Optimal design of directivity patterns for endfire linear microphone arrays

Directivity pattern or beampattern is an important performance measure in all fixed beamformers. Given a microphone array, how to design the beamforming filter so that the resulting directivity pattern is close to the desired one is a critical issue. In this paper, we study the design of such patterns for endfire uniform linear microphone arrays. By considering the frequency-independent Chebyshev pattern as the desired one, we derive an optimal beamforming filter based on the minimization of the mean-squared error (MSE) under the distortionless constraint. It is shown that the proposed beamformer design can generate beampatterns that are very close to the desired ones and, the larger is the number of microphones, the better is the designed beampattern.