In wireless networks assisted by intelligent reflecting surfaces (IRSs), jointly modeling the signal received over the direct and indirect (reflected) paths is a difficult problem. In this work, we show that the network geometry (locations of serving base station, IRS, and user) can be captured using the so-called triangle parameter $\Delta$. We introduce a decomposition of the effect of the combined link into a signal amplification factor and an effective channel power coefficient $G$. The amplification factor is monotonically increasing with both the number of IRS elements $N$ and $\Delta$. For $G$, since an exact characterization of the distribution seems unfeasible, we propose three approximations depending on the value of the product $N\Delta$ for Nakagami fading and the special case of Rayleigh fading. For two relevant models of IRS placement, we prove that their performance is identical if $\Delta$ is the same given an $N$. We also show that no gains are achieved from IRS deployment if $N$ and $\Delta$ are both small. We further compute bounds on the diversity gain to quantify the channel hardening effect of IRSs. Hence only with a judicious selection of IRS placement and other network parameters, non-trivial gains can be obtained.

翻译：在智能反射表面（IRS）辅助的无线网络中，联合建模通过直接路径和间接（反射）路径接收的信号是一个难题。本文研究表明，网络几何结构（服务基站、IRS和用户的位置）可通过所谓的三角形参数$\Delta$来刻画。我们引入了一种将组合链路效应分解为信号放大因子和有效信道功率系数$G$的方法。该放大因子随IRS单元数量$N$和参数$\Delta$单调递增。对于$G$，由于精确刻画其分布似乎不可行，我们针对Nakagami衰落及瑞利衰落的特殊情况，依据乘积$N\Delta$的取值提出了三种近似方法。针对两种典型的IRS部署模型，我们证明了在给定$N$时若$\Delta$相同，则其性能表现一致。研究还表明，当$N$和$\Delta$均较小时，IRS部署无法带来性能增益。我们进一步计算了分集增益的边界以量化IRS的信道硬化效应。因此，只有通过合理选择IRS部署位置及其他网络参数，才能获得显著的性能提升。