Adaptive Function Expansion 3-D Diagonal-Structure Bilinear Filter for Active Noise Control of Saturation Nonlinearity

In this paper, a general function expansion bilinear (FEB) filter with a 3-D diagonal structure is proposed to deal with the problem of saturation nonlinearity in active noise control (ANC) systems. In an ANC system, the reference microphone and/or loudspeaker may be saturated when the acoustic noise and/or the controller output exceeds the dynamic limits of electronic devices. Such saturation nonlinearity degrades the control performance of the linear and some nonlinear control filters equipped with a filtered-x least mean square (FXLMS) algorithm. In order to tackle the problem of signal saturation, we use a new nonlinear saturation ANC (NSANC) model and derive a function expansion diagonal-structure bilinear FXLMS (FEDBFXLMS) algorithm. The performance of the proposed filters equipped with the associated FEDBFXLMS algorithm is validated through the analysis of computational complexity and simulations of various nonlinearities for NSANC systems. Computer simulation results demonstrate that the proposed FEB filter can achieve significant performance improvement in reducing saturation effects in comparison with the diagonal-channel bilinear filter and the recursive second-order Volterra filter based on the FXLMS algorithm, which often outperform the conventional nonlinear Volterra and functional link artificial neural network (FLANN) filters.