Comparison of Sparse Arrays From Viewpoint of Coarray Stability and Robustness

Abstract

Sparse arrays, such as minimum redundancy arrays (MRA), nested arrays, and coprime arrays, can resolve O(N^2), uncorrelated sources with N physical sensors, since they possess an O(N2) -long uniform segment in the difference coarray, which is defined as the differences between sensor locations. Empirically, this O(N^2), property is susceptible to sensor failures. On the other hand, uniform linear arrays (ULA) are known to be robust, but they possess only O(N) elements in the difference coarray. This paper compares the size and the robustness of the difference coarray for a wide variety of array geometries. It is observed from numerical examples that, for a fixed N, increasing the size of the difference coarray typically makes it less robust to faulty sensors. Furthermore, it is noticed from examples that given two arrays with the same N and the same difference coarray, one could be much more robust than the other.