Connectivity based on shadow fading and interference in wireless ad hoc networks

Connectivity is one of the most fundamental properties in wireless ad hoc networks. Due to fading effects, the received power at certain distance becomes a random variable and a mass of unidirectional links emerged which is reflected by the shadowing model. Thus, research for network connectivity based on geometric model is inaccurate. Additionally, interference determines whether a link can be regarded as existence when the signal to interference and noise ratio (SINR) is larger than some threshold. In this paper, we propose a mathematical model to depict the impact of interference on the connectivity in a lognormal shadow fading environment. Based on the physical model of interference and mechanism of carrier sense, we first formulate the link connection probability, and obtain the probability of network connection with the random graph theory. Simulation shows effective carrier sense threshold has more important influence on the probability of network connection than other factors.