Non-linear behavioral models play a key role in designing digital pre-distorters (DPDs) for non-linear power amplifiers (NLPAs). In general, more complex behavioral models have better capability, but they should be converted into simpler versions to assist implementation. In this paper, a conversion from a complex fifth order inverse of a parallel Wiener (PRW) model to a simpler memory polynomial (MP) model is developed by using frequency domain expressions. In the developed conversion, parameters of the converted MP model are calculated from those of original fifth order inverse and frequency domain statistics of the transmit signal. Since the frequency domain statistics of the transmit signal can be precalculated, the developed conversion is deterministic, unlike the conventional conversion that identifies a converted model from lengthy input and output data. Computer simulations are conducted to confirm that conversion error is sufficiently small and the converted MP model offers equivalent pre-distortion to the original fifth order inverse.

In this paper, a robust fractional order memory polynomial pre-distorter with two novel schemes to conduct digital base-band power amplifier pre-distortion is proposed. For the first scheme, fractional order terms are included in the conventional memory polynomial containing the odd and even order polynomial terms, which is called Scheme One. The second scheme, called Scheme Two, simply replaces even order polynomial terms with fractional order polynomial terms to improve the linear performance of power amplifiers. The mathematical expressions for these two schemes are derived. The computer simulations and numerical analysis show that, compared with the conventional pre-distortion methods, 11 dB and 8.5 dB more out-of-band suppression gain can be obtained by Scheme One and Scheme Two, respectively. Corresponding FPGA realization shows that the two schemes are cost-effective in terms of hardware resources.

This paper discusses an efficient discrete model for nonlinear RF power amplifier (PA) with long-term memory effects and analyzes its error. The procedure of converting RF signals and systems into a discrete domain is explained for a discrete baseband memory polynomial model. Unlike a previous simple memory polynomial model, the proposed discrete model has two different sampling frequencies: one for nonlinear system with long-term memory effects and one for input signal. A method to choose an optimal sampling frequency for the system and a discrete memory depth is proposed to minimize the sensitivity of the system for perturbation of the measured data. A two-dimensional sensitivity function which is a product of relative residual and matrix condition number is defined for least square problem of the proposed model. Examples with a wideband WiBro 3FA signal and a WCDMA 4FA signal for nonlinear transmitters are presented to describe the overall procedure and effectiveness of the proposed scheme.