MUSIC, maximum likelihood and Cramer-Rao bound: further results and comparisons

A number of results have been presented recently on the statistical performance of the multiple signal characterization (MUSIC) and the maximum-likelihood (ML) estimators for determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements. It is shown that in the class of weighted MUSIC estimators, the unweighted MUSIC achieves the best performance (i.e. the minimum variance of estimation errors) in large samples. The covariance matrix of the ML estimator is derived, and detailed analytic studies of the statistical efficiency of MUSIC and ML estimators are presented. These studies include performance comparisons of MUSIC and MLE with each other as well as with the ultimate performance corresponding to the Cramer-Rao bound (CRB).