A novel stochastic geometry framework is proposed in this paper to study the downlink coverage performance in a millimeter wave (mmWave) cellular network by jointly considering the polar coordinates of the Base Stations (BSs) with respect to the typical user located at the origin. Specifically, both the Euclidean and the angular distances of the BSs in a maximum power-based association policy for the UE are considered to account for realistic beam management considerations, which have been largely ignored in the literature, especially in the cell association phase. For completeness, two other association schemes are considered and exact-form expressions for the coverage probability are derived. Subsequently, the key role of angular distances is highlighted by defining the dominant interferer using angular distance-based criteria instead of Euclidean distance-based, and conducting a dominant interferer-based coverage probability analysis. Among others, the numerical results revealed that considering angular distance-based criteria for determining both the serving and the dominant interfering BS, can approximate the coverage performance more accurately as compared to utilizing Euclidean distance-based criteria. To the best of the authors$'$ knowledge, this is the first work that rigorously explores the role of angular distances in the association policy and analysis of cellular networks.

翻译：本文提出了一种新颖的随机几何框架，通过联合考虑基站相对于位于原点的典型用户的极坐标，研究毫米波蜂窝网络的下行覆盖性能。具体而言，在用户设备的最大功率关联策略中，同时考虑了基站的欧几里得距离和角距离，以纳入实际波束管理因素的考量——这在现有文献中（尤其是在小区关联阶段）长期被忽略。为完整起见，本文还考虑了另外两种关联方案，并推导了覆盖概率的精确表达式。进一步地，通过基于角距离准则（而非欧几里得距离准则）定义主干扰源，并开展基于主干扰源的覆盖概率分析，突显了角距离的关键作用。数值结果表明，与采用欧几里得距离准则相比，基于角距离准则确定服务基站和主干扰基站能更准确地逼近覆盖性能。据作者所知，这是首个系统探索角距离在蜂窝网络关联策略与分析中作用的研究。