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On the Uplink and Downlink EMF Exposure and Coverage in Dense Cellular Networks: A Stochastic Geometry Approach

Quentin Gontier, Charles Wiame, Joe Wiart, François Horlin, Christo Tsigros, Claude Oestges, Philippe De Doncker

TL;DR

An enhanced stochastic geometry framework that includes the uplink and downlink coverage and EMFE is presented and the marginal and meta distributions of the downlink and uplink EMFE are derived and the uplink to downlink EMFE ratio is characterized.

Abstract

Existing studies analyzing electromagnetic field (EMFE) in wireless networks have primarily considered downlink communications. In the uplink, the EMFE caused by the user's smartphone is usually the only considered source of radiation, thereby ignoring contributions caused by other active neighboring devices. In addition, the network coverage and EMFE are typically analyzed independently for both the uplink and downlink, while a joint analysis would be necessary to fully understand the network performance and answer various questions related to optimal network deployment. This paper bridges these gaps by presenting an enhanced stochastic geometry framework that includes the above aspects. The proposed topology features base stations modeled via a homogeneous Poisson point process. The users active during a same time slot are distributed according to a mixture of a Matérn cluster process and a Gauss-Poisson process, featuring groups of users possibly carrying several equipments. In this paper, we derive the marginal and meta distributions of the downlink and uplink EMFE and we characterize the uplink to downlink EMFE ratio. Moreover, we derive joint probability metrics considering the uplink and downlink coverage and EMFE. These metrics are evaluated in four scenarios considering BS, cluster and/or intracluster densifications. Our numerical results highlight the existence of optimal node densities maximizing these joint probabilities.

On the Uplink and Downlink EMF Exposure and Coverage in Dense Cellular Networks: A Stochastic Geometry Approach

TL;DR

An enhanced stochastic geometry framework that includes the uplink and downlink coverage and EMFE is presented and the marginal and meta distributions of the downlink and uplink EMFE are derived and the uplink to downlink EMFE ratio is characterized.

Abstract

Existing studies analyzing electromagnetic field (EMFE) in wireless networks have primarily considered downlink communications. In the uplink, the EMFE caused by the user's smartphone is usually the only considered source of radiation, thereby ignoring contributions caused by other active neighboring devices. In addition, the network coverage and EMFE are typically analyzed independently for both the uplink and downlink, while a joint analysis would be necessary to fully understand the network performance and answer various questions related to optimal network deployment. This paper bridges these gaps by presenting an enhanced stochastic geometry framework that includes the above aspects. The proposed topology features base stations modeled via a homogeneous Poisson point process. The users active during a same time slot are distributed according to a mixture of a Matérn cluster process and a Gauss-Poisson process, featuring groups of users possibly carrying several equipments. In this paper, we derive the marginal and meta distributions of the downlink and uplink EMFE and we characterize the uplink to downlink EMFE ratio. Moreover, we derive joint probability metrics considering the uplink and downlink coverage and EMFE. These metrics are evaluated in four scenarios considering BS, cluster and/or intracluster densifications. Our numerical results highlight the existence of optimal node densities maximizing these joint probabilities.
Paper Structure (25 sections, 10 theorems, 61 equations, 15 figures, 3 tables)

This paper contains 25 sections, 10 theorems, 61 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Stochastic geometry for the SINR assessment in the UL
  4. Stochastic geometry for incident power density assessment
  5. Contributions
  6. Structure of the Paper
  7. System Model
  8. Topology
  9. Propagation Model
  10. Power control
  11. Network Size
  12. Quantities of Interest
  13. Mathematical Results
  14. Analysis of EM Pollution
  15. Meta Distribution of EMFE
  16. ...and 10 more sections

Key Result

Lemma 1

The CDF of the DL EMFE seen by the typical user is where $\phi_{\mathcal{P}^{d}}(q)$ is the DL EMFE characteristic function (CF)

Figures (15)

  • Figure 1: PV, model of type II Haenggi17. The pink dashed lines correspond to the BS-UE association in one given RB. The black solid lines correspond to the edge of the Voronoï cells. The typical BS is located at the origin.
  • Figure 2: Notations of the model. $X_i$ and $Y_i$ are respectively the locations of BS $i$ and UE $i$, with $X_0$ and $Y_0$ the typical BS-UE pair, $\rho_i$ is the distance between $X_i$ and $Y_0$, $D_i$ is the distance between $Y_i$ and $X_0$, $\Tilde{D}_i$ is the distance between $Y_i$ and $Y_0$ and $R_i$ is the distance between $X_i$ and $Y_i$.
  • Figure 3: Mean and median UL/DL EMFE in densification scenario (a).
  • Figure 4: Mean and median UL/DL EMFE in densification scenario (b).
  • Figure 5: Mean and median UL/DL EMFE in densification scenario (c).
  • ...and 10 more figures

Theorems & Definitions (17)

  • Lemma 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • Lemma 2
  • proof
  • Proposition 1
  • Theorem 3
  • ...and 7 more