Polynomials and LUTs in PA Behavioral Modeling: A Fair Theoretical Comparison

Traditionally, power amplifier behavioral modeling and digital predistortion have been based on polynomials or Volterra series. Recently, however, there has been a trend to substitute polynomial representations by interpolated lookup tables (LUTs) because of the known problems associated with the series´ identification. These problems, commonly recognized as ill-conditioning, are generally related to the poor orthogonality verified in the polynomial basis functions for many common input signals. However, in this paper we will show that polynomials can be reformulated to achieve the identification quality of interpolated LUTs, while maintaining their beneficial properties. At the same time we will provide a unified view between polynomial and spline interpolation basis functions. By doing this we will present polynomials that share the benefits of spline interpolated LUTs and argue that both descriptions can be used interchangeably and with similar advantages.