Performance study of the MVDR beamformer as a function of the source incidence angle

Linear microphone arrays combined with the minimum variance distortionless response (MVDR) beamformer have been widely studied in various applications to acquire desired signals and reduce the unwanted noise. Most of the existing array systems assume that the desired sources are in the broadside direction. In this paper, we study and analyze the performance of the MVDR beamformer as a function of the source incidence angle. Using the signal-to-noise ratio (SNR) and beampattern as the criteria, we investigate its performance in four different scenarios: spatially white noise, diffuse noise, diffuse-plus-white noise, and point-source-plus-white noise. The results demonstrate that the optimal performance of the MVDR beamformer occurs when the source is in the endfire directions for diffuse noise and point-source noise while its SNR gain does not depend on the signal incidence angle in spatially white noise. This indicates that most current systems may not fully exploit the potential of the MVDR beamformer. This analysis does not only help us better understand this algorithm, but also helps us design better array systems for practical applications.