# Rational Function Model for Amplifiers

Another important polynomial model that can be used for compensation of PA nonlinearity is the rational function model. Rational functions are universal approximators and can be used for the estimation and detection of signals, such as radar signals [13]. A rational polynomial is the ratio of two polynomials given by:

Here, *J* and *K* are the nonlinearity orders of the numerator and denominator, respectively. An absolute-term denominator rational function (ADRF) is given by [14]:

This model includes memory in the system represented by M_{1}, M_{2}, *J,* and *K* are the nonlinearity orders; and, *a _{m j}* and

*b*are the coefficients of the model.

_{m k}The method proposed in [14] uses a dynamic rational function (DRF) with a memoryless flexible order denominator (MFOD) as expressed in Equation 6.40. The DRF-MFOD model was shown to have the best performance compared to the conventional MP based model and the ADRF model [15]. In addition, the DFR-MFOD model described by Equation 6.40 is less complex and has fewer number of parameters than the ADRF model.

Here, *M* represents the memory depth, *a _{m}j* and

*b*are the coefficients of the model; and,

_{k}*J*and

*K*are the nonlinearity orders of the numerator and denominator, respectively.