5 - Nonlinear models with nonlinear memory

Summary

Introduction

This chapter contains a comprehensive overview of the approaches for modelling nonlinear PAs with nonlinear memory. The difference between linear and nonlinear memory effects was presented in subsection 1.2.2 on the basis of the model presented in Figure 1.6.

The simplest modelling approach is the memory polynomial model. It will be explained that introducing non-uniform time-delay taps yields better results. Two more elaborate approaches that are closely related to the memory polynomial model are the time-delay neural network (TDNN) model and the nonlinear autoregressive moving-average (NARMA) model.

In the case of the TDNN model, the memoryless nonlinear network is described by an artificial neural network (ANN). Since ANNs have gained importance in microwave PA behavioural modelling, the concept will be explained in a separate section. In the case of the NARMA model the output depends not only on past values of the input but also on past values of the output. Stability may be a problem with this modelling approach, but criteria are derived to check for this.

Another way to model nonlinear PAs with nonlinear memory effects is by an extension of the well-known Wiener modelling approach. By introducing parallel branches consisting of a linear time-invariant (LTI) system followed by a memoryless nonlinear system, nonlinear memory effects can be modelled adequately.

A further category of models comprises the Volterra-series-based models. It is often said that the computation of Volterra kernels is difficult when the system has complex nonlinearity. A number of extended approaches have been developed to overcome the intrinsic disadvantages of Volterra models.