Asymptotic Connectivity of Large-Scale Wireless Networks with a Log-Normal Shadowing Model

In this paper, we investigate connectivity of largescale wireless networks with a log-normal shadowing model from a percolation-based perspective, where all nodes have equal transmission capabilities and are uniformly and independently distributed at random over a large area. Firstly, based on the lognormal shadowing model, we discuss the probability that there is a link between two nodes with a distance d between them, named connection function. The connection function captures the connectivity characteristics of the wireless network in a shadow fading environment and distinguishes it from the purely random geometric graph or the purely random graph. Then, an analytical upper bound on the critical node density for asymptotic connectivity of the wireless network is derived based on the connection function. Furthermore, we also provide a more accurate estimation for the upper bound based on the previous empirical studies on purely random geometric graph, called the experiment-based upper bound. At last, the correctness and tightness of these two upper bounds are verified by extensive simulations.