M-estimate based diffusion active noise control algorithm over distributed networks and its performance analysis

Multi-channel active noise control (ANC) systems can achieve effective attenuation of low-frequency noise in spatial areas and have been extensively studied. Recent works have focused on the application of multitask diffusion strategies in ANC systems based on wireless acoustic sensor and actuator networks (WASAN), which show the advantages of saving computational burden and enhancing flexibility. However, these works all adopt the mean-square error minimization as the optimization criterion, which leads to severe performance degradation in the presence of impulsive noise interference. Therefore, in this paper, we exploit the M-estimate function and the augmented weight vector of the control filter to formulate a robust minimization problem and propose a distributed augmented diffusion filtered-x least mean M-estimate (DADFxLMM) algorithm for multichannel ANC systems. The proposed algorithm leverages the M-estimate function to overcome the influence of outliers in the error signal and achieves robustness against impulsive noise, and also eliminates the dependence on the symmetry of the acoustic paths by integrating the augmented weight vectors. Moreover, we replace the score function with the update probability of the weight vector to avoid the need for integration and Price's theorem, and analyze the mean and mean-square performance of the proposed DADFxLMM algorithm under the contaminated Gaussian (CG) noise model. Simulation results under different system configurations demonstrate that the proposed algorithm outperforms the existing multi-channel ANC algorithms in the presence of impulsive noise interference.