On the Design of Planar Differential Microphone Arrays with Specified Beamwidth or Sidelobe Level

This paper investigates the problem of designing differential beam-formers with planar microphone arrays to achieve not only the desired target directivity pattern but also control the beamwidth (BW) or sidelobe level (SLL). We first discuss the target directivity patterns and express the Dolph-Chebyshev polynomial based form of target directivity patterns into linear combination of cylindrical harmonics. We then address the problem of designing differential beamformers through beampattern approximation based on the Jacobi-Anger series expansion. Two methods are subsequently developed: the first one involves designing beamformers to achieve the target directivity pattern while minimizing SLL under a pre-specified value of BW and the second one aims to attain the target directivity pattern while minimizing the null-to-null BW under a pre-specified level of SLL. Simulations are carried out to validate the method and the results demonstrate the properties of the proposed method.