Two-Dimensional Multiple-Snapshot Grid-Free Compressive Beamforming Using Alternating Direction Method of Multipliers

Yang Yang,Zhigang Chu

doi:10.1155/2020/1310805

Abstract

Compressive beamforming with planar microphone arrays is capable of estimating the two-dimensional direction-of-arrivals (DOAs) and quantifying the strengths of acoustic sources effectively. The multiple-snapshot grid-free method has recently been concerned due to the advantages that it can circumvent the basis mismatch conundrum of the conventional grid-based method and improve the performance of the single-snapshot grid-free method. The existing atomic norm minimization based strategy uses an off-the-peg interior point method (IPM) based solver to solve the positive semidefinite programming equivalent to the atomic norm minimization. We present an alternative algorithm based on alternating direction method of multipliers (ADMM) in this paper. Both simulations and experiments demonstrate that whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is employed, the two-dimensional multiple-snapshot grid-free compressive beamforming using our ADMM based algorithm can estimate the DOAs and quantify the strengths of acoustic sources well, and reaching the same or even better DOA estimation accuracy as the one using the IPM based solver, our ADMM based algorithm is distinctly faster.

Highlights

Compressive beamforming, or concretely compressive sensing [1,2,3] based beamforming, is an emerging and powerful approach to realize the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources
In 2017-2018, the authors [14, 15] presented a two-dimensional grid-free compressive beamforming strategy for the measurements with planar microphone arrays based on the minimization of the atomic norm of microphone pressure induced by sources and the matrix enhancement and matrix pencil method [16]
In 2018, Park et al [17] extended Xenaki and Gerstoft’s strategy into the multiple-snapshot case through a group atomic norm. e same year, the authors [18] realize the two-dimensional multiple-snapshot grid-free compressive beamforming based on the minimization of the atomic norm of multiple-snapshot microphone pressure induced by sources and the matrix pencil and pairing (MaPP) method [19]. ey all have demonstrated that for sources that are active across multiple snapshots, for example, stationary sources, the multiple-snapshot grid-free compressive beamforming is distinctly superior to the single-snapshot one

Summary

Introduction

Compressive beamforming, or concretely compressive sensing [1,2,3] based beamforming, is an emerging and powerful approach to realize the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. In 2017-2018, the authors [14, 15] presented a two-dimensional grid-free compressive beamforming strategy for the measurements with planar microphone arrays based on the minimization of the atomic norm of microphone pressure induced by sources and the matrix enhancement and matrix pencil method [16]. E same year, the authors [18] realize the two-dimensional multiple-snapshot grid-free compressive beamforming based on the minimization of the atomic norm of multiple-snapshot microphone pressure induced by sources and the matrix pencil and pairing (MaPP) method [19].

Theory

Simulations

Experiments

Conclusions