Joint Coverage and EMF Compliance Analysis in RIS-Assisted TeraHertz Networks With Optimized RIS Deployment

This article presents a stochastic geometry framework for analyzing and optimizing the downlink performance of large-scale reconfigurable intelligent surface (RIS)-assisted terahertz (THz) networks. The study focuses on evaluating both the downlink coverage probability and the electromagnetic field exposure (EMFE) compliance probability. Our framework captures versatile Nakagami-m fading channels, thus can be customized for a variety of line-of-sight (LOS) and non-LOS fading environments and transmission frequencies. Existing works typically simplify the cascaded nature of RIS links, particularly when these links exhibit Nakagami-m fading, and apply far-field conditions where the user-to-RIS element distance can be approximated with the user-to-RIS center. To address the aforementioned limitations, we first characterize the statistics of the cascaded RIS-assisted channel, which follows a double Nakagami-m distribution, and demonstrate that the received signal power follows a non-central chi-square distribution. We then characterize the Laplace Transform of the received signal power and aggregate interferences from multiple RISs and THz base-stations (TBSs) for both near-field and far-field cases. Gil-Palaez inversion is then used to calculate joint downlink EMFE compliance and coverage probability. Lastly, we use the derived expressions to optimize both the number and locations of the RISs. Specifically, we use a grid-based approach in which the geographical region is divided into multiple units of equal size and then determine whether or not an RIS should be deployed on each grid intersection. Numerical results validate the accuracy of the derived analytical expressions. We note that while RISs are beneficial from a coverage perspective, they can introduce additional EMFE, thus the optimal RIS deployment planning is critical to jointly maximize the coverage and EMFE compliance.