  Millimeter wave offers a sensible solution to the capacity crunch faced by 5G
wireless communications. This paper comprehensively studies physical layer
security in a multi-input single-output (MISO) millimeter wave system where
multiple single-antenna eavesdroppers are randomly located. Concerning the
specific propagation characteristics of millimeter wave, we investigate two
secure transmission schemes, namely maximum ratio transmitting (MRT)
beamforming and artificial noise (AN) beamforming. Specifically, we first
derive closed-form expressions of the connection probability for both schemes.
We then analyze the secrecy outage probability (SOP) in both non-colluding
eavesdroppers and colluding eavesdroppers scenarios. Also, we maximize the
secrecy throughput under a SOP constraint, and obtain optimal transmission
parameters, especially the power allocation between AN and the information
signal for AN beamforming. Numerical results are provided to verify our
theoretical analysis. We observe that the density of eavesdroppers, the
spatially resolvable paths of the destination and eavesdroppers all contribute
to the secrecy performance and the parameter design of millimeter wave systems.
