Large-sample analysis of MUSIC and Min-Norm direction estimators in the presence of model errors

Abstract

We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. We separate the contributions to the MSE into a bias part caused by modelling errors and a variance part caused by finite (yet large) sample effects. The bias is simply evaluated by comparing the limiting estimate (corresponding to an infinite number of snapshots) with the true DOAs (which are known to the analyzer). To simplify the variance derivation we assume that the snapshots are complex i.i.d. Gaussian vectors and that the largest eigenvalues of their covariance matrix are distinct, but,otherwise, make none of the assumptions commonly used in previous analyses; in particular we do not constrain the snapshots to satisfy any model equation. The theoretical results obtained are illustrated by means of numerical examples using various modelling errors.