New simple filtered-x algorithm for parallel Hammerstein systems

A new nonlinear filtered-x algorithm is proposed for adaptive feedforward compensation for parallel Hammerstein systems, which has many applications such as nonlinear active noise control and predistortion for nonlinear high power amplifiers. To attenuate the compensation error, a virtual error and prediction error are introduced and forced into zero by adjusting three nonlinear adaptive filters in an on-line manner. It is shown that the convergence of the compensation error to zero can be assured by forcing the prediction error and virtual error to zero separately. The proposed method can adjust the adaptive feedforward controller by using the newly introduced virtual error, unlike the ordinary nonlinear filtered-x algorithm using the compensation error directly. Furthermore, the PE property of the reference signal is not needed, which is a great advantage of the proposed direct approach. Its effectiveness is examined and clarified in comparison with an ordinary nonlinear filtered-x algorithm in numerical simulations.