The Secrecy Outage Probability for the $i$th Closest Legitimate User in Stochastic Networks

Motivated by information-theoretic security, the Poisson model for secure connectivity in stochastic networks has recently received great attention. Although several expressions for secrecy characterization between a typical node and its neighbors were obtained, to the authors' knowledge, there are no exact closed-form expressions for the Rayleigh fading channel. In this letter, a method is proposed for obtaining the closed-form expressions for secrecy outage probability at the ith closest legitimate user for colluding eavesdroppers in the Rayleigh fading channel. Analytical results easily show that the secrecy outage probability exponentially increases with respect to the value of the index i, whereas the secrecy rate requirement must be sacrificed to realize secure connectivity for farther legitimate users. Furthermore, the method is also developed for non-colluding in Rayleigh fading and deterministic channels to better demonstrate the impact of collusion and Rayleigh fading on secure connectivity.