Impact of Network Geometry on Large Networks with Intelligent Reflecting Surfaces

TL;DR

This work develops a tractable framework for IRS-assisted large wireless networks by introducing the triangle parameter $\Delta$ to capture BS–IRS–UE geometry and by decomposing the joint direct/indirect channel into a signal amplification term and an ECPC $G$ that models fading improvement. It provides fading-aware approximations for the distribution of $G$ based on the key product $N\Delta$, and presents two IRS placement models to study geometry effects, showing that performance depends on $N$ and $\Delta$ but not on placement model when these are fixed. The analysis yields SIR distributions, outage/throughput performance, and diversity bounds, revealing linear-in-$N$ throughput growth and channel hardening with $N$ and $\Delta$. The results offer practical design guidelines for IRS deployment, highlighting when IRS gains are significant and how geometry and density influence performance. Overall, the triangle geometry framework and $G$-based decomposition enable scalable analysis and informed IRS placement in large networks.

Abstract

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 $Δ$. 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 $Δ$. For $G$, since an exact characterization of the distribution seems unfeasible, we propose three approximations depending on the value of the product $NΔ$ 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 $Δ$ is the same given an $N$. We also show that no gains are achieved from IRS deployment if $N$ and $Δ$ 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.

Figures (24)

• Figure 1: A realization of the network. The tBS, tUE and tIRS are shown in the typical cell.
• Figure 2: $\mu=1$ (Rayleigh fading)
• Figure 3: $\mu=5$
• Figure 5: $\mu=1$ (Rayleigh fading)
• Figure 6: $\mu=5$