Finite sample and modelling error effects on ESPRIT and MUSIC direction estimators

The large-sample mean square error (MSE) of MUSIC and ESPRIT direction-of-arrival (DOA) estimators under fairly general conditions is analysed. First, an expression for the MSE of ESPRIT is derived, in a manner similar to a previous analysis of MUSIC. The essential assumption made to evaluate the variance of the estimates is that the snapshots are i.i.d. complex Gaussian vectors. This assumption includes almost any kind of deterministic error in the array manifold or noise covariance as special cases. Next, small random errors in the model of the array manifold are examined to derive the variance of both ESPRIT and MUSIC. Under this assumption the DOA´s bias is zero (to within a first-order approximation) and the variance is composed of two terms: one describes the effect of processing a finite (yet large) sample; the other is caused by modelling errors. The results are illustrated by means of numerical examples using different modelling errors