A statistical analysis of wireless connectivity in three dimensions

In this paper, the results reported in (J. Orriss et al, IEEE Trans. on Comm., vol.51, no.4, 2003), where some probability distributions for the number of nodes which can communicate with one another are derived, are extended from the 2D to the 3D case. The nodes are assumed to be randomly and uniformly distributed over an area, and subject to random channel fluctuations. The analytical handling of the problem leads to closed form solutions, showing that, among the other results, the number of audible nodes from the infinite space, or a given volume, is Poisson with mean depending on the propagation parameters and the maximum loss. The model can be useful to investigate networks of tiny nodes (such as RFIDs, or wireless sensors) where the vertical dimension of the environment (a building, or a room, or a container) becomes very significant with respect to the short range of the single communication links.