Robust spiked random matrices and a robust G-MUSIC estimator

TL;DR

This paper introduces a robust scatter estimator for spiked random matrices with impulsive noise, characterizes its spectral properties, and develops an improved array processing algorithm called robust G-MUSIC for angle of arrival estimation.

Contribution

It generalizes previous models to spiked random matrices, fully characterizes the spectrum of the robust estimator, and proposes a new robust G-MUSIC algorithm for practical array processing.

Findings

Robust estimator has bounded spectrum unlike sample covariance matrices.

Isolated eigenvalues enable statistical inference beyond a detectability threshold.

The robust G-MUSIC algorithm improves angle of arrival estimation accuracy.

Abstract

A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random matrix models. It is precisely shown that, as opposed to sample covariance matrices which may have asymptotically unbounded (eigen-)spectrum due to the sample impulsiveness, the robust estimator of scatter has bounded spectrum and may contain isolated eigenvalues which we fully characterize. We show that, if found beyond a certain detectability threshold, these eigenvalues allow one to perform statistical inference on the eigenvalues and eigenvectors of the information matrix. We use this result to derive new eigenvalue and eigenvector estimation procedures, which we apply in practice to the popular array processing problem of angle of arrival estimation. This gives birth to an improved algorithm based on the MUSIC method, which we refer to as robust G-MUSIC.