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In this paper, four delay-and-sum (DAS) beamformers formulated in the modal domain and the space domain for open and solid spherical apertures are examined through numerical simulations. The resulting beampatterns reveal that the mainlobe of the solid spherical DAS array is only slightly narrower than that of the open array, whereas the sidelobes of the modal domain array are more significant than those of the space domain array due to the discrete approximation of continuous spherical Fourier transformation. To verify the theory experimentally, a three-dimensionally printed spherical array on which 32 micro-electro-mechanical system microphones are mounted is utilized for localization and separation of sound sources. To overcome the basis mismatch problem in signal separation, source localization is first carried out using minimum variance distortionless response beamformer. Next, Tikhonov regularization (TIKR) and compressive sensing (CS) are employed to extract the source signal amplitudes. Simulations and experiments are conducted to validate the proposed spherical array system. Objective perceptual evaluation of speech quality test and a subjective listening test are undertaken in performance evaluation. The experimental results demonstrate better separation quality achieved by the CS approach than by the TIKR approach at the cost of computational complexity.

Source localization and extraction using spherical microphone arrays is presented in this paper. Both freefield and solid spherical arrays are examined. To minimize the basis mismatch problem in signal extraction, source localization is executed first using two beamforming methods, delay and sum (DAS) and minimum variance distortionless response (MVDR). The beamformers are formulated in both the spatial domain and the modal domain. After source localization, Tikhonov regularization (TIKR) and compressive sensing (CS) are used to extract the source amplitude signals. Simulations and experiments are conducted for spherical arrays of radius 5 cm with 32 microphones mounted on the vertices and faces of an icosahedron. The results demonstrate better localization performance of the spatial beamformer that the modal beamformer. In addition, the source speech signals are extracted by using the proposed arrays with superior quality.