Wireless physical-layer security: The case of colluding eavesdroppers

We consider the fundamental security limits of stochastic wireless networks in the presence of colluding eavesdroppers. By establishing a direct connection with the single-input multiple-output (SIMO) Gaussian wiretap channel, we are able to provide a complete characterization of the secrecy capacity for the case in which the eavesdroppers are scattered according to a spatial Poisson process. Our analysis, which includes the probabilities of existence and outage of secrecy capacity, helps clarify how the spatial density of eavesdroppers can jeopardize the success of wireless physical-layer security based on information-theoretic principles.