Orthonormal basis functions for memory predistorter in oversampled systems
Volterra model or memory polynomial model are commonly used to describe the nonlinearity with memory effects for power amplifier (PA) modeling as well as digital predistorter designs. Different monomial terms of the Volterra model or memory polynomial model are highly correlated, which become a challenge during the fixed-point implementation of the coefficients estimation as the data matrix is ill-conditioned. Previous works derived orthogonal basis functions to eliminate the correlation among different monomial terms. Conversely, models of the PAs or the digital predistorters work in the oversampled domain to capture the adjacent band and/or out of band emissions. The correlation among data samples, which was neglected in previous works, can also be a major issue to the numerical instability in the coefficients estimation. In this article, we propose a set of new orthonormal basis functions to eliminate the correlation among different monomial terms as well as the correlation among data samples. As the proposed orthonormal basis functions can be predetermined and implemented with look up tables, the fixed-point implementation is feasible and online computational complexity is greatly reduced. Simulation and experimental results show that the proposed orthonormal basis functions outperform the conventional ones in terms of condition number reduction as well as spectral regrowth suppression.  2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:202212, 2015.
orthonormal basis functions oversampling nonlinearity power amplifiers digital predistorter