Design of differential microphone array beampatterns with sidelobe level constraints

The target beampattern of differential microphone arrays (DMAs) often satisfies design requirements to optimize the performance of the beamformer by maximizing a specific advantage. This paper focuses on designing and implementing the minimum mainlobe width beampattern under the constrained sidelobe level. The main works are as follows. (1) We derive the minimum mainlobe width target beampattern under certain sidelobe level constraints from the Chebyshev-Type pattern that satisfies the sufficient conditions for effective target beampatterns. (2) We design a Jacobi–Anger expansion approximation differential beamforming filter for the Chebyshev-Type target beampattern to ensure that the resulting beampattern is consistent with the Chebyshev-type target beampattern and the beamformer’s robustness can be improved by using more microphones to obtain a minimum-norm solution. Compared with the conventional frequency-independent pattern Jacobi–Anger expansion method, the Chebyshev-Type Jacobi–Anger expansion beamformer we designed can flexibly limit the sidelobe level and obtain the minimum mainlobe beamwidth.