Array Manifold Effects In Signal Subspace Techniques
Jeffrey M. Speiser, Hal B. Arnold · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
This paper examines the effect of array geometry on signal detection and signal estimation using the Schmidt MUSIC algorithm and related techniques. Upper and lower bounds are found for the separation between signal and noise eigenvalues as a function of the eigenvalues of the beam response matrix and the source correlation matrix. It is shown that the condition number of the steering phase shift matrix is determined almost entirely by its smallest singular value. Limited numerical evaluations for planar arrays suggest that the smallest singular value is determined by arrival spacing relative to array aperture, and is insensitive to the details of the array geometry. For the special case when all arrivals are closely spaced, it is shown that the steering phase shift matrix is the product of a Vandermonde matrix depending on the arrival spacing with a second matrix determined by the array geometry.