  A K-tier heterogeneous mmWave uplink cellular network with clustered user
equipments (UEs) is considered in this paper. In particular, UEs are assumed to
be clustered around small-cell base stations (BSs) according to a Gaussian
distribution, leading to the Thomas cluster process based modeling. Specific
and practical line-of-sight (LOS) and non-line-of-sight (NLOS) models are
adopted with different parameters for different tiers. The probability density
functions (PDFs) and complementary cumulative distribution functions (CCDFs) of
different distances from UEs to BSs are characterized. Coupled association
strategy and largest long-term averaged biased received power criterion are
considered, and general expressions for association probabilities are provided.
Following the identification of the association probabilities, the Laplace
transforms of the inter-cell interference and the intra-cluster interference
are characterized. Using tools from stochastic geometry, general expressions of
the SINR coverage probability are provided. As extensions, fractional power
control is incorporated into the analysis, tractable closed-form expressions
are provided for special cases, and average ergodic spectral efficiency is
analyzed. Via numerical and simulation results, analytical characterizations
are confirmed and the impact of key system and network parameters on the
performance is identified.
