Joint Coverage and Electromagnetic Field Exposure Analysis in Downlink and Uplink for RIS-assisted Networks

Reconfigurable intelligent surfaces (RISs) have shown the potential to improve signal-to-interference-plus-noise ratio (SINR) related coverage, especially at high-frequency communications. However, assessing electromagnetic field exposure (EMFE) and establishing EMFE regulations in RIS-assisted large-scale networks remain open issues. This paper proposes a stochastic geometry (SG) based framework to characterize SINR and EMFE in such networks for downlink and uplink scenarios. Particularly, we carefully consider the association rule with the presence of RISs, accurate antenna pattern at base stations (BSs), fading model, and power control mechanism at mobile devices in the system model. Under the proposed framework, we derive the marginal and joint distributions of SINR and EMFE in downlink and uplink, respectively. The first moment of EMFE is also provided. Additionally, we design the compliance distance (CD) between a BS/RIS and a user to comply with the EMFE regulations. To facilitate efficient identification, we further provide approximate closed-form expressions for CDs. From numerical results of the marginal distributions, we find that in the downlink scenario, deploying RISs may not always be beneficial, as the improved SINR comes at the cost of increased EMFE. However, in the uplink scenario, RIS deployment is promising to enhance coverage while still maintaining EMFE compliance. By simultaneously evaluating coverage and compliance metrics through joint distributions, we demonstrate the feasibility of RISs in improving uplink and downlink performance. Insights from this framework can contribute to establishing EMFE guidelines and achieving a balance between coverage and compliance when deploying RISs.

💡 Research Summary

This paper develops a comprehensive stochastic‑geometry framework to jointly evaluate coverage (SINR) and electromagnetic‑field exposure (EMFE) in large‑scale reconfigurable intelligent surface (RIS)‑assisted cellular networks, for both downlink and uplink. The authors model base stations (BSs), users, RISs, and obstacles as independent homogeneous Poisson point processes (PPPs) and represent obstacles as line segments in a Boolean model. RISs are placed on a fraction μ of obstacles, and three possible serving‑link types are defined: direct line‑of‑sight (DL), cascaded LOS via a RIS (CL), and direct non‑LOS (DN). For each link type, association probabilities and the joint distribution of the three distances forming the BS‑RIS‑user triangle are derived analytically.

The channel model incorporates Nakagami‑m fading for both LOS and NLOS conditions, distinct path‑loss exponents, and a realistic antenna pattern for multi‑antenna BSs (main‑lobe gain G_b and beamwidth Δ). RIS phase shifts are assumed to perfectly align the reflected beam toward the associated user. In the uplink, a novel power‑control law is introduced that accounts for both the user‑BS distance and the RIS gain, thereby making the transmit power of an interfering user dependent on its own serving‑link type.

Using Laplace transforms and a discretized antenna pattern, the authors obtain closed‑form expressions for the marginal complementary cumulative distribution functions (CCDFs) of downlink SINR (Υ) and EMFE (W), as well as the first moment of EMFE. By preserving the correlation between path loss, fading, and the interdependent distances, they further derive the joint probability J(γ, ω)=P(Υ>γ, W≤ω). This joint distribution reveals that a higher SINR does not necessarily imply higher exposure, and it quantifies the trade‑off introduced by RIS deployment.

For the uplink, the analysis is extended to obtain marginal and joint distributions of uplink SINR and EMFE. Because the RIS‑assisted link can compensate path loss with both transmit power and RIS gain, the interference field becomes more complex. The authors propose an accurate approximation that replaces the random interfering powers with their averages while retaining dependence on link type, yielding tractable expressions that match simulations.

A key contribution is the formulation of compliance distance (CD) – the minimum safe separation between a BS (or RIS) and a user required to keep EMFE below regulatory limits (e.g., ICNIRP, FCC). The CD is obtained by solving an optimization problem based on the EMFE CDF. Since the exact CDF involves serving and interfering signal distributions, a closed‑form approximation is derived by focusing on the dominant serving‑signal contribution. Separate CD expressions are provided for BSs and RISs.

Numerical results validate the analytical formulas and illustrate several important insights:

1. Downlink – Deploying RISs improves SINR considerably by creating strong reflected paths, but the concentrated beam also raises EMFE in the reflected direction, leading to larger CD values. In some scenarios the exposure increase outweighs the SINR gain, suggesting that RIS deployment must be carefully planned for downlink‑only services.

2. Uplink – RISs enhance coverage by providing a low‑loss cascaded path, allowing users to reduce their transmit power. Consequently, both uplink SINR and EMFE improve, and the required CD shrinks. This makes RIS deployment particularly attractive for uplink‑heavy applications (e.g., massive IoT, uplink‑centric URLLC).

3. The joint SINR‑EMFE distribution enables network designers to select operating points (SINR thresholds, power‑control factors) that satisfy both performance and safety constraints simultaneously.

Overall, the paper offers the first large‑scale, joint SINR‑EMFE analysis for RIS‑assisted networks, introduces a realistic antenna and blockage model, proposes a RIS‑aware uplink power‑control scheme, and provides practical CD formulas. These contributions lay a solid theoretical foundation for future 6G and millimeter‑wave deployments where RISs are expected to play a pivotal role, while ensuring compliance with electromagnetic exposure regulations.