Ambiguities in Direction-of-Arrival Estimation with Linear Arrays

TL;DR

This paper introduces a new mixed-integer programming method to identify ambiguities in direction-of-arrival estimation for sparse linear arrays, enhancing understanding of non-unique solutions in array signal processing.

Contribution

It develops a novel approach using Young tableaux and mixed-integer programming to systematically compute ambiguities in sparse array configurations.

Findings

The method successfully enumerates ambiguous DOA sets in example arrays.

It reveals the structure of ambiguities related to vanishing sums of roots.

The approach improves the analysis of array ambiguities in signal processing.

Abstract

In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of directions-of-arrival. We derive a method to enumerate such ambiguous sets using a mixed-integer program and present results on several examples.