Grid-free compressive beamforming for arbitrary linear microphone arrays

Grid-free compressive beamforming is a new attractive method for acoustic source identification based on compressive sensing theory, which extracts the source information from the microphone array measurements without discretizing the target source region. In the framework of linear microphone array measurements, many studies have been carried out around this method. They have strict requirements on the distribution of microphones. Specifically, only the uniform arrays with equally spaced microphones and sparse arrays consisting of a selection of microphones from uniform arrays are available. In this paper, based on the prolate spheroidal wave functions, we propose a grid-free compressive beamforming method compatible with arbitrary linear microphone arrays. Some examples are conducted to demonstrate the correctness and superiority of the proposed method. Plenty of Monte Carlo simulations are performed to reveal the effects of source coherence, source separation, noise, and number of snapshots. This study helps to promote the popularization and application of grid-free compressive beamforming method and offers the possibility to improve the acoustic source identification performance by optimizing microphone distribution.