Design of Optimal Linear Differential Microphone Arrays Based Array Geometry Optimization

This paper presents a method to design optimal linear differential microphone arrays (DMAs) by optimizing the array geometry. By constraining the DMA beamformer to achieve a given target value of the directivity factor (DF) with a specified target frequency-invariant beampattern while achieving also the highest possible white noise gain (WNG), an optimization algorithm is developed, which consists of the following two steps. 1) The full frequency band of interest is divided into a few subbands. At every subband, the entire linear array is divided into subarrays and the number of subarrays depends on the total number of the sensors and the order of the DMA. A cost function is then defined, which is minimized to determine what subarray produces the optimal performance. 2) The subband optimal subarrays are then combined across the entire frequency band to form a fullband cost function, from which the geometry of the entire array is optimized. These two steps are repeated with the particle swarm optimization (PSO) algorithm until the desired array performance is reached. Simulation results demonstrate that the proposed method can obtain the target DF with a frequency-invariant beampattern over a wide band of frequencies while maintaining a reasonable level of WNG.