Design of Highly Directive Beamformers Under General SNR Gain Constraints

The increasing demand for high-fidelity acoustic signal acquisition, driven by applications such as smart-home and human-machine interface systems, has spurred the development of compact microphone arrays equipped with highly directive (HD) beamformers. In practical settings, the design of HD beamformers, including superdirective and differential beamformers, is typically framed as a constrained optimization problem to improve noise suppression and robustness. Although several methods have been proposed, most are based on convex quadratic constrained quadratic programming. However, designing HD beamformers under general signal-to-noise ratio (SNR) gain constraints presents a fundamental nonconvex challenge, requiring a more comprehensive approach. In this work, we propose a novel method for designing fixed HD beamformers under general SNR gain constraints by converting the nonconvex optimization problems into generalized eigenvalue problems. A detailed filter design methodology is then developed. The major contributions of this work are twofold: 1) the introduction of an innovative approach to fixed HD beamformer design under SNR gain constraints, and 2) the provision of a versatile solution applicable to a broad range of related problems. Simulations validate the proposed method and demonstrate its advantages over existing approaches.