Analysis of Local Secure Connectivity of Legitimate User in Stochastic Wireless Networks

In this paper, we investigate the local secure connectivity in terms of the probability of existing a secure wireless connection between two legitimate users and the isolated security probability of a legitimate user in stochastic wireless networks. Specifically, the closed-form expressions of the probability that there is a secure wireless communication between two legitimate users are derived first. Then, based on these equations, the corresponding isolated secure probability are given. The characteristics of local secure connectivity are examined in four scenarios combined from two wireless channel conditions (deterministic/Rayleigh fading) and two eavesdropper configurations (non-colluding/colluding). All the derived mathematical equations are validated by the Monte-Carlo simulation. The obtained numerical results in this paper reveal some interesting features of the impact of eavesdropper collusion, wireless channel fading, and density ratio on the secure connection probability and the isolated security probability of legitimate user in stochastic networks.