Enumeration of fully correlated signals by modified rank sequences

A method for determining the number of sources impinging on a uniform linear array, which is applicable even in the extreme case of fully correlated sources, is presented. This technique uses modified rank sequences, a modification of the construction implicit in the matrix decomposition methods of A. Di (1985). The authors prove that if a particular rank sequence stabilizes to a value strictly less than the common row size of the defining block matrices, then this value equals the number of sources provided that the number has not exceeded a Bressler-Macovski (1986) type bound. Using the above characterization of stability, they formulate an algorithm that 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 threshold that approximates the largest singular value of the error matrix is determined and used to separate the large and small singular values of the matrices that induce the rank sequence