In the field of cognitive radio (CR), radio frequency (RF) transceivers must be efficient to save the terminal battery autonomy. Therefore, when designing the CR power amplifier (CR-PA), an obvious objective is to optimize efficiency over a large bandwidth. As a consequence, the CR-PA operates in its non-linear region and then frequency-dependent distortions are generated. This issue is all the more critical as one deals with high peak-to-average power ratio (PAPR) like those of OFDM signals. In this paper, we develop a digital post-distortion and detection technique in order to compensate the non-linearities generated by the CR-PA. It is based on a dynamic Volterra model to take into account the non-linear behavior of the CR-PA. The key feature of the proposed technique is the joint estimations of the model parameters and the CR-PA input samples. For this reason, an extended Kalman filter (EKF) is considered. However, as the model parameters can vary over time, several EKFs are combined by means of an interacting multiple model (IMM) algorithm. Simulation results confirm the relevance of the proposed postdistortion and detection technique.