On spatial security outage probability derivation of exposure region based beamforming with randomly located eavesdroppers

This paper presents the closed-form expression for a circular array, of the spatial security outage probability which is a novel performance metric that measures the security level of the legitimate transmission from the spatial aspect in the presence of Poisson Point Process distributed eavesdroppers. In this paper, it is shown how beamforming is used to create an exposure region where any randomly located eavesdropper causes secrecy outage, based on which the general expression of the spatial security outage probability is derived. Using this, the closed-form expression is obtained for the circular array, which reveals the impact of the array parameters on the security performance.