Using random shape theory to model blockage in random cellular networks

Shadow fading is severe in downtown areas where buildings are densely located. This paper proposes a stochastic model to quantify blockages due to shadowing, using methods from random shape theory. Buildings inside a cell are modeled as line segments with random sizes and orientations, with locations from a spatial Poisson point process. Dense urban areas can be modeled by the parameters of the line process. Based on this construction, the distribution of the power loss caused by shadowing in a particular path is expressed in closed form. The distribution can be used to compute several performance metrics of interest in random systems. Simulations illustrate coverage and connectivity as a function of the metrics of blockages, such as the density and the average size of buildings.