On Sparse Beamformer Design with Reverberation

Microphone array beamforming is one of the most important techniques to enhance the signal of interest from its observations corrupted by interference, noise and reverberation. In designing the beamformer to fulfill a desire performance, the transfer function governing sound propagation is required in the formulation. In general, the beamformer usually contains a number of FIR filters with long length behind each of microphone element, especially in reverberant environment. In order to reduce complexity, it is favourable to have many zero coefficients in the FIR filters. In this paper, we study this kind of sparse beamformer design problem. We first describe the transfer function developed for reverberant environment. Then we develop an L₂−L_p minimization model with 0 < p < 1 for the design of sparse beamformers and introduce the smoothing Barzilai–Borwein (BB) step gradient method for solving the problem. Experimental results show that the designed beamformers achieve comparable performance with rather sparse filter coefficients.