Sparse Distortionless Beamformer Based on Nonconvex Optimization

Abstract

Minimum power distortionless response (MPDR) beamformer is a popular beamformer that minimizes its output power under the distortionless constraint. To improve the performance of the MPDR beamformer, a sparse distortionless beamformer has been proposed. It minimizes the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> norm of the output signal under the same constraint so that the output has sparse time-frequency representation. While the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> -norm-based formulation is theoretically advantageous owing to its convexity, its practical performance might not be excellent because of the bias of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{1}$</tex> norm. To reduce the bias and improve the performance, we propose a sparse distortionless beamformer based on a nonconvex sparsity-inducing objective function. The proposed beamformer is performed via a heuristic application of a primal-dual splitting algorithm. The experiments showed that the proposed beamformer can achieve higher performance and is more robust against mismatch of the target direction.