A key element for many fading-compensation techniques is a (long-range) prediction tool for the fading channel. A linear approach, usually used to model the time evolution of the fading process, does not perform well for long-range prediction applications. In this article, we propose an adaptive fading channel prediction algorithm using a sum-sinusoidal-based state-space approach. This algorithm utilizes an improved adaptive Kalman estimator, comprising an acquisition mode and a tracking algorithm. Furthermore, for the sake of a lower computational complexity, we propose an enhanced linear predictor for channel fading, including a multi-step linear predictor and the respective tracking algorithm. Comparing the two methods in our simulations show that the proposed Kalman-based algorithm significantly outperforms the linear method, for both stationary and non-stationary fading processes, and especially for long-range predictions. The performance and the self-recovering structure, as well as the reasonable computational complexity, makes the algorithm appealing for practical applications 1 .