An Active Set Approximation Method for the Design of Broadband Beamformer

The microphone array beamformer 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. This paper applies an active set approximation method to solve this problem. First, this paper transforms this problem into a semi-infinite programming problem. Next, this paper finds 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.