  In this paper, a novel Poisson hole process (PHP) modeling of wireless
networks is proposed. We consider a more general hole shape, i.e. circular
sector holes in a random direction, to capture the spatial separation between
tiers in a millimeter wave (mmWave) heterogeneous cellular network (HCN). In
this case, small cell BSs (SBSs) and macrocell BSs (MBSs) are distributed as a
PHP and Poisson point process (PPP). Due to fundamental propagation differences
between mmWave and microwave frequencies, we incorporate blockage and
directional beamforming in the network model. Using tools from stochastic
geometry, the evaluation of the coverage performance in a two-tier mmWave HCN
is provided. Since the exact formulation of distance distribution, association
probability and coverage probability based on PHP modeling of SBSs is not
known, fairly accurate expressions for them are derived and validated by
simulation results. Moreover, some interesting facts about the effect of holes
on coverage probability and the relation between proposed hole configuration
and prior models with circular holes is discovered. It turns out that the
analysis based on the proposed PHP model can provide a more general study than
prior works and the proposed approaches are more accurate for two-tier HCNs
than independent PPP-based analysis.
