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We introduce novel iterative and recursive joint estimators for the frequency offset and fading rate in mobile multipath channels. In essence, we show how the instantaneous values of the frequency offset and fading rate can be efficiently extracted from the estimated autoregressive channel parameters, which by themselves give a parametric description of the fading statistics (i.e. the scattering function of the channel). The estimated fading statistics can be exploited in designing advanced receiver and transmitter algorithms for future high bitrate and high mobility applications. Especially, an adaptivity of many transmitter algorithms like channel encoders, interleavers and modulators could be based on the estimated fading statistics rather than instantaneous channel conditions. At the receiver side, the channel equalizer, including the channel estimators, can be configured with the aid of estimated fading statistics.