A new variable spatial regularized FxLMS algorithm for diffusion active noise control

Distributed multi-channel active noise control (ANC) systems attract a lot of attention due to the reduced computational complexity than centralized control methods and improved stability than decentralized control methods. However, the combination of controllers within a neighborhood in a diffusion manner introduces an estimation bias and may degrade the control accuracy. This is because the secondary sources and error microphones of an ANC system are usually physically placed at different locations and the optimal solution to each controller is different. In this paper, a new diffusion filtered-x least mean squares algorithm (Diff-FxLMS) has been developed that balances combination strength and estimation bias via a variable spatial regularization. The mean squares error criterion subject to a bias constraint is used such that the spatial regularization parameter could be adapted according to the penalized Lagrangian. A detailed performance analysis is carried out, based on which user parameters can be selected automatically. Performance of the proposed variable spatial regularized Diff-FxLMS (VSR-Diff-FxLMS) algorithm and theoretical analysis is verified by simulations.