  Millimeter wave (mm-wave) communications is considered a promising technology
for 5G networks. Exploiting beamforming gains with large-scale antenna arrays
to combat the increased path loss at mm-wave bands is one of its defining
features. However, previous works on mm-wave network analysis usually adopted
oversimplified antenna patterns for tractability, which can lead to significant
deviation from the performance with actual antenna patterns. In this paper,
using tools from stochastic geometry, we carry out a comprehensive
investigation on the impact of directional antenna arrays in mm-wave networks.
We first present a general and tractable framework for coverage analysis with
arbitrary distributions for interference power and arbitrary antenna patterns.
It is then applied to mm-wave ad hoc and cellular networks, where two
sophisticated antenna patterns with desirable accuracy and analytical
tractability are proposed to approximate the actual antenna pattern. Compared
with previous works, the proposed approximate antenna patterns help to obtain
more insights on the role of directional antenna arrays in mm-wave networks. In
particular, it is shown that the coverage probabilities of both types of
networks increase as a non-decreasing concave function with the antenna array
size. The analytical results are verified to be effective and reliable through
simulations, and numerical results also show that large-scale antenna arrays
are required for satisfactory coverage in mm-wave networks.
