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This paper expounds the systematic modeling of the behavior of radio frequency (RF) power amplifiers (PAs) exhibiting nonlinear, dynamic behavior. The approach begins with an analysis of the PA output signal to deduce the minimum embedding parameters required to accurately model its response, particularly the nonlinearity order and memory effects depth. The knowledge of the RF PA is then exploited in limiting the number of kernels consequently addressing the complexity of the Volterra series which has been the key hindrance to its wider practical adoption. In the proposed Volterra series model, performance is assessed and compared to memory polynomial model and dynamic deviation reduction Volterra models when used to linearize different high-power amplifiers driven with wideband signals of bandwidth up to 40 MHz. Significant linearization performance is achieved using a reduced number of kernels. [ABSTRACT FROM PUBLISHER]