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

The problem of 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 are studied. A number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization (MUSIC) and the maximum likelihood (ML) estimators for the above problems. This work extends those results in several directions. First, it establishes 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. Next, it derives the covariance matrix of the ML estimator and presents detailed analytic studies of the statistical efficiency of MUSIC and ML estimators. 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. Finally, some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays