BY MODIFIED RANK SEQUENCES
John H. Cozzens, Robert C. DiPiedro, Michael J. Sousa · 1989
We present a simple method for determining the number of sources impinging on a uniform linear array, a method which is applicable even in the extreme case of fully correlated sources. This technique uses what we term modified rank sequences, a modification of the construction implicit in the matrix decomposition methods of Di 141. We prove that if a particular rank sequence stabilizes (the last two terms of the sequence are equal) to a value strictly less then the common row size of the defining block matrices, then this value equals the number of sources provided that the number of sources has not exceeded a Bressler-Macovski type bound [2]. Using the above characterization of stability, we formulate an algorithm which either determines the number of sources, or indicates that the resolution capability of the algorithm has been exceeded. Rank determinations are based on an additive perturbation model. A threshhold, which approximates the largest singular value of the error matrix, is determined and then used to separate the “large” and the “small” singular values of the matrices which induce the rank sequence.