A Diffusion FXLMS Algorithm for Multi-Channel Active Noise Control and Variable Spatial Smoothing

This paper studies the diffusion (Diff) control for multichannel ANC systems, where a group of controllers and error microphones are physically distributed at different locations within a large area. In this case, the conventional consensus agreement for controllers cannot be reached. To solve this problem, a new Diff filtered-x least mean squares (Diff-FxLMS) algorithm that incorporates the knowledge of spatial smoothness is proposed. Compared to conventional Diff control criteria that have a fixed spatial smoothing strategy, the proposed Diff-FxLMS adjusts a so called spatial regularization (SR) coefficient adaptively such that the neighboring controllers keep their decision variables close to one another to minimize the global cost function while giving preference to possibly distinct local signals. A detailed performance analysis is carried out and verified by simulation. Based on the analysis, a variable SR formula is derived. The performance of the proposed algorithm is also compared with conventional methods.