Optimal beamformer design in spherical sector harmonics domain

Abstract

Beamforming using spherical microphone arrays (SMAs) with processing in spherical harmonics (SH) domain is widely being studied. This is due to the ease of array processing in SH domain with no spatial ambiguity. Despite the widespread applications of SMA in beamforming, its size makes it inconvenient for practical or commercial use. Building of SMA over a rigid sphere is also a challenging task. Additionally, use of the entire sphere comes at the cost of more microphones and signals to process. Hence, it is uneconomic to use full SMA when sources are only present in restricted regions of the environment. Attempts have been made in literature to use hemispherical microphone array for beamforming. Acoustic image principle was utilized to enable application of SH but with greater computational complexity. In this paper, the use of a spherical sector microphone array is proposed for beamforming. An orthonormal spherical sector harmonics (S2H) basis function is used for data model development. An ideal direction-invariant beampattern using S2H basis function is utilized. Subsequently, to make the beamformer robust against sensor noise with a sharp directivity pattern at the direction of arrival and zero elsewhere, a new maximum directivity and white noise gain (MD-WNG) beamformer is designed for a spherical sector microphone array. Performance analysis of the proposed beamformer is presented using various experiments on directivity pattern and array gain. The proposed method is additionally compared with several existing beamforming techniques. The comparison reveals that the S2H based beamforming provides reasonably better results compared to the existing methods.