Multi-frequency synchronous two-dimensional off-grid compressive beamforming

Abstract

Two-dimensional (2D) compressive beamforming with planar microphone arrays has attracted much attention because it has a wide source identification space, clear imaging, and no acoustic source coherence restriction. However, its early versions encounter the basis mismatch issue and suffer from performance degradation in the case of closely-spaced sources or low signal to noise ratios (SNRs). Hitherto, there is still a lack of a 2D compressive beamforming that can solve these two problems and concurrently be compatible with arbitrary geometry planar arrays and both stationary and nonstationary acoustic sources. Hence, we propose a multi-frequency synchronous two-dimensional off-grid compressive beamforming. Firstly, a maximum likelihood estimation model for multi-frequency synchronous source identification is established, which uses the source coordinates and the source strengths of all frequencies as parameters. Then, a block Newtonized orthogonal matching pursuit algorithm (BNOMP) is developed to solve this model. The proposed method is suitable for arbitrary geometry planar arrays and works well for both stationary and nonstationary acoustic sources. Simulations and experiments show that the proposed method has high spatial resolution and strong anti-interference while overcoming basis mismatch, and can locate and quantify the sources accurately even under small source spacings or low SNRs.