The optimum weight of angle-dependent weighted MUSIC and its approximations

Angle-dependent weighted MUSIC or weighted norm MUSIC is a broad class of MUSIC-like parameter estimators which includes as special case the standard “spectral” MUSIC. Based on a general approach for deriving the point statistics of the signal-subspace estimators, the relation between the large-sample moments of MUSIC and angle-dependent weighted MUSIC is presented in this paper. The optimum weight function resulting in the estimator with zero bias of order N^-1 is derived. The approximate realizations of this optimum estimator in a parametric subclass of angle-dependent weighted MUSIC for arrays measuring closely spaced sources are discussed. Simulation examples verify the theoretical analysis and demonstrate the proposed estimators have small estimation biases over a wide range of signal-to-noise ratio