Placement design of microphone arrays in near-field broadband beamformers

In beamformer design, the microphone array configuration is often prescribed and the filter coefficients are varied in order to improve on the noise reduction performance. However, the positions of the microphone elements play an important role in the overall performance and should be optimized at the same time. This problem is addressed in this paper. In order to understand the performance improvement through location movements, we first look at the design with an infinite filter length, which gives the performance limit for finite filter length designs. When the filter length is finite, both the filter coefficients and the placement of the microphone array are decision variables. In both situations, the problems can be formulated as constrained optimization problems. As the filter length increases, we show that the performance converges quickly to the limit. For illustration, two numerical examples are solved. Comparing with several popular configurations, we show that the performance of the optimized configuration improves significantly.