Resolution Threshold for Closely Spaced Noncircular Emitters

This paper addresses the resolution of the standard and non-circular MUSIC algorithms for arbitrary distribution and non-circularity of two closely spaced transmitters. Using an analysis based on perturbations of the noise projector instead of those of the eigenvectors, interpretable closed-form expressions of the threshold array signal to noise ratios (ASNR) at which these two algorithms are able to resolve the transmitters along the Cox and the Sharman and Durrani criteria are given. We prove in particular that the threshold ASNRs given by the noncircular MUSIC algorithm are sensitive to the non-circularity phase separation of the sources and are comfortably smaller that those given by the standard MUSIC algorithm. Numerical examples illustrate these results.