Differential and Constant-Beamwidth Beamforming with Uniform Rectangular Arrays

This paper presents a differential and constant-beamwidth (CB) beamforming approach, which is based on Kronecker-product (KP) beamforming with uniform rectangular arrays (URAs). We decompose a global rectangular beamformer into a KP of two subbeamformers: a constant-beamwidth beamformer along the y-axis and a super-directive (SD) beamformer along the x-axis. We propose two design methods to derive global rectangular beamformers whose either white noise gain (WNG) or directivity factor (DF) may be set by design. We show that the proposed rectangular beamformers exhibit improved directivity with respect to the linear CB beamformer, particularly in high frequencies, and improved robustness to spatially white noise with respect to the linear SD beamformer. Finally, the proposed rectangular beamformers exhibit the constant-beamwidth property, with an inherent tradeoff between the constant-beamwidth threshold frequency and the array directivity, which is tuned by the number of microphones along each axis.