Unequally Spaced Sound Field Interpolation for Rotation-Robust Beamforming

In this paper, we present an enhanced method designed to facilitate sound field interpolation (SFI) for rotation-robust beamforming using unequally spaced circular microphone arrays (unes-CMAs). Unlike the previous approach that necessitated an equally spaced circular microphone array (es-CMA), our method addresses the challenge of handling non-uniformly spaced microphones, making it suitable for real-world applications where unes-CMAs are more prevalent. Our proposed method enables the estimation of a virtual signal of an unes-CMA before rotation, derived from the observed signal after rotation. A modified SFI technique is utilized to compensate for the positional errors of microphones on an unes-CMA and to estimate a virtual signal at equally spaced positions after rotation. As an intermediate step, the previous SFI method is utilized to obtain equally spaced signals before rotation. Subsequently, the target signal of the unes-CMA before rotation is reconstructed, effectively achieving rotation-robust beamforming on the unes-CMA. Moreover, we provide an in-depth analysis of our proposed method's properties. We conducted simulated experiments, including online beamforming applications, to evaluate its performance. The experimental results demonstrated that our method effectively mitigates the adverse effects of unequal microphone placement, yielding significant improvements in estimating the signal before rotation under various conditions. Moreover, our proposed method consistently outperformed the previous approach, significantly enhancing the performance of beamforming.