Modeling Dense Urban Networks with 3D Stochastic Geometry

Over the past decade, many works on the modeling of wireless networks using stochastic geometry have been proposed. Results about probability of coverage, throughput or mean interference, have been provided for a wide variety of networks (cellular, ad-hoc, cognitive, sensors, etc). These results notably allow to tune network protocol parameters. Nevertheless, in their vast majority, these works assume that the wireless network deployment is flat: nodes are placed on the Euclidean plane. However, this assumption is disproved in dense urban environments where many nodes are deployed in high buildings. In this letter, we derive the exact form of the probability of coverage for the cases where the interferers form a 3D Poisson Point Process (PPP) and a 3D Modified Matern Process (MMP), and compare the results with the 2D case. The main goal of this letter is to show that the 2D model, although being the most common, can lead either to an optimistic or a pessimistic evaluation of the probability of coverage depending on the parameters of the model.