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

Area of Science:

• Acoustics
• Signal Processing
• Array Signal Processing

Background:

• Steerable differential beamforming is crucial for acoustic sensor arrays.
• Maclaurin series expansion (MSE) based methods suffer from performance degradation.
• This degradation is linked to truncated errors in the MSE approach.

Purpose of the Study:

• To propose a novel differential beamforming design for linear acoustic vector sensor arrays.
• To address the performance degradation observed in MSE-based methods.
• To establish a theoretical link between MSE and Jacobi-Anger expansion (JAE).

Main Methods:

• Jacobi-Anger expansion (JAE) combined with Chebyshev polynomial for higher-order beampatterns.
• Development of a closed-form solution for the JAE-based differential beamformer.
• Theoretical analysis linking MSE and JAE, identifying truncated error as the cause of MSE performance loss.

Main Results:

• A novel JAE-based differential beamformer design is realized with a closed-form solution.
• The truncated error in MSE is identified as the primary cause of performance degradation.
• The proposed JAE method demonstrates superior performance compared to alternatives at equivalent truncation orders.
• Factors influencing white noise gain for the JAE method were analyzed.

Conclusions:

• The proposed Jacobi-Anger expansion (JAE) based differential beamforming method effectively solves the performance degradation issues of Maclaurin series expansion (MSE) methods.
• The JAE approach provides a more robust and accurate solution for steerable differential beamforming in linear acoustic vector sensor arrays.
• Experimental validation, including a sea experiment, confirms the practical effectiveness of the JAE-based method.