Reconfigurable intelligent surface (RIS) is a promising solution to deal with the blockage-sensitivity of millimeter wave band and reduce the high energy consumption caused by network densification. However, deploying large scale RISs may not bring expected performance gain due to significant channel estimation overhead and non-negligible reflected interference. In this paper, we derive the analytical expressions of the coverage probability, area spectrum efficiency (ASE) and energy efficiency (EE) of a downlink RIS-aided multi-cell network. In order to optimize the network performance, we investigate the conditions for the optimal number of training symbols of each antenna-to-antenna and antenna-to-element path (referred to as the optimal unit training overhead) in channel estimation. Our study shows that: 1) RIS deployment is not `the more, the better', only when blockage objects are dense should one deploy more RISs; 2) the coverage probability is maximized when the unit training overhead is designed as large as possible; 3) however, the ASE-and-EE-optimal unit training overhead exists. It is a monotonically increasing function of the frame length and a monotonically decreasing function of the average signal-to-noise-ratio (in the high signal-to-noise-ratio region). Additionally, the optimal unit training overhead is smaller when communication ends deploy particularly few or many antennas.

翻译：可重构智能表面（RIS）是应对毫米波频段阻挡敏感性和降低网络密集化导致的高能耗问题的有前景方案。然而，由于信道估计开销和不可忽略的反射干扰，大规模部署RIS可能无法带来预期的性能增益。本文推导了下行RIS辅助多小区网络的覆盖概率、区域频谱效率（ASE）和能量效率（EE）的解析表达式。为优化网络性能，我们研究了信道估计中天线间及天线-单元路径的最优训练符号数量条件（即最优单位训练开销）。研究表明：1）RIS部署并非"越多越好"，仅当阻挡物密集时需部署更多RIS；2）当单位训练开销设计为最大值时，覆盖概率达到最优；3）然而，存在最优单位训练开销（兼顾ASE与EE），该开销是帧长的单调递增函数，且在高信噪比区域是平均信噪比的单调递减函数。此外，当通信端部署天线数量极少或极多时，最优单位训练开销较小。