RF PA modeling considering odd-even and odd order polynomials

The use of “even” order polynomial terms in radio frequency power amplifier behavioral modeling and digital pre-distortion linearization has long been discussed. This contribution mathematically shows that the purely odd polynomials and the odd-even polynomials are equivalent up to the truncation error inherent in the model itself. The choice of odd or odd-even polynomial is equivalent to a choice of basis functions wherein the odd-even representation does not provide a richer set of basis functions, as earlier has been claimed. Modeling using measured data from a power amplifier shows that the difference in performance between the odd and odd-even polynomials is negligible for models at high nonlinear order. These findings are important to explain the appearance and use of the odd and odd-even models in power amplifier modeling and digital pre-distortion.