Unit circle MVDR beamformer

TL;DR

This paper introduces the unit circle MVDR (UC MVDR) beamformer, which projects sample matrix inversion MVDR polynomial zeros onto the unit circle to improve interferer suppression and noise gain performance.

Contribution

The novel UC MVDR method constrains polynomial zeros on the unit circle, enhancing beamformer nulling and noise suppression compared to existing SMI MVDR approaches.

Findings

UC MVDR better suppresses interferers.

UC MVDR improves white noise gain.

Numerical results validate the approach.

Abstract

The array polynomial is the z-transform of the array weights for a narrowband planewave beamformer using a uniform linear array (ULA). Evaluating the array polynomial on the unit circle in the complex plane yields the beampattern. The locations of the polynomial zeros on the unit circle indicate the nulls of the beampattern. For planewave signals measured with a ULA, the locations of the ensemble MVDR polynomial zeros are constrained on the unit circle. However, sample matrix inversion (SMI) MVDR polynomial zeros generally do not fall on the unit circle. The proposed unit circle MVDR (UC MVDR) projects the zeros of the SMI MVDR polynomial radially on the unit circle. This satisfies the constraint on the zeros of ensemble MVDR polynomial. Numerical simulations show that the UC MVDR beamformer suppresses interferers better than the SMI MVDR and the diagonal loaded MVDR beamformer and also improves the white noise gain (WNG).