Relaxing nulls for robust differential microphone array in the STFT domain

Differential microphone array (DMA) has attracted many research efforts recently, since it is generally small in size and possible to achieve maximum spatial directivity. However, its poor robustness to system error seriously hinders its applications. The traditional way to improve its robustness is to use redundant microphones, but generally the array topology is fixed so that the DMA order has to be decreased. In this paper, we suggest another way to improve its robustness by simply relaxing the null constraints in its design in the STFT domain. With this modification, the popular methods to improve additive beamformer's robustness can also be used in DMA design, such as the diagonal loading method and the second-order cone programming. The design results verify the effectiveness of the proposed method, and the robustness of the DMA can be adjusted flexibly.