Theoretical comparison for biases of MUSIC-like DOA estimators

Many MUSIC-like DOA estimators, such as Min-Norm, Beamspace MUSIC, Likelihood MUSIC, FINE and FINES, have been proposed to improve the performance of MUSIC. Since in the difficult estimation situations the large-sample bias of MUSIC may become the dominant estimation error, a comparative study of biases of MUSIC-like estimators in these cases is necessary for their performance evaluation. This paper first identifies the dominant part of the bias of MUSIC for two closely-spaced sources. Then the paper presents a theoretical analysis of a hierarchy of the performances of these MUSIC-like estimators based on their abilities at reducing this major part of the bias and maintaining the asymptotic variance of MUSIC. The theoretical results in the paper explain analytically many previous observations resulting from simulations and numerical computations and may be useful for developing new MUSIC-like algorithms with reduced resolution threshold over that of MUSIC.