Differential constant-beamwidth beamforming with cube arrays

Abstract

In this paper, we present an azimuth and elevation constant-beamwidth (CB) differential beamforming approach for cube arrays. We decompose a global cube beamformer into a Kronecker-product (KP) of three sub-beamformers: two constant-beamwidth beamformers along the y and z axes, and a tunable super-directive (SD) beamformer along the x-axis. We propose two design methods to derive cube beamformers whose either white noise gain (WNG) or directivity factor (DF) may be set by design. We show that the CB threshold frequency with respect to the azimuth and elevation angles, and the WNG and DF performance, can be controlled by the number of microphones along each axis. In addition, we focus on the particular case of merely a single microphone along the x-axis, which yields a rectangular azimuth and elevation CB beamformer. We demonstrate that its CB threshold frequencies are controlled by the number of microphones along the y and z axes, and show that the WNG and DF performance measures are maximized when the two axes are equal in size. Finally, we analyze the performance of the proposed beamformers through simulations of speech signals in various reverberant scenarios, including deviations in the desired speech signal’s direction of arrival (DOA). We show that the proposed beamformers outperform previously-presented beamformers and the traditional SD and delay-and-sum (DS) beamformers, particularly in terms of the intelligibility of their corresponding time-domain enhanced signals.