Function Designable Beamformer Based on Probabilistic Assumptions on Filter and Its Auxiliary Variables

Abstract

We propose a novel beamformer design method that exploits probabilistic assumptions on auxiliary variables derived from filters and observed signals. Many conventional beamformer design methods can be understood in the context of optimization problems for some probabilistic cost functions. However, the class of cost functions used with these methods is quite limited to reflect multiple pieces of information and our demands on the filter, such as the sparsity assumption of the source signals and the low-latency constraint of the filter. We propose a method to design cost functions that incorporate multiple probabilistic assumptions. The assumptions are expressed as the sum of many convex terms, and every term has different auxiliary variables that are linearly constrained. Such cost functions can be optimized by iteratively optimizing with regard to each term alternately. This method enables us to more arbitrarily tune the beamformer. We conducted numerical simulations showing that our method effectively improves the performance from multiple perspectives.