Kronecker-Product Beamforming With Sparse Concentric Circular Arrays

This article presents a Kronecker-product (KP) beamforming approach incorporating sparse concentric circular arrays (SCCAs). The locations of the microphones on the SCCA are optimized concerning the broadband array directivity over a wide range of direction-of-arrival (DOA) deviations of a desired signal. A maximum directivity factor (MDF) sub-beamformer is derived accordingly with the optimal locations. Then, we propose two global beamformers obtained as a Kronecker product of a uniform linear array (ULA) and the SCCA sub-beamformer. The global beamformers differ by the type of the ULA, which is designed either as an MDF sub-beamformer along the
$\mathsf {x}$
-axis or as a maximum white noise gain sub-beamformer along the
$\mathsf {y}$
-axis. We analyze the performance of the proposed beamformers in terms of the directivity factor, the white noise gain, and their spatial beampatterns. Compared to traditional beamformers, the proposed beamformers exhibit considerably larger tolerance to DOA deviations concerning both the azimuth and elevation angles. Experimental results with speech signals in noisy and reverberant environments demonstrate that the proposed approach outperforms traditional beamformers regarding the perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) scores when the desired speech signals deviate from the nominal DOA.