Performance analysis of MUSIC-type high resolution estimators for direction finding in correlated and coherent scenes

Abstract

An asymptotic analysis is presented of a class of high-resolution estimators for resolving correlated and coherent plane waves in noise. These estimators are in turn constructed from certain eigenvectors associated with spatially smoothed (or unsmoothed) covariance matrices generated from a uniform array. The analysis is first carried out for the smoothed case, and from this the conventional (i.e., unsmoothed) multiple signal classification (MUSIC) scheme follows as a special case. Independent of the total number of sources present in the scene, the variance of the conventional MUSIC estimator along the true arrival angles is shown to be zero within a first-order approximation. The bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent, equipowered plane waves in white noise, and the result is compared to the one derived by Kaveh et al. (1986) for two uncorrelated, equipowered plane waves.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>