  In this paper, a new mathematical framework to the analysis of millimeter
wave cellular networks is introduced. Its peculiarity lies in considering
realistic path-loss and blockage models, which are derived from recently
reported experimental data. The path-loss model accounts for different
distributions of line-of-sight and non-line-of-sight propagation conditions and
the blockage model includes an outage state that provides a better
representation of the outage possibilities of millimeter wave communications.
By modeling the locations of the base stations as points of a Poisson point
process and by relying on a noise-limited approximation for typical millimeter
wave network deployments, simple and exact integral as well as approximated and
closed-form formulas for computing the coverage probability and the average
rate are obtained. With the aid of Monte Carlo simulations, the noise-limited
approximation is shown to be sufficiently accurate for typical network
densities. The proposed mathematical framework is applicable to cell
association criteria based on the smallest path-loss and on the highest
received power. It accounts for beamforming alignment errors and for multi-tier
cellular network deployments. Numerical results confirm that sufficiently dense
millimeter wave cellular networks are capable of outperforming micro wave
cellular networks, both in terms of coverage probability and average rate.
