Predistortion of Hammerstein and Wiener systems using the Nonlinear Filtered-x Prediction Error Method algorithm

Abstract

Adaptive predistortion of nonlinear systems described using Hammerstein and Wiener models is considered in this paper. The adaptive predistorter is modeled as a Wiener or Hammerstein system, respectively. The parameters of the linear and nonlinear blocks of the predistorter are estimated simultaneously using the Nonlinear Filtered-x Prediction Error Method (NFxPEM) algorithm. The NFxPEM algorithm is derived under the assumption that the parameters of the Wiener and Hammerstein predistorters are changing slowly during adaptation. Simulation study shows that the suggested predistorter using the NFxPEM algorithm can well compensate nonlinear distortion and effectively reduce spectral regrowth. Moreover, the suggested NFxPEM algorithm achieves much better results as compared to the Nonlinear Filtered-x Least Mean Squares (NFxLMS) algorithm. Vorverzerrung von Hammerstein-und Wiener-Systemen unter Anwendung des Nichtlineare Filter-x PredictionError-Methode-Algorithmus.Dieser Artikel behandelt die adaptive Vorverzerrung von nichtlinearen Systemen. Die Nichtlinearit€ at wird als Hammerstein-bzw. Wiener-Modell dargestellt und die adaptive Vorverzerrung entsprechend mit einem Wiener-bzw. Hammerstein-System durchgef€ uhrt. Der "Nonlinear Filtered-x Prediction Error Method (NFxPEM)"-Algorithmus sch€ atzt gleichzeitig die Parameter des linearen und des nichtlinearen Blocks des Vorverzerrungssystems. Der NFxPEM-Algorithmus wird unter der Bedingung, dass sich die Parameter des Vorverzerrungssystems w€ ahrend der Adaptation nur langsam € andern, hergeleitet. Simulationen zeigen, dass der vorgeschlagene NFxPEM-Algorithmus in der Lage ist, nichtlineare Verzerrungen zu kompensieren und die spektrale Fortpflanzung effektiv zu reduzieren. Zus€ atzlich wird gezeigt, dass der vorgeschlagene NFxPEM-Algorithmus wesentlich bessere Ergebnisse als der "Nonlinear Filtered-x Least Mean Squares (NFxLMS)"-Algorithmus erzielt.Schlü sselwö rter: Verzerrung; nichtlineare Systeme; Parameter-Sch€ atzung; Prediktionsmethoden IntroductionCancelling or reducing nonlinear distortion due to nonlinearity characteristic of some electronic devices is essential requirement in many areas. In wireless communication systems, the nonlinearity of the high power amplifiers is an obstacle to increase the transfer data rate and mobility. In Hi-Fi systems, small distortion produced by nonlinear components dominates the overall performance. Examples can be found in communication systems, speech processing and control engineering, see (Gao, Snelgrove, 1990;Lim et al., 1998;Gan, 2009).Several adaptive predistortion techniques based on using Volterra series as a model for the nonlinear system have been proposed (Gao, Snelgrove, 1990;Lim et al., 1998). However, since these techniques are based on using Volterra models, high computation complexity and slow convergence speed are expected problems during real-time implementation. Recently, an approach based on polyphase representation for Volterra filters that helps to reduce the computation complexity has been introduced in...