Defining Spatial Security Outage Probability for Exposure Region Based   Beamforming
  With increasing number of antennae in base stations, there is considerable interest in using beamfomining to improve physical layer security, by creating an `exposure region' that enhances the received signal quality for a legitimate user and reduces the possibility of leaking information to a randomly located passive eavesdropper. The paper formalises this concept by proposing a novel definition for the security level of such a legitimate transmission, called the `Spatial Secrecy Outage Probability' (SSOP). By performing a theoretical and numerical analysis, it is shown how the antenna array parameters can affect the SSOP and its analytic upper bound. Whilst this approach may be applied to any array type and any fading channel model, it is shown here how the security performance of a uniform linear array varies in a Rician fading channel by examining the analytic SSOP upper bound. 
Yuanrui Zhang and Youngwook Ko and Roger Woods and Alan Marshall
cs.IT math.IT