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).

In vehicle-to-vehicle (V2V) communication scenarios, the antenna heights of the communicating nodes are typically lower than the heights of scattering objects in the vicinity of these nodes such that signal propagation in the elevation plane cannot be ignored. Therefore, it is necessary to consider three-dimensional (3D) space for modeling radio propagation in V2V communication environments. In this paper, the temporal characteristics of a 3D semi-ellipsoid geometrical channel model for V2V communication scenarios is presented by assuming uniform scatterer distribution around the mobile stations (MSs). Using the 3D semi-ellipsoid channel model, closed-form expressions for the joint probability density function (PDF) of the time-of-arrival (ToA) and angle-of-arrival (AoA) in azimuth and elevation planes is derived. A closed-form expression for the marginal PDF of ToA of the received signal is also provided. The proposed analytical results are compared with those obtained from some notable geometric channel models found in the literature.

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