  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.
