A nonlinear dynamic behavioral model for radio frequency power amplifiers is presented. It uses orthonormal basis functions, Kautz functions, with complex poles that are different for each nonlinear order. It has the same general properties as Volterra models, but the number of parameters is significantly smaller. Using frequency weighting the out-of-band model error can be reduced. Using experimental data it was found that the optimal poles were the same for different input powers and for the different nonlinear orders. The optimal poles were also the same for direct and inverse models, which could be explained theoretically to be a general property of nonlinear systems with negligible linear memory effects. The model can be used as either a direct or inverse model with the same model error for power amplifiers with negligible linear memory effects.

A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA.

A digital predistortion algorithm for radio frequency power amplifiers based on orthonormal basis functions is presented. It has the same general properties as a Volterra model, but fewer parameters. Experimentally, using a 3.84 MHz wide signal at 2.14 GHz, the adjacent channel power was suppressed 12 to 15 dB, which was 5 to 7 dB more than a polynomial predistorter.

A stepped three-tone measurement technique based on digitally modulated baseband signals is used in characterizing radio-frequency power amplifiers (PAs). The bandwidths of the stepped measurement were 8.8 MHz for the input signal and 26.4 MHz for the output signal. A PA designed for third-generation mobile telecommunication system was analyzed. The amplitude and phase of the third-order Volterra kernel were determined from the identified intermodulation products. The properties of the Volterra kernel along certain paths in the 3-D frequency space were analyzed and compared to some box models for nonlinear systems. The main symmetry of the third-order Volterra kernel of this PA was found to be of the type given by the cascaded quadratic nonlinearities with a linear filter in between (a Hammerstein-Wiener system), and frequency dependence, i.e., memory effects, was found to be due to the effects at the baseband.