Partitioned block frequency-domain adaptive second-order Volterra filter

Finite-length Volterra filters are known to be able to model a wide range of real world nonlinear systems. In this paper, we present an algorithm that allows for different memory lengths of the linear and quadratic Volterra kernel while preserving the advantages of fast convolution techniques in the frequency domain for a second-order Volterra filter. This is achieved by extending partitioned block methods to second-order Volterra filters. To obtain corresponding adaptive realizations of the proposed approach, we present generalizations of known frequency-domain algorithms for Volterra filters and partitioned block frequency-domain adaptive filters for linear systems, respectively. To exploit the advantages of adaptive frequency-domain algorithms with respect to convergence speed, we provide a frequency bin-wise normalization of the step-size parameters. To evaluate the performance of the proposed approach, simulation results are given for the application to nonlinear acoustic echo cancellation. The results confirm the improved convergence of a second-order partitioned block frequency-domain adaptive Volterra filter (PBFDAVF) compared with time-domain adaptation of the kernel coefficients.