A Novel Method to Design Steerable Differential Beamformer Using Linear Acoustics Vector Sensor Array

Differential beamforming techniques have gained significant attention due to their frequency-independent beampatterns, applicability for small apertures, and super-directivity. It is commonly known that the main lobe of a beam pattern based on a linear array is typically aligned with the end-fire direction. However, in some application scenarios, aligning the main lobe in the end-fire direction may not meet the actual requirements. This article focuses on studying the steering problem of differential beamformers based on linear acoustics vector sensor arrays (LAVSs). We propose a steerable differential beamformer for LAVSs, which addresses the problem of non-steerable beam patterns of linear arrays. Our approach involves approximating the beam pattern using a series expansion of the weighted steering vector to achieve frequency-independent differential directivity. The major contributions of this article include, but are not limited to, the following: First, we derive the first-order to third-order differential directivity based on the acoustics vector sensor (AVS) signal model, and obtain the weights of the corresponding channels using the least squares method. Second, we provide a theoretical analysis of the steering differential beamformer, demonstrating that the maximum directivity factor (DF) is a function of the steering angle. Finally, we conduct simulation experiments to validate the proposed method.