We investigate the performance of a downlink ultra-dense network (UDN) with directional transmissions via stochastic geometry. Considering the dual-slope path loss model and sectored beamforming pattern, we derive the expressions and asymptotic characteristics of the coverage probability and constrained area spectrum efficiency (ASE). Several special scenarios, namely the physically feasible path loss model and adjustable beam pattern, are also analyzed. Although signal-to-interference-plus-noise ratio collapsing still exists when the path loss exponent in the near-field is no larger than 2, using strategies like beam pattern adaption, can avoid the decrease of the coverage probability and constrained ASE even when the base station density approaches infinity.

中文翻译：

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具有定向传输的超密集网络的覆盖范围和容量

我们通过随机几何研究具有定向传输的下行链路超密集网络 (UDN) 的性能。考虑双斜率路径损耗模型和扇形波束形成模式，我们推导出覆盖概率和约束区域频谱效率（ASE）的表达式和渐近特性。还分析了几种特殊情况，即物理上可行的路径损耗模型和可调波束模式。尽管在近场路径损耗指数不大于2时信干噪比的下降仍然存在，但使用波束图自适应等策略，即使在以下情况下也可以避免覆盖概率的下降和受约束的ASE基站密度接近无穷大。