Spherical-Harmonic-Domain Feedforward Active Noise Control Using Sparse Decomposition of Reference Signals from Distributed Sensor Arrays

Active acoustic noise attenuation over a sizable space is a challenging problem in signal processing. The noise attenuation performance of feedforward active noise control (ANC) relies on the preciseness of a reference signal of a primary noise field. To capture the precise reference signal for controlling a sizable space, a large number of reference microphones are required, which reduces system viability. In this study, we exploit an efficient representation of the reference signal in spherical harmonic (SH) domain by utilizing the inherent sparseness of the noise field. The main contributions of this work are as follows. (1) A general reference microphone geometry can be used. The implementation difficulty in the array structure, which is recognized as the common issue of SH-domain signal processing, e.g., use of a fully surrounding spherical array, is reduced by using the fields translation based on the addition theorem. (2) The accuracy of low-frequency signal decomposition is improved. The low accuracy of low-frequency signal decomposition in compressive sensing (CS), which is commonly reported in the literature, is improved by applying signal representation in SH domain. (3) System robustness is increased. The robustness of the system is increased by considering a noise source spatial distribution of both the interior and exterior sound fields, which is not possible in the case of a general signal representation in SH domain. Experimental results indicate that the noise attenuation performance of our proposed method exceeds that of existing solutions. The flexibility of the array structure is also increased, which leads to a more feasible practical system setup.