Pipelined set-membership approach to adaptive Volterra filtering

Due to the high computational complexity required by Volterra filter, some of its practical implementations consider pipelined adaptive Volterra filter architecture with two layers structure. However, its main challenges are the poor robustness against impulsive noise, slow convergence and high computational complexity for long memory high order expansion on each module. In this paper, we firstly extend the pipelined second-order adaptive Volterra filter to its high order version. Then, to reduce the computational complexity and improve the robust performance of pipelined adaptive Volterra filter architecture, the pipelined adaptive Volterra set-membership (PAVF-SM) algorithm and its robust version (PAVF-RSM) are proposed, which are derived from the least-perturbation property and adaptive approximation principle. Due to the inherent variable step size and nonlinear selective update mechanisms, the proposed PAVF-SM and PAVF-RSM algorithms achieve lower complexity and improved convergence performance. Simulations also verify the improved performance of the PAVF-SM and PAVF-RSM algorithms under Gaussian noise and impulsive noise environments.