The millimeter wave (mmWave) has received considerable interest due to its expansive bandwidth and high frequency. However, a noteworthy challenge arises from its vulnerability to blockages, leading to reduced coverage and achievable rates. To address these limitations, a potential solution is to deploy distributed reconfigurable intelligent surfaces (RISs), which comprise many low-cost and passively reflected elements, and can facilitate the establishment of extra communication links. In this paper, we leverage stochastic geometry to investigate the ergodic coverage probability and the achievable rate in both distributed RISs-assisted single-cell and multi-cell mmWave wireless communication systems. Specifically, we first establish the system model considering the stochastically distributed blockages, RISs and users by the Poisson point process. Then we give the association criterion and derive the association probabilities, the distance distributions, and the conditional coverage probabilities for two cases of associations between base stations and users without or with RISs. Finally, we use Campbell's theorem and the total probability theorem to obtain the closed-form expressions of the ergodic coverage probability and the achievable rate. Simulation results verify the effectiveness of our analysis method, and demonstrate that by deploying distributed RISs, the ergodic coverage probability is significantly improved by approximately 50%, and the achievable rate is increased by more than 1.5 times.

翻译：毫米波因其大带宽和高频特性而备受关注，但其对阻塞的脆弱性导致覆盖范围和可达速率下降，成为显著挑战。为克服这些限制，部署分布式可重构智能表面（RIS）是一种潜在解决方案——该技术由大量低成本被动反射单元组成，可辅助建立额外通信链路。本文利用随机几何理论，研究分布式RIS辅助单小区与多小区毫米波无线通信系统中的遍历覆盖概率和可达速率。具体而言，首先基于泊松点过程建立考虑随机分布阻塞物、RIS与用户的系统模型；然后给出关联准则，推导无RIS与有RIS两种基站-用户关联场景下的关联概率、距离分布及条件覆盖概率；最后利用坎贝尔定理和全概率定理，获得遍历覆盖概率与可达速率的闭式表达式。仿真结果验证了所提分析方法的有效性，表明部署分布式RIS后，遍历覆盖概率显著提升约50%，可达速率提高1.5倍以上。