead of the sample covariance matrix (SCM)). We prove, for the first time, interpretable closed-form expressions of the asymptotic variance of the estimated DOA of two equi-power correlated sources, which allows us to derive a number of properties describing the DOA variance's dependence on signals parameters and non-Gaussian distribution of the noise. Different robustness properties are theoretically analyzed. In particular, we prove in the framework of NC-CES distributed observations, that Tyler's M -estimator enhances the performance for heavy-tailed distributions w.r.t. the SCM, with negligible loss in performance for circular Gaussian distributed observations. Finally, some Monte Carlo illustrations are given for quantifying this robustness and specifying the domain of validity of our theoretical asymptotic results. [ABSTRACT FROM AUTHOR]

• Asymptotic (in the number of measurements) distributions of estimates of the orthogonal projector associated with different M -estimates of the covariance matrix in the context of RES, C-CES, and NC-CES distributed observations whose covariance is low rank structured are given in the same framework. • The asymptotically minimum variance (AMV) subspace-based estimator of the parameter of interest characterized by the column subspace of the mixing matrix for general linear mixtures models, associated with the M -estimates of the covariance matrix is derived. • A common closed-form expression of the AMV bound which can be used as a benchmark against which any subspace-based algorithms are tested is derived. • It is proved that the AMV bound attains the stochastic CRB in the case of ML M -estimate of the covariance matrix for RES, C-CES, and NC-CES distributed observations • We specify the conditions for which the AMV bound based on Tyler's M -estimate attains this stochastic CRB for complex Student t and complex generalized Gaussian distributions. • It is proved that the stochastic CRB is equal to the semiparametric CRB recently introduced for this model. Subspace-based algorithms that exploit the orthogonality between a sample subspace and a parameter-dependent subspace have proved very useful in many applications in signal processing. The purpose of this paper is to complement theoretical results already available on the asymptotic (in the number of measurements) performance of subspace-based estimators derived in the Gaussian context to real elliptical symmetric (RES), circular complex elliptical symmetric (C-CES) and non-circular CES (NC-CES) distributed observations in the same framework. First, the asymptotic distribution of M -estimates of the orthogonal projection matrix is derived from those of the M -estimates of the covariance matrix. This allows us to characterize the asymptotically minimum variance (AMV) estimator based on estimates of orthogonal projectors associated with different M -estimates of the covariance matrix. A closed-form expression is then given for the AMV bound on the parameter of interest characterized by the column subspace of the mixing matrix of general linear mixture models. We also specify the conditions under which the AMV bound based on Tyler's M -estimate attains the stochastic Cramér-Rao bound (CRB) for the complex Student t and complex generalized Gaussian distributions. Finally, we prove that the AMV bound attains the stochastic CRB in the case of maximum likelihood (ML) M -estimate of the covariance matrix for RES, C-CES and NC-CES distributed observations, which is equal to the semiparametric CRB (SCRB) recently introduced. [ABSTRACT FROM AUTHOR]