Study and Design of Robust Differential Beamformers for Maximum Front-to-Back Ratio

Differential microphone arrays (DMAs) are widely used to capture high-fidelity acoustic signals due to their compact size, broadband spatial response, and high directivity. However, achieving high directivity often makes DMAs vulnerable to imperfections within the array. As a result, robust DMA design has attracted significant attention. This paper focuses on the design of a particular class of DMAs, specifically for maximizing the front-to-back ratio (FBR) under robustness constraints. While existing studies have explored the robust design of DMAs with a maximum directivity factor (MDF), these methods are not directly applicable to robust-maximum-FBR (RMFBR) differential beamformers due to the unique nature of the optimization problem. This work aims to address this challenge by framing the design of RMFBR beamformers as a fractional programming problem with a quadratic constraint. We then convert this fractional programming problem into a quadratic eigenvalue problem and introduce an iterative method for robust design. The primary contribution of this study is the proposal of a general optimization-based method for the design of robust MFBR differential beamformers, which has significant implications in practice. The performance of the proposed RMFBR beamformers is evaluated through both simulations and experiments, whose results justify their properties.