Grid-free compressive beamforming

TL;DR

This paper introduces a grid-free compressive sensing method for high-resolution DOA estimation that overcomes basis mismatch issues and works effectively with limited, noisy, and non-uniform array data.

Contribution

It develops a continuous optimization framework for DOA estimation using semidefinite programming, eliminating grid mismatch limitations.

Findings

Achieves high-resolution imaging with non-uniform arrays

Effective with single-snapshot and noisy data

Demonstrated on experimental towed array data

Abstract

The direction-of-arrival (DOA) estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors, thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve high-resolution imaging. On a discrete angular grid, the CS reconstruction degrades due to basis mismatch when the DOAs do not coincide with the angular directions on the grid. To overcome this limitation, a continuous formulation of the DOA problem is employed and an optimization procedure is introduced, which promotes sparsity on a continuous optimization variable. The DOA estimation problem with infinitely many unknowns, i.e., source locations and amplitudes, is solved over a few optimization variables with semidefinite programming. The grid-free CS reconstruction provides high-resolution imaging even with non-uniform arrays, single-snapshot data and under noisy conditions as demonstrated on experimental towed array data.