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Joint Metrics for EMF Exposure and Coverage in Real-World Homogeneous and Inhomogeneous Cellular Networks

Quentin Gontier, Charles Wiame, Shanshan Wang, Marco Di Renzo, Joe Wiart, François Horlin, Christo Tsigros, Claude Oestges, Philippe De Doncker

TL;DR

Evaluating the downlink performance of cellular networks in terms of coverage and electromagnetic field (EMF) exposure, in the framework of stochastic geometry, finds inhomogeneous Poisson point processes with a radial intensity measure to be a good approximation for motion-variant networks.

Abstract

This paper evaluates the downlink performance of cellular networks in terms of coverage and electromagnetic field exposure (EMFE), in the framework of stochastic geometry. The model is constructed based on datasets for sub-6~GHz macro cellular networks but it is general enough to be applicable to millimeter-wave networks as well. On the one hand, performance metrics are calculated for $β$-Ginibre point processes which are shown to faithfully model a large number of motion-invariant networks. On the other hand, performance metrics are derived for inhomogeneous Poisson point processes with a radial intensity measure, which are shown to be a good approximation for motion-variant networks. For both cases, joint and marginal distributions of the EMFE and the coverage, and the first moments of the EMFE are provided and validated by Monte Carlo simulations using realistic sets of parameters from two sub-6~GHz macro urban cellular networks, i.e., 5G~NR~2100 (Paris, France) and LTE~1800 (Brussels, Belgium) datasets. In addition, this paper includes the analysis of the impact of the network parameters and discusses the achievable trade-off between coverage and EMFE.

Joint Metrics for EMF Exposure and Coverage in Real-World Homogeneous and Inhomogeneous Cellular Networks

TL;DR

Evaluating the downlink performance of cellular networks in terms of coverage and electromagnetic field (EMF) exposure, in the framework of stochastic geometry, finds inhomogeneous Poisson point processes with a radial intensity measure to be a good approximation for motion-variant networks.

Abstract

This paper evaluates the downlink performance of cellular networks in terms of coverage and electromagnetic field exposure (EMFE), in the framework of stochastic geometry. The model is constructed based on datasets for sub-6~GHz macro cellular networks but it is general enough to be applicable to millimeter-wave networks as well. On the one hand, performance metrics are calculated for -Ginibre point processes which are shown to faithfully model a large number of motion-invariant networks. On the other hand, performance metrics are derived for inhomogeneous Poisson point processes with a radial intensity measure, which are shown to be a good approximation for motion-variant networks. For both cases, joint and marginal distributions of the EMFE and the coverage, and the first moments of the EMFE are provided and validated by Monte Carlo simulations using realistic sets of parameters from two sub-6~GHz macro urban cellular networks, i.e., 5G~NR~2100 (Paris, France) and LTE~1800 (Brussels, Belgium) datasets. In addition, this paper includes the analysis of the impact of the network parameters and discusses the achievable trade-off between coverage and EMFE.
Paper Structure (33 sections, 15 theorems, 97 equations, 15 figures, 3 tables)

This paper contains 33 sections, 15 theorems, 97 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Evaluation of the SINR by using SG
  4. Evaluation of the IPD by using SG
  5. Joint evaluation of the IPD and SINR by using SG
  6. Contributions
  7. Motion-invariant networks
  8. Motion-variant networks
  9. Structure of the Paper
  10. System Model
  11. Mathematical Background
  12. Motion-Invariant Networks
  13. Motion-Variant Networks
  14. Propagation Model
  15. Mathematical Framework
  16. ...and 18 more sections

Key Result

Theorem 1

The mean of the EMFE of a $\beta$-GPP given the propagation model in eq:model is given by where The associated variance is given by $\mathbb V\left[\mathcal{P}\right] = \mathbb E\left[\mathcal{P}^2\right] - \left(\mathbb E\left[\mathcal{P}\right]\right)^2$, where $\mathbb E\left[\mathcal{P}^2\right]$ is given in eq:BGPP_varexpeq shown at the top of the next page. We denote $[f(x)]_{x=a}^{x=b}

Figures (15)

  • Figure 1: Organization of Section \ref{['sec:analytical_results']}
  • Figure 2: CDF of EMFE with the model parameters from Table \ref{['tab:BGPP_study']}
  • Figure 3: CCDF of the SINR with the model parameters from Table \ref{['tab:BGPP_study']}
  • Figure 4: Isocurves of the joint CDF of the EMFE and SINR with the model parameters from Table \ref{['tab:BGPP_study']}.
  • Figure 5: CDF of the EMFE for different values of $\beta$ in a $\beta$-GPP
  • ...and 10 more figures

Theorems & Definitions (29)

  • Theorem 1
  • proof
  • Corollary 1
  • proof
  • Proposition 1
  • proof
  • Theorem 2
  • proof
  • Corollary 2
  • proof
  • ...and 19 more