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Mobile systems operate in a variety of different scenarios. These include remote rural areas, where the terrain is irregular, dense urban areas where buildings dominate, and even inside those buildings. Equipment can either be carried by pedestrians or be in a high-speed vehicle or train. Various alternative methods of predicting the mean signal strength and its variability are surveyed and their applicability to a particular situation is discussed. Ray-tracing methods are introduced in connection with indoor propagation. Multipath, probably the single most destructive influence on mobile systems is extensively characterised, and its effects on narrowband and wideband systems are discussed. Channel sounders, used to obtain practical measurements, are described and methods of hardware and software simulation are reviewed. The emphasis throughout is on a physical understanding of the phenomena which influence radio signals in mobile radio systems.