This paper studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random matrix theory, we prove that, for sample vectors made of independent entries having some moment conditions, the difference between the sample covariance matrix and (a scaled version of) such robust estimator tends to zero in spectral norm, almost surely. This result can be applied to various statistical methods arising from random matrix theory that can be made robust without altering their first order behavior.

An original interface between robust estimation theory and random matrix theory for the estimation of population covariance matrices is proposed. Consider a random vector x = ANy ∈ CNwith y ∈ CMmade of M ≥ N independent entries, E[y] = 0, and E[yy*] = IN. It is shown that a class of robust estimators ĈNof CN= ANA*N, obtained from n independent copies of x, is (N, n)-consistent with the traditional sample covariance matrix r̂Nin the sense that ∥ĈN- αr̂N∥ → 0 in spectral norm for some α > 0, almost surely, as N, n → ∞ with N/n and M/N bounded. This result, in general not valid in the fixed N regime, is used to propose improved subspace estimation techniques, among which an enhanced direction-of-arrival estimator called robust G-MUSIC.

In this article, novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided. These results are used to characterize the ergodic rate region of multiple antenna multiple access channels, when each point-to-point propagation channel is modelled according to the Kronecker model. Specifically, an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water-filling algorithm to obtain these precoders are provided. An original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides. The above results are validated by Monte Carlo simulations.

In this paper, a new method is introduced to blindly estimate the transmit power of multiple signal sources in multiantenna fading channels, when the number of sensing devices and the number of available samples are sufficiently large compared to the number of sources. Recent advances in the field of large dimensional random matrix theory are used that result in a simple and computationally efficient consistent estimator of the power of each source. A criterion to determine the minimum number of sensors and the minimum number of samples required to achieve source separation is then introduced. Simulations are performed that corroborate the theoretical claims and show that the proposed power estimator largely outperforms alternative power inference techniques.

This paper introduces a new method to estimate the power transmitted by multiple signal sources, when the number of sensing devices and the available samples are sufficiently large compared to the number of sources. This work makes use of recent advances in the field of random matrix theory that prove more efficient than previous “moment-based” approaches to the problem of multi-source power detection. Simulations are performed which corroborate the theoretical claims.