Optimal beamformer design in the reverberant environment

Abstract

Most existing methods on beamformer design, such as the minimum variance distortionless response (MVDR) method and the linearly constrained minimum variance (LCMV) method, assume that the group delay is known and often heuristically preselected to be half of the filter length. However, the optimal group delay is problem-dependent in practice, and the beamformer design performance based on the optimal beamformer response can be significantly better than the one based on the preselected beamformer response in the reverberant environment. In this paper, we consider the optimal beamformer design problem, i.e., the joint beamformer response and beamformer design problem. We introduce a new variable to represent the beamformer response and formulate the joint beamformer response design and beamformer design problem as a structured constrained convex optimization (SCCO) problem. Moreover, we exploit the separable structures of the SCCO problem and propose to use the alternating direction method of multipliers (ADMM) to solve it, and give a simple proof for the analysis of convergence. Numerical simulation results show the effectiveness of the proposed method in the reverberant environment by comparing it with the LCMV method.