Asymptotic Secrecy Analysis of Random Networks With Colluding Eavesdroppers

Abstract

We perform an analysis of the secrecy outage and transmission capacity of random networks under Nakagami-m fading with colluding eavesdroppers, in the asymptotic case of large reference signal-to-noise ratios. In literature, secrecy analysis from the perspective of collusion pool has still not been well characterized. Considering a network model that accounts for uncertainties both in node locations and channel coefficients, we approximate the distribution of the aggregate path gain received by a collusion of eavesdroppers. Using this result, the asymptotic secrecy rate distribution, the secrecy outage probability, and the secrecy transmission capacity of random networks with colluding eavesdroppers are obtained, with basic factors such as density of nodes, the guarding distance, and the fading figure all accounted for by explicit parameters. Since secrecy in low-outage random networks are found to be most significant when the density of active nodes is small, the expressions derived can be seen as upper-bounds on the three aforementioned secrecy performance metrics in random networks, offering particular insight on the impact of fading, density, and guarding distances, while taking into account cooperation among eavesdroppers. Furthermore, we give a bound on colluding pool size, which is pragmatic in creating a nonprotected communication zone for the typical destination.