Estimating models of inverse systems

This paper considers the problem of how to estimate a model of the inverse of a system. The use of inverse systems can be found in many applications, such as feedforward control and power amplifier predistortion. The inverse model is here estimated with the purpose of using it in cascade with the system itself, as an inverter. A good inverse model in this setting would be one that, when used in series with the original system, reconstructs the original input. The goal here is to select suitable inputs, experimental conditions and loss functions to obtain a good input estimate. Both linear and nonlinear systems will be discussed. For nonlinear systems, one way to obtain a linearizing prefilter is by Hirschorn´s algorithm. It is here shown how to extend this to the postdistortion case, and some formulations of how the pre- or postinverter could be estimated are also presented.