This paper deals with digital post-distortion for radio frequency (RF) power amplifiers (PAs) used in cognitive radio (CR) systems. This technique is based on a new approach modelling the PA behavior. The latter characterizes not only the PA non-linearities and memory effects but also its highly-varying behavior with carrier frequency in CR context. Given this modelling, a Kalman algorithm based post-distortion and detection is used to compensate the CR-PA non-linear effect and restore the input signal. This method is suitable for uplink communications in CR context because it saves the consumed power at the transmitter. Finally, this on-line technique does not require known test signals to estimate the PA model parameters.