Robust M-Estimation for Array Processing: A Random Matrix Approach

This article studies the limiting behavior of a robust M-estimator of population covariance matrices as both the number of available samples and the population size are large. Using tools from random matrix theory, we prove that the difference between the sample covariance matrix and (a scaled version of) the robust M-estimator tends to zero in spectral norm, almost surely. This result is applied to prove that recent subspace methods arising from random matrix theory can be made robust without altering their first order behavior.