Rank Properties of Manifold Matrices of Sparse Arrays

Abstract

It is well known that the manifold matrix of a sensor array has to satisfy certain rank conditions in order for certain algorithms such as MUSIC and ESPRIT to work without creating ambiguity. For the case of sparse arrays this condition is often not satisfied, although there exist some sparse arrays which satisfy them. This paper develops the constraints on the sensor locations which allow such conditions to be satisfied. After a number of examples to develop insights, two results are given: one is a necessary and sufficient condition for two specific cases and the other is a necessary condition for the general case. The necessary condition for the general case reduces to the necessary and sufficient condition in the two specific cases. In order for sparse arrays to satisfy these conditions, it is not required that there be a uniform linear subarray with more sensors than sources.