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Exposure-Aware Beamforming for mmWave Systems: From EM Theory to Thermal Compliance

Zihan Zhou, Ang Chen, Yunfei Chen, Weidong Wang, Li Chen

Abstract

Electromagnetic (EM) exposure compliance has long been recognized as a crucial aspect of communications terminal designs. However, accurately assessing the impact of EM exposure for proper design strategies remains challenging. In this paper, we develop a long-term thermal EM exposure constraint model and propose a novel adaptive exposure-aware beamforming design for an mmWave uplink system. Specifically, we first establish an equivalent channel model based on Maxwell's radiation equations, which accurately captures the EM physical effects. Then, we derive a closed-form thermal impulse response model from the Pennes bioheat transfer equation (BHTE), characterizing the thermal inertia of tissue. Inspired by this model, we formulate a beamforming optimization problem that translates rigid instantaneous exposure limits into a flexible long-term thermal budget constraint. Furthermore, we develop a low-complexity online beamforming algorithm based on Lyapunov optimization theory, obtaining a closed-form near-optimal solution. Simulation results demonstrate that the proposed algorithm effectively stabilizes tissue temperature near a predefined safety threshold and significantly outperforms the conventional scheme with instantaneous exposure constraints.

Exposure-Aware Beamforming for mmWave Systems: From EM Theory to Thermal Compliance

Abstract

Electromagnetic (EM) exposure compliance has long been recognized as a crucial aspect of communications terminal designs. However, accurately assessing the impact of EM exposure for proper design strategies remains challenging. In this paper, we develop a long-term thermal EM exposure constraint model and propose a novel adaptive exposure-aware beamforming design for an mmWave uplink system. Specifically, we first establish an equivalent channel model based on Maxwell's radiation equations, which accurately captures the EM physical effects. Then, we derive a closed-form thermal impulse response model from the Pennes bioheat transfer equation (BHTE), characterizing the thermal inertia of tissue. Inspired by this model, we formulate a beamforming optimization problem that translates rigid instantaneous exposure limits into a flexible long-term thermal budget constraint. Furthermore, we develop a low-complexity online beamforming algorithm based on Lyapunov optimization theory, obtaining a closed-form near-optimal solution. Simulation results demonstrate that the proposed algorithm effectively stabilizes tissue temperature near a predefined safety threshold and significantly outperforms the conventional scheme with instantaneous exposure constraints.
Paper Structure (14 sections, 6 theorems, 83 equations, 8 figures, 1 table, 1 algorithm)

This paper contains 14 sections, 6 theorems, 83 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Geometric Model
  4. Radiation Model
  5. Channel Model
  6. EM Exposure Constraints
  7. Thermal Model
  8. Thermal Response to Time-Varying Exposure
  9. Exposure-Aware Beamforming Problem
  10. Exposure-Aware Beamforming Design
  11. Lyapunov Optimization Formulation
  12. Algorithm Performance Analysis
  13. Numerical Results And Discussion
  14. Conclusion

Key Result

Lemma 1

(Single-Antenna Radiation Model): Consider the transmit antenna positioned at $\mathbf{r}_0$ and oriented along the orientation unit vector $\mathbf{n}_t$. The electric field vector $\boldsymbol{\mathcal{E}}(\mathbf{r})$ at an observation point $\mathbf{r}$ is given by where $\eta$ is the free-space impedance, $d = \|\mathbf{r}-\mathbf{r}_0\|$, $\hat{\mathbf{r}} = (\mathbf{r}-\mathbf{r}_0)/d$ is

Figures (8)

  • Figure 1: Illustration of the mmWave uplink system. A spherical head model of the user lies close to the UE array.
  • Figure 2: Illustration of the EM propagation model (a) Single antenna; (b) Parallel array.
  • Figure 3: Averaged power density versus the reference distance $d_{\text{ref}}$ for different UE tilt and polar angles.
  • Figure 4: Temporal evolution of average temperature under different control parameter $V$ and temperature thresholds.
  • Figure 5: Trade-off between the received SNR and average queue length versus control parameter for different temperature thresholds.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Proposition 2: Thermal Impulse Response
  • Lemma 3: Constraint Satisfaction via Queue Stability
  • Proposition 3