Nonlinear adaptive bilinear filters for active noise control systems

The reference and error channels of active noise control (ANC) systems may be saturated in real-world applications if the noise level exceeds the dynamic range of the electronic devices. This nonlinear saturation degrades the performance of ANC systems that use linear adaptive filters with the filtered-X least-mean-square (FXLMS) algorithm. This paper derives a bilinear FXLMS algorithm for nonlinear adaptive filters to solve the problems of signal saturation and other nonlinear distortions that occur in ANC systems used for practical applications. The performance of this bilinear adaptive filter is evaluated in terms of convergence speed, residual noise in steady state, and the computational complexity for different filter lengths. Computer simulations verify that the nonlinear adaptive filter with the associated bilinear FXLMS algorithm is more effective in reducing saturation effects in ANC systems than a linear filter and a nonlinear Volterra filter with the FXLMS algorithm.