# A Joint Robust Estimation and Random Matrix Framework with Application to Array Processing

Conference Paper

### Authors:

Romain Couillet; Frédéric Pascal; Jack W. Silverstein

ICASSP (2013)

### Abstract:

An original interface between robust estimation theory and random matrix theory for the estimation of population covariance matrices is proposed. Consider a random vector $x = AN y ∈ C N$ with $y ∈ C M$ made of $M ≥ N$ independent entries, E[y] = 0, and $E[yy^∗] = IN$. It is shown that a class of robust estimators $CˆN$ of $CN = AN A^∗N$ , obtained from $n$ independent copies of $x$, is $(N, n)$-consistent with the traditional sample covariance matrix $SˆN$ in the sense that $kCˆN − αSˆN k → 0$ in spectral norm for some $α > 0$, almost surely, as $N, n → \infty$ 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.

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