# Box-Oriented Models

## Introduction

Various behavioral modeling techniques have been introduced and detailed in previous chapters. Chapter 5 explains polynomial based modeling and compensation of nonlinear distortions introduced by PAs with reasonably large memory effects. It has been shown that these polynomial models result in high performance. However, implementation of these models results in hardware complexity as these models yield a large number of coefficients. Hence, low complexity is essential for the design of behavioral models and their hardware implementation.

In this chapter, box-/block-oriented models that model the dynamic nonlinear effects of the PA are explained. These models aim to reduce the complexity and enhance the numerical stability of the system. The box-oriented models tend to reduce the number of coefficients required to compute the model and improve the matrix conditioning and dispersion coefficient.

## Hammerstein and Wiener Models

Earlier behavioral models, such as the Saleh model, model the static nonlinear behavior of PAs and do not consider the important memory effects that have gained enormous importance, due to the increasing bandwidth. In this section, two simple box-oriented models for modeling the nonlinear behavior of PAs are described. These models - the Wiener model and the Hammerstein model - represent a class of two-block models where one block accounts for the static nonlinear behavior of the PA, while the other deals with the linear memory effects in the system.

*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 6.1 **Block diagram of the Wiener model