Meta Distribution of the Secrecy Rate in the Presence of Randomly Located Eavesdroppers

This letter studies the meta distribution of the secrecy rate for a legitimate link in the presence of eavesdroppers (EDs) with locations modeled as a Poisson point process. Both colluding and non-colluding EDs are considered. The meta distribution of the secrecy rate can provide the fraction of the realizations of EDs fulfilling a target secrecy rate. It can either be formulated using the Gil-Pelaez theorem with the imaginary moments of the conditional secrecy success probability (CSSP) given the realization of EDs or approximated by the beta distribution with the first two moments only. Hence, we first derive the ${b}$ th moment of the CSSP for the colluding scenario. Then, we formulate the exact first moment and the approximated second moment of the CSSP for the non-colluding scenario using the Fortuin-Kasteleyn-Ginibre inequality. Finally, simulations are used to validate the analytic results.