Nonlinear adaptive filter-based simplified bilinear model for multichannel active control of nonlinear noise processes

• A scheme of multichannel nonlinear ANC systems based on the adaptive bilinear filter is designed.
• A simplified bilinear leaky filtered-x LMS algorithm for multichannel nonlinear ANC systems is derived.
• The computational complexity of the proposed algorithm for multichannel nonlinear ANC systems is analyzed.

To circumvent nonlinear distortions which occur in multichannel nonlinear active noise control (ANC) systems used for practical applications, a simplified bilinear leaky filtered-x least mean square (SBLFXLMS) algorithm for nonlinear adaptive filter is presented in this paper. The performance of the simplified bilinear adaptive filter is evaluated in terms of computational complexity and convergence characteristics. Computer simulations have been carried out to verify that the nonlinear adaptive filter with the SBLFXLMS algorithm is more effective in eliminating nonlinear distortions in multichannel nonlinear ANC systems than the linear FXLMS, second-order Volterra FXLMS (VFXLMS) and filtered-s LMS (FSLMS) algorithms. Furthermore, the analysis of the computational requirements and simulations results both show that the SBLFXLMS algorithm requires less computations without suffering from any performance degradation of mutichannel nonlinear ANC systems.