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Line-of-sight paths over random terrain

Line-of-sight paths are important as VHF radio channels. In a mobile radio system, for example, the landscape determines the communication possibilities in a complicated way. This paper analyzes a simple model of rough terrain to relate statistical terrain properties to line-of-sight paths. The model is constructed from conical hills, all the same height, distributed at random over the surface of a spherical earth. The parameters of the model are the earth's radius a, the density σ of hills, and the grade g of the hills. Although a simpler planar model is obtained by letting a → ∞, a finite spherical earth is needed for most questions. Assuming that a base station is located at the peak of a hill, the most interesting line-of-sight paths are those from a typical hilltop. A large number of statistics of these paths are then derived, usually as simple functions of a, σ, and g. These include properties of paths to other peaks, to the horizon, and to random points on the ground.