ABF limitations when using either Toeplitz covariance matrix estimators or the parametric vector AR technique

Two methods which have been proposed for estimating adaptive beamformer weights from a small number of samples are the parametric vector AR technique and the use of Toeplitz covariance matrix estimation. In this paper the relationship between these two techniques is derived. This relationship is used to show that both methods have the same performance limitations when used with antenna arrays which are not precisely uniform linear (or uniform rectangular for two dimensional arrays). In the presence of non-ideal arrays it is shown that both methods degrade to performance levels consistent with deterministic (i.e. non-adaptive) nulling.