Sound Field Interpolation for Rotation-Invariant Multichannel Array Signal Processing

In this paper, we present a sound field interpolation for array signal processing (ASP) that is robust to rotation of a circular microphone array (CMA), and we evaluate beamforming as one of its applications. Most ASP methods assume a time-invariant acoustic transfer system (ATS) from sources to the microphone array. This assumption makes it challenging to perform ASP in real situations where sources and the microphone array can move. Therefore, considering a time-variant ATS is an essential task for the use of ASP. In this study, we focus on one such movement, the rotation of the CMA. Our method interpolates the sound field on the circumference of a circle, where microphones are equally spaced, based on the sampling theorem on the circle. The interpolation enables us to estimate the signals at the microphone positions before the rotation. Hence, conventional ASP, which assumes a time-invariant ATS, is applicable after interpolation without modification. We developed two beamforming schemes, one for batch and one for online processing, that combine the minimum power distortionless response beamformer and sound field interpolation. We evaluated the dependences of the interpolation on frequency and rotation angle using the signal-to-error ratio. Additionally, simulation results demonstrated that the two proposed schemes improve the beamformer's performance when the CMA rotates.