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Smooth Actual EIRP Control for EMF Compliance with Minimum Traffic Guarantees

Lorenzo Maggi, Alois Herzog, Azra Zejnilagic, Christophe Grangeat

TL;DR

This work addresses EMF exposure limits for base stations by enforcing time-averaged EIRP constraints via an actual EIRP control framework. It introduces an EIRP budget, defined by $\Omega_t$ and the feasible upper bound $\Gamma_t$, and provides exact linear-time and conservative constant-time algorithms to compute the budget. A Drift-Plus-Penalty (DPP) control scheme is then developed to preemptively reduce EIRP when future resource shortages are likely, using a virtual queue and a tunable parameter $V$ to balance emissions with user traffic guarantees. The approach yields EMF-compliant operation with minimum EIRP guarantees and smooth resource usage, with practical guidance on parameter tuning and complexity trade-offs for real-time deployment.

Abstract

To mitigate Electromagnetic Fields (EMF) human exposure from base stations, international standards bodies define EMF emission requirements that can be translated into limits on the "actual" Equivalent Isotropic Radiated Power (EIRP), i.e., averaged over a sliding time window. We aim to enable base stations to adhere to these constraints while mitigating any impact on user performance. Specifically, our objectives are to: i) ensure EMF exposure compliance using actual EIRP control when implementing the "actual maximum approach" described in IEC 62232:2022, ii) guarantee a minimum EIRP level, and iii) prevent resource shortages at all times. We first investigate exact and conservative algorithms, with linear and constant complexity, respectively, to compute the maximum allowed EIRP consumption under constraints i) and ii), referred to as EIRP "budget". Subsequently, we design a control method based on Drift-Plus-Penalty theory that preemptively curbs EIRP consumption only when needed to avoid future resource shortages.

Smooth Actual EIRP Control for EMF Compliance with Minimum Traffic Guarantees

TL;DR

This work addresses EMF exposure limits for base stations by enforcing time-averaged EIRP constraints via an actual EIRP control framework. It introduces an EIRP budget, defined by and the feasible upper bound , and provides exact linear-time and conservative constant-time algorithms to compute the budget. A Drift-Plus-Penalty (DPP) control scheme is then developed to preemptively reduce EIRP when future resource shortages are likely, using a virtual queue and a tunable parameter to balance emissions with user traffic guarantees. The approach yields EMF-compliant operation with minimum EIRP guarantees and smooth resource usage, with practical guidance on parameter tuning and complexity trade-offs for real-time deployment.

Abstract

To mitigate Electromagnetic Fields (EMF) human exposure from base stations, international standards bodies define EMF emission requirements that can be translated into limits on the "actual" Equivalent Isotropic Radiated Power (EIRP), i.e., averaged over a sliding time window. We aim to enable base stations to adhere to these constraints while mitigating any impact on user performance. Specifically, our objectives are to: i) ensure EMF exposure compliance using actual EIRP control when implementing the "actual maximum approach" described in IEC 62232:2022, ii) guarantee a minimum EIRP level, and iii) prevent resource shortages at all times. We first investigate exact and conservative algorithms, with linear and constant complexity, respectively, to compute the maximum allowed EIRP consumption under constraints i) and ii), referred to as EIRP "budget". Subsequently, we design a control method based on Drift-Plus-Penalty theory that preemptively curbs EIRP consumption only when needed to avoid future resource shortages.
Paper Structure (18 sections, 4 theorems, 20 equations, 3 figures, 4 algorithms)

This paper contains 18 sections, 4 theorems, 20 equations, 3 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. EIRP budget
  4. Budget computation
  5. Iterative computation
  6. Low-complexity conservative approximation
  7. Smooth EIRP control
  8. Preliminaries on Drift-Plus-Penalty (DPP)
  9. DPP-based heuristic
  10. Numerical evaluations
  11. Conclusions
  12. Proposition \ref{['thm:feasible']}
  13. Proposition \ref{['prop:recursive_Omega']}
  14. Property \ref{['prop:recurs_algo']}
  15. Property \ref{['prop:recursive_ell']}
  16. ...and 3 more sections

Key Result

Proposition 1

Define the variable $\Omega_t$ as: To fulfill constraints eq:EMFconstr-eq:rhoC, the EIRP control $\gamma_t$ must satisfy:

Figures (3)

  • Figure 1: Illustrative example of the behaviour of multiple EIRP control strategies---(b) cautious, (c) greedy and (d) the proposed DPP---on EIRP consumption under identical input traffic, shown in (a). Parameters: $W=10,\rho=0.15,\alpha=1,\beta=0.95, V=15$.
  • Figure 2: Value of parameter $V$ maximizing proportional fairness as the traffic load $\ell$ varies.
  • Figure 3: Exact budget $\Gamma$ versus conservative $\widetilde{\Gamma}$ as the traffic load $\ell$ varies.

Theorems & Definitions (11)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • ...and 1 more