SOURCE ENUMERATION IN A CORRELATED SIGNAL ENVIRONMENT

In this paper, we present a simple method for determining the number of signals impinging on a uniform linear array that is applicable even in the extreme case of fully correlated signals. This technique uses what we term modified rank sequences, which is a modification of the construction implicit in the matrix decomposition method of Di. 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 signals, provided that the number of signals has not exceeded a Bresler-Macovski-type bound. Using the above characterization of stability, we formulate an algorithm that either determines the number of signals or indicates that the resolution capability of the algorithm has been exceeded. We also provide theorems that show that under certain conditions, a rank sequence can stabilize to a value strictly less than the number of signals. This result allows us to find simple counterexamples to all of the existing rank sequence methods.