Design of time-domain modal beamformer for broadband spherical microphone arrays

An approach to real-valued time-domain implementation of modal beamformer for spherical microphone arrays is proposed. The advantage of the time-domain implementation is that we can update the beamformer when each new snapshot arrives. Our technique is based on a modified filter-and-sum spherical harmonics domain (SHD) beamforming structure. The time series received at the microphones are converted into SHD data using spherical Fourier transform. The SHD data input to the steering unit and then feed a bank of finite impulse response (FIR) filters. The filter outputs are summed to produce the beamformer output time series. The FIR filters tap weights are optimally designed by making a compromise among multiple conflicting array performance measures such as directivity, mainlobe spatial response variation (MSRV), sidelobe level, and robustness. The design problem is formulated as a multiply constrained problem which is solved using second-order cone programming (SOCP). Results of simulations show good performance of the proposed time-domain SHD beamformer design approach.