Multiple and single snapshot compressive beamforming

TL;DR

This paper demonstrates that compressive sensing (CS) can effectively estimate the direction-of-arrival of sound sources using both single and multiple snapshots, outperforming traditional methods especially in low SNR and coherent scenarios.

Contribution

It introduces a MAP-based sparse source distribution approach for both single and multiple snapshot DOA estimation, improving resolution without covariance matrix inversion.

Findings

CS provides higher resolution than conventional beamforming for single snapshots.

CS outperforms traditional high-resolution methods with multiple snapshots, even with coherent signals.

Demonstrated effective DOA estimation on real vertical array data from SWellEx96.

Abstract

For a sound field observed on a sensor array, compressive sensing (CS) reconstructs the direction-of-arrival (DOA) of multiple sources using a sparsity constraint. The DOA estimation is posed as an underdetermined problem by expressing the acoustic pressure at each sensor as a phase-lagged superposition of source amplitudes at all hypothetical DOAs. Regularizing with an $\ell_1$-norm constraint renders the problem solvable with convex optimization, and promoting sparsity gives high-resolution DOA maps. Here, the sparse source distribution is derived using maximum a posteriori (MAP) estimates for both single and multiple snapshots. CS does not require inversion of the data covariance matrix and thus works well even for a single snapshot where it gives higher resolution than conventional beamforming. For multiple snapshots, CS outperforms conventional high-resolution methods, even with coherent arrivals and at low signal-to-noise ratio. The superior resolution of CS is demonstrated with vertical array data from the SWellEx96 experiment for coherent multi-paths.