Phase Transition Width of Connectivity of Wireless Multi-Hop Networks in Shadowing Environment

In this paper, we study the well-known phase transition behavior of connectivity in a wireless multi-hop network, but, in contrast to other studies, in a shadowing environment. We consider that a total of n nodes are randomly, independently and uniformly distributed on a unit square in R², each node has a uniform transmission power and any two nodes are directly connected if and only if the power received by one node from the other node, as determined by the log-normal shadowing model, is larger than or equal to a given threshold. We extend the results obtained under the unit disk communication model in previous work to the more realistic log-normal shadowing model, and derive an analytical formula for the phase transition width of connectivity for large n. We also demonstrate how our results can be extended to higher dimensional networks and to other channel models.