Single Snapshot Super-Resolution DOA Estimation for Arbitrary Array Geometries

TL;DR

This paper extends search-free super-resolution DOA estimation methods to arbitrary array geometries using atomic norm minimization, polynomial representation, and semidefinite programming, enabling accurate single-snapshot source localization.

Contribution

It introduces a novel approach for DOA estimation with arbitrary array geometries, generalizing previous methods limited to uniform linear arrays, and provides an efficient computational framework.

Findings

Perfect DOA estimation in noise-free simulations

Effective polynomial rooting for source localization

Applicable to circular and random planar arrays

Abstract

We address the problem of search-free direction of arrival (DOA) estimation for sensor arrays of arbitrary geometry under the challenging conditions of a single snapshot and coherent sources. We extend a method of searchfree super-resolution beamforming, originally applicable only for uniform linear arrays, to arrays of arbitrary geometry. The infinite dimensional primal atomic norm minimization problem in continuous angle domain is converted to a dual problem. By exploiting periodicity, the dual function is then represented with a trigonometric polynomial using a truncated Fourier series. A linear rule of thumb is derived for selecting the minimum number of Fourier coefficients required for accurate polynomial representation, based on the distance of the farthest sensor from a reference point. The dual problem is then expressed as a semidefinite program and solved efficiently. Finally, the searchfree DOA estimates are obtained through polynomial rooting, and source amplitudes are recovered through least squares. Simulations using circular and random planar arrays show perfect DOA estimation in noise-free cases.