A K-tier heterogeneous downlink millimeter wave (mmWave) cellular network
with user-centric small cell deployments is studied in this paper. In
particular, we consider a heterogeneous network model with user equipments
(UEs) being distributed according to a Poisson Cluster Process (PCP).
Specifically, we address two cluster processes, namely (i) Thomas cluster
process, where the UEs are clustered around the base stations (BSs) and the
distances between UEs and the BS are modeled as Gaussian distributed, and (ii)
Matern cluster process, where the UEs are scattered according to a uniform
distribution. In addition, distinguishing features of mmWave communications
including directional beamforming and a sophisticated path loss model
incorporating both line-of-sight (LOS) and non-line-of-sight (NLOS)
transmissions, are taken into account. Initially, the complementary cumulative
distribution function (CCDF) and probability density function (PDF) of path
loss are provided. Subsequently, using tools from stochastic geometry, we
derive a general expression for the signal-to-interference-plus-noise ratio
(SINR) coverage probability. Our results demonstrate that coverage probability
can be improved by decreasing the size of UE clusters around BSs, decreasing
the beamwidth of the main lobe, or increasing the main lobe directivity gain.
Moreover, interference has noticeable influence on the coverage performance of
our model. We also show that better coverage performance is achieved in the
presence of clustered users compared to the case in which the users are
distributed according to a Poisson Point Process (PPP).

本文研究了具有用户中心的小型基站部署的 K 层异构下行毫米波（mmWave）蜂窝网络。使用随机几何工具，提供了信干比（SINR）覆盖概率的一般表达式，并探讨了 UE 聚类大小、主波束宽度和主波束直接收益增益等因素对该网络的覆盖概率的影响。

用户中心小型基站部署下异构毫米波蜂窝网络的覆盖

Coverage in Downlink Heterogeneous mmWave Cellular Networks with  User-Centric Small Cell Deployment

Existing cellular network analyses, and even simulations, typically use the
standard path loss model where received power decays like $\|x\|^{-\alpha}$
over a distance $\|x\|$. This standard path loss model is quite idealized, and
in most scenarios the path loss exponent $\alpha$ is itself a function of
$\|x\|$, typically an increasing one. Enforcing a single path loss exponent can
lead to orders of magnitude differences in average received and interference
powers versus the true values. In this paper we study \emph{multi-slope} path
loss models, where different distance ranges are subject to different path loss
exponents. We focus on the dual-slope path loss function, which is a piece-wise
power law and continuous and accurately approximates many practical scenarios.
We derive the distributions of SIR, SNR, and finally SINR before finding the
potential throughput scaling, which provides insight on the observed
cell-splitting rate gain. The exact mathematical results show that the SIR
monotonically decreases with network density, while the converse is true for
SNR, and thus the network coverage probability in terms of SINR is maximized at
some finite density. With ultra-densification (network density goes to
infinity), there exists a \emph{phase transition} in the near-field path loss
exponent $\alpha_0$: if $\alpha_0 >1$ unbounded potential throughput can be
achieved asymptotically; if $\alpha_0 <1$, ultra-densification leads in the
extreme case to zero throughput.

本文研究了多坡度路径损耗模型及单坡度路径损耗模型的局限性，分析了信号干扰比、信噪比和信干噪比的表现形式，并探讨了潜在的吞吐量扩展和临界密度。