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：本文提出一种新颖的随机几何框架，通过联合考虑基站相对于原点处典型用户的极坐标，研究毫米波蜂窝网络中的下行链路覆盖性能。具体而言，该框架同时考量了基于最大功率关联策略中基站的欧氏距离和角度距离，以纳入实际波束管理因素。这些因素在现有文献中（尤其是小区关联阶段）长期被忽略。为全面性起见，本文还考虑了另外两种关联方案，并推导出覆盖概率的精确表达式。随后，通过采用基于角度距离而非欧氏距离的准则定义主干扰基站，并开展基于主干扰基站的覆盖概率分析，凸显了角度距离的关键作用。数值结果表明，与基于欧氏距离的准则相比，采用基于角度距离的准则来确定服务基站和主干扰基站能更准确地近似覆盖性能。据作者所知，这是首项系统探索角度距离在蜂窝网络关联策略与分析中作用的研究工作。