On transmission secrecy outage of a multi-antenna system with randomly located eavesdroppers

This letter studies the physical-layer security of a multi-antenna transmission system in the presence of Poisson distributed eavesdroppers. The transmission secrecy outage probability (TSOP) is adopted to evaluate the security. We derive an accurate integral expression as well as a closed-form upper bound on TSOP for the noncolluding eavesdroppers' case and a closed-form solution for the colluding eavesdroppers' case, respectively. Based on these, we define a novel concept of security region to intuitively illustrate the security from a spatial perspective. We further analyze the impacts of various factors on the security, such as the number of transmit antennas, the node intensity, and the target secrecy rate.