Robust spiked random matrices and a robust G-MUSIC estimator

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 (Couillet et al., 2013) (restricted to a noise only setting) 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.