Percolation on the Information-Theoretically Secure Signal to Interference Ratio Graph

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes (PPPs) in R2 of intensities λ and λE respectively. A directed edge from one legitimate node A to another legitimate node B exists provided the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the received signal at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter γ. The graph is said to percolate when there exists an infinite connected component.