An active set approximation method for the design of broadband beam former

Abstract

The microphone array beam former design problem in far-field environment is to design the coefficients of FIR filters such that the maximum error between the actual response and the desired response in a specified domain is minimized. The specified domain is always very large and this problem is a large scale optimization problem. In general the complexity of the optimal method for solving this problem is very expensive. In this paper, we apply an active set approximation method to solve this problem. First, we transform this problem into a semi-infinite programming problem. Next, we find an approximate active set such that the scale of the problem can be mostly reduced. Then, this problem can be solved efficiently and the approximate solution is very close to the optimal solution. Numerical experiments are illustrated to show the efficiency of the proposed method.