In this paper, we have derived stochastic geometry based generalized mathematical expressions for the uplink signal-to-interference-plus-noise-ratio (SINR) coverage probability, rate coverage probability and area spectral efficiency (ASE) of millimeter wave cellular network. The locations of base stations (BSs) and the user equipments (UEs) are modeled as two independent homogeneous Poisson Point Process (PPP) while location of interfering UEs is modeled as non-homogeneous PPP (non-HPPP). To model distinct line-of-sight (LOS) and non-line-of-sight (NLOS) propagation characteristics due to signal blockage at millimeter wave frequencies, a distance-dependent path loss model is employed and directional beamforming with antenna radiation pattern having Gaussian main lobe is considered. Minimum path loss based user association scheme is assumed for coverage analysis. The derived expressions are validated through simulations. It has been found that the SINR coverage probability and ASE increases with the increasing base station density at first, then decreases as the network becomes denser and eventually collapse as the density is further increased. Also, rate coverage probability decreases as the network goes dense. Hence, an optimum value of base station density can be determined that maximizes SINR coverage probability and area spectral efficiency. The analysis is also simplified for dense network using LOS ball blockage model. We have compared coverage probability estimate using homogeneous and non-homogeneous PPP model of interferer, where it is shown that for dense network both models have similar performance whereas for low density network, our non-homogeneous PPP model gives better coverage performance.

在本文中，我们针对毫米波蜂窝网络的上行链路信噪比（SINR）覆盖概率，速率覆盖概率和区域频谱效率（ASE），导出了基于随机几何的广义数学表达式。基站（BS）和用户设备（UE）的位置被建模为两个独立的同质泊松点过程（PPP），而干扰UE的位置则被建模为非同质PPP（non-HPPP）。为了对由于毫米波频率上的信号阻塞而产生的独特的视线（LOS）和非视线（NLOS）传播特性进行建模，采用了距离相关的路径损耗模型，并且采用天线辐射方向图进行定向波束成形考虑高斯主瓣。假设基于最小路径损耗的用户关联方案用于覆盖率分析。通过仿真验证派生的表达式。已经发现，SINR覆盖概率和ASE首先随着基站密度的增加而增加，然后随着网络变得更密集而降低，并随着密度的进一步增加而最终崩溃。而且，速率覆盖概率随着网络的密集而降低。因此，可以确定使SINR覆盖概率和区域频谱效率最大化的基站密度的最佳值。对于使用LOS球阻塞模型的密集网络，分析也得到了简化。我们使用干扰源的同质和非同质PPP模型比较了覆盖概率估计，