Further Results of the Analysis of the Music for Closely Spaced, Non-Equal Power Plane Waves

In this paper, a detailed performance analysis of the multiple signal classification (MUSIC) algorithm for non-resolvable sources with non-equal power is carried out. The signals considered consist of clusters of sources, in which the directions of arrival (DOAs) of the sources are close in each cluster. Only one of the source is of interest, while the others are treated as interferences. In this scenario, the estimation accuracy is influenced by both the finite sample effect and the perturbation caused by the interferences, the latter of which is the focus of this paper. By using the first order of the Taylor series expansion of the perturbation caused by the interferences, the bias of the DOAs are derived in a closed form. It is shown that if the closely spaced signals exist, the MUSIC algorithm become biased, and the bias depends on their power and the distance between their DOAs. Simulation results are also conducted to verify the derived analytic expressions.