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A unified three-dimension probabilistic model is presented to describe multipath phenomena in various built-up areas with randomly distributed buildings placed on rough terrain. The joint information regarding angle-of-arrival and time delay spread is obtained through study of the main propagation mechanisms in urban wireless communication channels. Comparison with other models and with measurements carried out in different urban environments is presented. It is shown that in dense urban areas the distribution of the obstructions surrounding the base station and the moving vehicle, as well as the elevations of both antennas contribute to the signal power profiles in the space and time domains. Using a combination of the statistical description of the built-up terrain and the 3D deterministic approach based on Kirchhoff approximation, the effects of scattering and diffraction phenomena on signal power spatial and temporal distribution are examined.