  We provide a comprehensive overview of mathematical models and analytical
techniques for millimeter wave (mmWave) cellular systems. The two fundamental
physical differences from conventional Sub-6GHz cellular systems are (i)
vulnerability to blocking, and (ii) the need for significant directionality at
the transmitter and/or receiver, which is achieved through the use of large
antenna arrays of small individual elements. We overview and compare models for
both of these factors, and present a baseline analytical approach based on
stochastic geometry that allows the computation of the statistical
distributions of the downlink signal-to-interference-plus-noise ratio (SINR)
and also the per link data rate, which depends on the SINR as well as the
average load. There are many implications of the models and analysis: (a)
mmWave systems are significantly more noise-limited than at Sub-6GHz for most
parameter configurations; (b) initial access is much more difficult in mmWave;
(c) self-backhauling is more viable than in Sub-6GHz systems which makes
ultra-dense deployments more viable, but this leads to increasingly
interference-limited behavior; and (d) in sharp contrast to Sub-6GHz systems
cellular operators can mutually benefit by sharing their spectrum licenses
despite the uncontrolled interference that results from doing so. We conclude
by outlining several important extensions of the baseline model, many of which
are promising avenues for future research.
