# Memory Polynomial Based Models

## Introduction

Radio frequency (RF) power amplifiers and transmitters are considered to be dynamic nonlinear systems that concurrently exhibit static nonlinearities as well as nonlinear memory effects. Thus, the most comprehensive behavioral model that can be adopted to fully model such systems is the Volterra series described in Chapter 2. However, full Volterra series (which do not include any simplifying assumptions) are typically difficult to manipulate and result in unrealistically large models that are not suitable in practice.

The memory polynomial model represents a very compact version of the Volterra series and has been widely applied in the behavioral modeling and predistortion of power amplifiers and transmitters having memory effects. A wide assortment of structures based on the memory polynomial has been proposed for the modeling and predistortion of RF power amplifiers and transmitters. Although the functions reported in this chapter are commonly referred to as models, they can be seamlessly used in both behavioral modeling and digital predistortion applications.

Figure 5.1 illustrates the two methodologies that can be recognized as the rationals behind the development of a large number of memory polynomial based structures. As shown in this figure, the memory polynomial model has low complexity but relatively limited performance; whereas the Volterra series model has a higher complexity but leads to better performance. Thus, the first approach in the development of memory polynomial based models is aimed at reducing the number of coefficients of the Volterra series, while maintaining satisfactory accuracy. Conversely, the second approach consists in augmenting the memory polynomial model to improve its performance with minimal increase in the model complexity. The goal is an ideal model that combines both high performance and low complexity.

*Behavioral Modeling and Predistortion of Wideband Wireless Transmitters*, First Edition. Fadhel M. Ghannouchi, Oualid Hammi and Mohamed Helaoui.

© 2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd.

**Figure 5.1 **Trends in single-box memory polynomial models development