Analysis of the asymptotic relative efficiency of the MUSIC algorithm

An analytical performance evaluation of the errors of the direction-of-arrival estimates obtained by the MUSIC algorithm for uncorrelated sources is provided. Explicit asymptotic formulas are derived for the means and the covariance of the estimates. The covariances are then compared to the Cramer-Rao lower bound. It is shown that for a single course, the MUSIC algorithm is asymptotically efficient. For multiple sources, the algorithm is not efficient in general. However, it approaches asymptotic efficiency when the SNRs (signal-to-noise ratios) of all sources tend to infinity. It is illustrated by several test cases that the relative efficiency of the MUSIC algorithm is nearly one under a wide range of parameter variations. The analytic performance evaluation thus confirms empirical evidence to the excellent performance of the MUSIC algorithm for narrowband signals