Key Takeaways & Executive Findings
- •• EFGraGAN integrates field gradient loss to reconstruct high-resolution mmWave E-fields, preserving both local magnitude and spatial structure. • Training with plane-wave integral representation (PWIR) and randomized incidence significantly improves generalization across antenna types. • Achieves maximum mean relative error below 9% up to 60 GHz in a 4×4 dipole array, satisfying IEC/IEEE 63195-2 standards for exposure assessment. • Demonstrates robustness to noise, enabling existing measurement systems to perform accurate and efficient mmWave exposure assessment.
Abstract
Accurate assessment of human exposure to millimeter-wave (mmWave) electric fields (E-fields) has recently become critical for public health and safety. High-spatial-resolution E-field distribution is required for assessment of mmWave electromagnetic exposure according to the International Electrotechnical Commission (IEC) and the Institute of Electrical and Electronics Engineers (IEEE) (IEC/IEEE 63195-2 standard). This study proposes a generative adversarial network (GAN) integrated with field gradient loss, termed EFGraGAN, for superresolution reconstruction of mmWave E-fields. The incorporation of E-field gradient loss enables the network to learn both local field magnitudes and spatial structures, thereby enhancing the accuracy and fine structural details of reconstructed E-field maps. To improve generalization across antenna types, the training dataset is generated using plane-wave integral representation (PWIR) and randomized parametric incidence, simulating diverse field distributions. Combined with bilinear interpolation, the method achieves high-resolution reconstruction at 30 GHz and 60 GHz, meeting the requirements of the IEC/IEEE 63195-2 standard for exposure assessment. Numerical simulations show that EFGraGAN reconstructs E-field distributions in a skin phantom with a maximum mean relative error (MRE) of <9% up to 60 GHz in a 4×4 dipole array scenario, outperforming conventional interpolation and traditional GAN methods. The approach also demonstrates strong robustness to noise, enabling current measurement systems to achieve accurate and efficient evaluation of mmWave exposure.
1. Introduction
With the rapid application of millimeter-wave (mmWave) technology, public concerns regarding the potential adverse health effects of excessive exposure to electromagnetic (EM) fields have increased (Lin, 2016; Yang et al., 2021). Accurate evaluation of mmWave exposure has become an increasingly significant issue. At frequencies >6 GHz, the specific absorption rate (SAR) becomes less relevant for exposure assessment due to the extremely shallow penetration depth of millimeter waves. Instead, the incident power density (IPD) is adopted as the primary compliance metric, particularly for measurement (Wu et al., 2013; IEC/IEEE, 2022a). IPD refers to the power per unit area of EM radiation incident on a surface in free space and can be assessed at distances close to the radiating source.
As IPD can be derived from the electric field (E-field) (Wu et al., 2024), measurement systems equipped with either a single probe or probe arrays are commonly used to determine the values at discrete sampling points. In such kinds of systems, the spacing between these sampling points drastically influences the precision of assessment. Denser sampling can reduce the uncertainty in E-field distributions. However, it will introduce pronounced coupling effects (Qamar et al., 2016) and lead to measurement errors. Currently, the minimal spacing of probes has not been standardized, while the interval for the current measurement system is claimed to be around 7–8 mm (Liu et al., 2020). Meanwhile, sampling resolution and spatial gradients are critical for the accurate localization and assessment of the maximum exposure value (IEC/IEEE, 2020, 2022a). Specifically, when assessing mmWave exposure, for evaluating the peak spatial-average IPD, the value is calculated with a step size of 1 mm or λ/10, whichever is less (IEC/IEEE, 2022a, 2022b). In such a case, there is an urgent need to reconstruct the E-field at much higher resolution, for instance, from the spatial interval of 8 mm to 1 mm (e.g., 10 GHz) and even to 0.5 mm (up to 60 GHz). Traditional interpolation methods often fail to provide sufficient details and accuracy (Wang X et al., 2023), necessitating the development of advanced reconstruction techniques. Otherwise, the current measurement systems, which are of high cost, would become obsolete.
In recent years, generative adversarial networks (GANs) have emerged as a powerful tool for image reconstruction. Conditional GAN (CGAN) introduces conditional information to enable the generator to produce specific types of data on demand (Mirza and Osindero, 2014). Notably, superresolution GAN (SRGAN) (Ledig et al., 2017) uses adversarial training combined with perceptual loss to g
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Shiwei YI, Congsheng LI, Tongning WU (2025). Superresolution reconstruction of E-field for assessing millimeter-wave exposure based on gradient-informed generative adversarial networks with plane-wave integral representation. Engineering Information Technology & Electronic Engineering. https://doi.org/10.1631/ENG_ITEE_2025_0021
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Frequently Asked Questions
What is EFGraGAN?
EFGraGAN is a generative adversarial network that integrates field gradient loss for superresolution reconstruction of millimeter-wave electric fields. It learns both local field magnitudes and spatial structures to produce high-resolution E-field maps.
How does EFGraGAN improve E-field reconstruction compared to traditional methods?
EFGraGAN outperforms conventional interpolation and traditional GAN methods by incorporating field gradient loss, which enhances accuracy and fine structural details. It achieves a maximum mean relative error of less than 9% up to 60 GHz in a 4×4 dipole array scenario.
What is the role of plane-wave integral representation (PWIR) in training?
PWIR is used to generate a training dataset with randomized parametric incidence, simulating diverse field distributions. This improves the network's generalization across different antenna types.
Does EFGraGAN meet international standards for mmWave exposure assessment?
Yes, EFGraGAN meets the requirements of the IEC/IEEE 63195-2 standard for exposure assessment, achieving high-resolution reconstruction at 30 GHz and 60 GHz with a step size as low as 0.5 mm.
How robust is EFGraGAN to measurement noise?
EFGraGAN demonstrates strong robustness to noise, enabling current measurement systems to achieve accurate and efficient evaluation of mmWave exposure without significant degradation in performance.
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