A new method of second-order parallel adaptive Volterra filter

The adaptive Volterra filter (AVF), based on the discrete Volterra series, has been proposed to identify a nonlinear system, remove nonlinear distortion, etc. In AVF algorithms, the fast transversal filter (FTF) algorithm (Junghsi Lee and Mathews, V.J., IEEE Trans. Acoust., Speech, Signal Process., vol.41, no.3, p.1087-102, 1993), which has O(N
³
) multiplications per iteration, has perfect convergence properties, where N represents the memory span of the nonlinear system model. However, in practical applications, we require more reduction in computational complexity. Until now, although the technique of dividing AVF by the order of the Volterra kernel has been proposed (Takeichi, K. and Furukawa, T., 16th Digital Signal Process. Symp., 2001), it can only reduce calculations in the second-order AVF by 20%. The paper presents a design method for a second-order parallel adaptive Volterra filter (PAVF) to decrease calculations further. Finally, to illustrate the effectiveness of the proposed method, the results of computer simulation with the FTF algorithm are presented