Fully steerable differential beamforming for linear acoustic vector sensor arrays based on series expansion

In order to solve the degradation of the performance of the steerable differential beamforming based on Maclaurin series expansion (MSE), a differential beamforming design for linear acoustic vector sensor arrays based on Jacobi–Anger expansion (JAE) is proposed. First, JAE is combined with Chebyshev polynomial to construct the higher-order steerable directional differential beampattern, and a closed-form solution for the JAE-based differential beamformer is realized. Second, the theoretical link between MSE and JAE is established, demonstrating that the truncated error in MSE is the cause of performance degradation in MSE-based method. Furthermore, the factors affecting the white noise gain of the proposed method are analyzed and simulations demonstrate that the proposed method outperforms alternative methods at the same truncation order. Finally, the effectiveness of the proposed method is further verified by a sea experiment.