Asymptotic properties of robust complex covariance matrix estimates

TL;DR

This paper investigates the asymptotic behavior of robust complex covariance matrix estimators, extending Tyler's results to complex data and demonstrating their effectiveness in signal processing applications like DOA estimation and radar detection.

Contribution

It extends Tyler's asymptotic distribution results to complex elliptical distributions and analyzes their impact on practical signal processing algorithms.

Findings

Asymptotic distribution of complex M-estimators derived

Improved performance in DOA estimation with MUSIC algorithm

Enhanced radar detection using adaptive covariance estimates

Abstract

In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses on covariance matrix estimation problems in non-Gaussian environments and particularly, the M-estimators in the context of elliptical distributions. Firstly, this paper extends to the complex case the results of Tyler in [1]. More precisely, the asymptotic distribution of these estimators as well as the asymptotic distribution of any homogeneous function of degree 0 of the M-estimates are derived. On the other hand, we show the improvement of such results on two applications: DOA (directions of arrival) estimation using the MUSIC (MUltiple SIgnal Classification) algorithm and adaptive radar detection based on the ANMF (Adaptive Normalized Matched Filter) test.