The Resolution Threshold of MUSIC with Unkown Spatially Colored Noise
C. Zhou, F. Haber, D.L. Jaggard · IEEE Transactions on Signal Processing · 1993
In this correspondence, we present a resolution analysis for the MUSIC algorithm in a spatially colored noise environment. By applying Wilkinson's first-order perturbation theory to the colored- noise term, we have shown that the MUSIC spectrum estimates at spa- tial frequencies of plane wave arrivals are proportional to the square of array signal-to-interference ratio (ASIR), and that the resolution threshold ASIR for a uniform array is proportional to the inverse square of normalized spatial frequency separation between two ar- rivals. Derivations and simulations are given for the case of two equi- power plane wave arrivals. The presence of unknown spatially colored noise in spatial fre- quency estimation of plane wave arrivals can cause significant per- formance degradation for the MUSIC algorithm. For signal arrivals in a spatially white-noise environment, a complete eigenspace sep- aration between signal subspace and noise subspace can be ob- tained, and MUSIC spectrum exhibits infinite peaks at signal fre- quencies. In a spatially colored noise (SCN) environment, an eigenspace separation with such properties can be made only if the correlation structure of the SCN is known a priori (I). For an un- known SCN, any partitioned subspace designated as the signal sub- space will include components from part of the SCN, and the or- thogonal relation between signal direction vectors and the noisc subspace will be destroyed. As a result,' spectral peaks in the MU- SIC estimator are finite and resolutions are limited. In this paper, spatially colored noise (SCN) is radiation sources whose spatial correlation matrix has a nonidentity structure. Spa- tially colored noise typically arises from sources continuously dis- tributed in spatial frequency. Examples are cosmic noise and at- mospheric noise. It also arises from additive sensor noise sources when they are nonwhite with unknown correlations or, when they are uncorrelated but of unequal powers. Mathematically, SCN may be represented by a matrix component Q in a spatial correlation matrix R (1)