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In this paper, we develop a three-dimensional geometrical channel model for mobile-to-mobile (M2M) communication environment. The proposed model combines most of the existing two-dimensional (2D) and three-dimensional (3D) geometrical channel models for M2M and fixed-to-mobile (F2M) communication channels into one generalized model. Using the proposed model, closed-form expressions for the joint probability density function (PDF) of angle-of-arrival (AoA) and time-ofarrival (ToA) in azimuth and elevation planes are derived. These results are then verified by simulations and available field measurements. Furthermore, comprehensive comparisons of the proposed channel model are carried out with the existing 2D and 3D channel models in the literature, which show that many notable geometrical channel models in M2M and F2M communication environments become the special cases of our proposed generalized 3D geometrical channel model by adjusting corresponding channel parameters. Consequently, the proposed 3D channel model can be taken as a useful tool for modeling mobile ad hoc networks (MANET), Vehicular Ad hoc Networks (VANET) and Intelligent Transportation Systems (ITS).

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