Comparative study of the biases of MUSIC-like estimators

Abstract

This paper presents a theoretical analysis of the bias of a number of spectral MUSIC-like estimators of the directions of arrival of two closely spaced plane waves. The dominant part of the bias of MUSIC for two closely spaced sources is first identified. Then the performances of Beamspace MUSIC, Weighted-Norm MUSIC, such as Likelihood MUSIC, and Weighted MUSIC, such as Minimum-Norm, FINE and FINES, are analyzed in terms of the degree by which these estimators reduce this dominant part of the MUSIC bias, while incurring an increase in asymptotic variance over the asymptotic variance of MUSIC. The results explain, analytically, many previous observations resulting from simulations and numerical computations of the bias expressions, and may be useful in the development of new MUSIC-like algorithms with reduced bias and resolution threshold over those of MUSIC.