MUSICs and Cramer-Rao bound in fourth-order cumulant domain

A unifying asymptotic performance analysis of a class of MUSIC algorithms for direction-of-arrival (DOA) estimation in fourth-order cumulant domain (FOCD-MUSIC) is presented in this paper. A simple and explicit formula for the asymptotic variances of DOA estimation by FOCD-MUSIC's is given. The Cramer-Rao bound for DOA estimation in fourth-order cumulant domain (FOCD-CRB) is also derived. The performances of three typical FOCD-MUSICs and the conventional covariance-based MUSIC are compared. It is shown that the FOCD-MUSICs are inefficient and they are not superior to the conventional MUSIC algorithm in any case. Nevertheless, the FOCD-MUSICs outperform the conventional MUSIC with reduced variances and improved robustness when the spatial sources are closely spaced and the signal-to-noise ratios (SNRs) are relatively low. Simulations are included to validate the analytical results.