Efficient Implementation of Volterra Diagonal Bilinear Filter for Nonlinear Active Noise Control

In this paper, a channel reduced implementation with a bounded input bounded output (BIBO) stable control strategy of the Volterra expansion diagonal-structure bilinear filtered-x least mean square (VDBFXLMS) algorithm is proposed for nonlinear active noise control (NANC) system. We analyze the computational complexity to show the significant reduction of computational load. Using 2 channels for feedforward Volterra section and 2 channels for bilinear cross section in the proposed implementation, the channel reduced VDBFXLMS (CRVDBFXLMS) algorithm achieves 79.6% reduction of multiplications given the secondary path with a length of 15 coefficients when comparing with the standard VDBFXLMS algorithm. We also derive the sufficient BIBO stable condition and design a control strategy to remedy the unstable problem. The computer simulations are given to validate the efficiency and effectiveness.