Realizing higher-order nonlinear Wiener adaptive systems [Wiener filter example]

A popular model used for nonlinear adaptive system modeling is the truncated nonlinear Volterra model. The difficulty of using the truncated Volterra models has limited typical applications to second order. Very few papers in the literature consider third or higher order. The drawbacks of the Volterra models include slow convergence speed, large number of coefficients, high computational complexity and difficulty with using higher-order models. Recently, we introduced a new method of implementing polynomial nonlinear adaptive filters using the discrete-time nonlinear Wiener model. The advantages of the nonlinear Wiener model over the Volterra model include faster convergence, smaller number of coefficients, less number of computations and avoidance of the dilemma of multiple local minima. In this paper, we present a fourth-order nonlinear Wiener adaptive filter suitable for polynomial-based nonlinearity applications. We also present some computer simulations results which verify the advantages of our algorithm over Volterra-model based ones.