Pascal Vallet

Performance Analysis of an Improved MUSIC DoA Estimator

This paper addresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while this is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.

An improved music algorithm based on low rank perturbation of large random matrices

This paper is devoted to subspace DoA estimation, when the number of available snapshots N is of the same order of magnitude as the number of sensors M. In this context, traditional subspace methods fail because the empirical covariance matrix of the observations is a poor estimate of the true covariance matrix. The goal of the paper is to propose a new consistent estimator of the DoAs in the case where M, N → + ∞ at the same rate, using large random matrix theory. It is assumed that the number of sources is constant, and recent results on the so called spiked matrix models are used. First and second order results are provided

Performance Analysis of Spatial Smoothing Schemes in the Context of Large Arrays

This paper addresses the statistical behavior of spatial smoothing subspace DoA estimation schemes using a sensor array in the case where the number of observations

Asymptotic analysis of a consistent subspace estimator for observations of increasing dimension

N

A statistical comparison between music and G-music

is significantly smaller than the number of sensors

Performance analysis of spatial smoothing schemes in the context of large arrays

M

On the consistency of the G-MUSIC DoA estimator

, and that the smoothing parameter

On the Performance of MUSIC With Toeplitz Rectification in the Context of Large Arrays

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On the statistical performance of music for distributed sources

is such that

Analysis of a GLRT for the detection of an extended target

M