Matrix decomposition and multiple source location

In this paper we present a method, based on the decomposition of matrix, for determination of the number d and the directions of sources with making no assumption about d. We at first give the uniqueness of the decomposition. Then we give an algorithm which can be used for either coherent or non-coherent case with d unknown. In our procedure a number p is calculated and used for determination of the maximum number of sources distinguishable by a given array system.