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From the beginnings of mobile communication, there is a high demand for realistic models for mobile fading channels. The reason for the demand is that channel models are essential for the performance evaluation, parameter optimisation, and test of mobile communication systems. Design methods for mobile fading channels are therefore of great importance for system engineers who are involved in the development of present and future mobile communication systems. In this presentation, an overview will be given about several design methodologies commonly used for the design of mobile radio channel models in present and future wireless communication systems. All presented channel models have in common that they are derived from a superposition of a finite number of complex sinusoids. However, the design methodologies differ in the way of computing the model parameters determining the statistical behaviour of the channel model. It will be shown that the proposed channel models are widely flexible, which allows an excellent fitting of their principal statistical properties against measurement data of real-world channels or against the statistics of any given reference channel model. Special interest will be paid to the state-of-the-art in modelling and simulation of mobile-to-mobile MIMO channel models as well as fading channel models for relay-based cooperative networks. The statistical properties of these channel models will be investigated analytically with emphasis on the distribution of the received envelope and with respect to the channelspsila correlation properties in the space, time, and frequency domain. The obtained results show that the statistical properties of the channel models required for future mobile communication systems are quite different from the statistics of the channel models used in present mobile communication systems.