High resolution beamforming using L1 minimization

Abstract

We consider the problem of beamforming using fewer snapshots than the number of sensors, using sparse recovery of the signal vector. Given an array of sensors in an environment and signals impinging on the array, it is of practical interest to be able to estimate the direction of arrival and power of the signals using as few snapshots as possible. In a sparse recovery framework, the signal vector is modeled as a sparse vector in the bearing domain. By casting the beamforming operation as an $\ell∧1$ minimization problem (as opposed to the conventional $\ell∧2$ minimization), the signal vector can be recovered. The angular resolution of this approach is much higher than the Rayleigh limit, which determines the resolution for the conventional beamformer. The results are demonstrated using simulations. © 2013 Acoustical Society of America.