Pipelined robust M-estimate adaptive second-order Volterra filter against impulsive noise

The main limits on adaptive Volterra filters are their computational complexity in practical implementation and significant performance degradation under the impulsive noise environment. In this paper, a low-complexity pipelined robust M-estimate second-order Volterra (PRMSOV) filter is proposed to reduce the computational burdens of the Volterra filter and enhance the robustness against impulsive noise. The PRMSOV filter consists of a number of extended second-order Volterra (SOV) modules without feedback input cascaded in a chained form. To apply to the modular architecture, the modified normalized least mean M-estimate (NLMM) algorithms are derived to suppress the effect of impulsive noise on the nonlinear and linear combiner subsections, respectively. Since the SOV-NLMM modules in the PRMSOV can operate simultaneously in a pipelined parallelism fashion, they can give a significant improvement of computational efficiency and robustness against impulsive noise. The stability and convergence on nonlinear and linear combiner subsections are also analyzed with the contaminated Gaussian (CG) noise model. Simulations on nonlinear system identification and speech prediction show the proposed PRMSOV filter has better performance than the conventional SOV filter and joint process pipelined SOV (JPPSOV) filter under impulsive noise environment. The initial convergence, steady-state error, robustness and computational complexity are also better than the SOV and JPPSOV filters.