On the Design of a Robust Superdirective Beamformer and Topology Parameter Optimization with Frustum-Shaped Microphone Arrays Featuring Multiple Rings

Superdirective beamformers using concentric circular microphone arrays are widely used in various applications for their steering capabilities, high directional gains, and robustness. However, their performance often degrades when the beamformer is steered outside the sensor plane, a limitation common in real-world scenarios due to the array's planar configuration. To address this challenge, this paper introduces a novel class of co-axial frustum-shaped concentric circular microphone arrays, where multiple rings are distributed across different horizontal planes. A robust superdirective beamformer is designed by converting beamforming optimization into a quadratic eigenvalue problem. Additionally, an approach is proposed to optimize the array topology parameters using the particle swarm optimization algorithm. Simulation results demonstrate that the proposed method significantly improves beampattern steering and directivity, while effectively controlling the white noise gain.