Diagonal-structure adaptive bilinear filters for multichannel active noise control of nonlinear noise processes

Abstract To accommodate multichannel nonlinear active noise control, the second-order Volterra filtered-x LMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms are usually applied in practical noise control systems. These two algorithms are effective in dealing with polynomial nonlinearity. Recently, a simplified bilinear leaky filtered-x least mean square (SBLFXLMS) algorithm is proposed based on a bilinear model in order to further reduce the computational load but it may have performance degradation. In this paper, we propose a novel nonlinear adaptive algorithm named as the diagonal-structure bilinear filtered-x least mean square (DBFXLMS) algorithm for multichannel nonlinear active noise control. In addition, the developed multichannel DBFXLMS algorithm is equipped with a stability control scheme to maintain a stable condition of the adaptive bilinear filter during the adaptive process. The performance of the proposed algorithm is validated through computer simulations and the computational complexity of the developed algorithm is analyzed. Computer simulations demonstrate that the proposed method has an improvement in terms of control performance in comparison with the conventional first-order FSLMS, second-order VFXLMS, and SBLFXLMS algorithms.