Incremental Strategy Based ANC Using Hybrid Adaptive Nonlinear Filters

The prevalence of nonlinearities in adaptive filters poses a challenging issue for noise reduction. Several methods are introduced to enhance the effectiveness of distributed active noise control (DANC) systems while dealing with nonlinearities. In this context, DANC algorithms utilizing Mish functions are being proposed to address noise reduction challenges. The Mish function addresses the issue of the vanishing gradient problem and enhances the speed at which convergence occurs by leveraging the smoothness and unboundedness characteristics. Considering this, the present manuscript introduces a collection of nonlinear methods for the DANC system that employs the Mish framework into an incremental strategy for filtered-x least mean fourth (IMF-xLMF) and filtered-x least mean square (IMF-xLMS). The proposed approaches entail designing weight update equations specific to the developed algorithms and performing a comprehensive convergence analysis. The suggested methods yield a quantitatively significant gain of 1–4 dB in noise reduction, effectively handling nonlinearities and reference signals, all while converging faster than previous techniques.