: Due to correlated fading in frequency hopping (FH) wireless communication systems, it is possible to predict the future channel state information (CSI) for one frequency based on past channel observations of other frequencies. This prediction capability enables adaptive transmission techniques for mobile radio FH systems. We investigate the optimal Minimum Mean Square Error (MMSE) Long Range Prediction (LRP) algorithm for slow frequency hopping (SFH) systems that employ coherent detection. A recursive filter update algorithm is proposed to reduce the complexity of this method. Statistical model of the prediction accuracy is developed and used in the design of reliable adaptive modulation techniques. Moreover, adaptive modulation is combined with adaptive transmitter frequency diversity to mitigate the effect of fading and partial-band interference in frequency hopping communications. Both standard Jakes model and a realistic non-stationary physical model are employed to test the perf...