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Meta Distribution of Passive Electromagnetic Field Exposure in Cellular Networks

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

Abstract

This paper focuses on the meta distribution of electromagnetic field exposure (EMFE) experienced by a passive user in a cellular network implementing dynamic beamforming. The meta distribution serves as a valuable tool for extracting fine-grained insights into statistics of individual passive user EMFE across the network. A comprehensive stochastic geometry framework is established for this analysis. Given the pivotal role of accurately modeling the main and side lobes of antennas in this context, a multi-cosine gain model is introduced. The meta distribution is closely approximated by a beta distribution derived from its first- and second-order moments, which is demonstrated to be mathematically tractable. The impact of the number of antennas in the ULA on the meta distribution is explored, shedding light on its sensitivity to this parameter.

Meta Distribution of Passive Electromagnetic Field Exposure in Cellular Networks

Abstract

This paper focuses on the meta distribution of electromagnetic field exposure (EMFE) experienced by a passive user in a cellular network implementing dynamic beamforming. The meta distribution serves as a valuable tool for extracting fine-grained insights into statistics of individual passive user EMFE across the network. A comprehensive stochastic geometry framework is established for this analysis. Given the pivotal role of accurately modeling the main and side lobes of antennas in this context, a multi-cosine gain model is introduced. The meta distribution is closely approximated by a beta distribution derived from its first- and second-order moments, which is demonstrated to be mathematically tractable. The impact of the number of antennas in the ULA on the meta distribution is explored, shedding light on its sensitivity to this parameter.
Paper Structure (19 sections, 4 theorems, 32 equations, 5 figures)

This paper contains 19 sections, 4 theorems, 32 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Works
  4. DBF Models in SG
  5. EMFE Assessment Using SG
  6. Meta Distributions in SG
  7. Contributions
  8. System Model
  9. Topology
  10. Propagation Model
  11. Antenna Pattern Model
  12. Mathematical Results
  13. CDF of EMFE Conditioned on $\Psi$
  14. Meta Distribution of EMFE and Beta-Approximation
  15. Numerical Results
  16. ...and 4 more sections

Key Result

Theorem 1

The CDF of EMFE conditioned on the PPP $\Psi$ for the propagation model in eq:model and the antenna gain in eq:Gmc can be written by where is the conditional CF of the EMFE of the PU and

Figures (5)

  • Figure 1: Network topology. The PU's location is represented by the star, the BSs are represented with the three ULA gains.
  • Figure 2: Theoretical ULA antenna gain and its approximations
  • Figure 3: First- and second-order moments of the CDF of EMFE of PUs computed from the mathematical expressions (Math.) or from MC simulations (MC). The first-order moment corresponds to the CDF of EMFE of PUs.
  • Figure 4: Meta distribution of EMFE of PUs for different EMFE limits $T_e$ and approximation by a beta distribution ($N = 64$)
  • Figure 5: Meta distribution of EMFE of PUs for different values of $N$ and approximation by a beta distribution ($T_e = \numprint[dBm/m^2]{-32}$)

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Proposition 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof