Study of nonuniform linear differential microphone arrays with the minimum-norm filter

The performance of differential microphone arrays (DMAs) depends on many factors such as the number of sensors and the array geometry. This paper develops an approach that exploits nonuniform linear geometries and the minimum-norm filter to improve the robustness of DMAs against white noise. Unlike the conventional way that forms an Nth-order DMA by subtractively combining the outputs of two DMAs of order N - 1, this approach works in the short-time Fourier transform (STFT) domain and applies a complex weight to the output of each sensor and then sum the weighted outputs to form the beamforming output in every STFT subband. The minimum-norm filter is obtained by maximizing the white noise gain of the beamformer subject to the so-called fundamental constraints. The nonuniform linear arrays are created by adjusting the interelement spacing according to some rule. We show that the use of nonuniform linear geometries can significantly improve the robustness of DMAs, particularly at low frequencies. We also show that the diagonal loading technique can help improve the robustness of DMA beamformers, though the improvement is not significant.