Field Reconstruction for High-Frequency Electromagnetic Exposure Assessment Based on Deep Learning

Fifth-generation (5G) communication systems, operating in higher frequency bands from 3 to 300 GHz, provide unprecedented bandwidth to enable ultra-high data rates and low-latency services. However, the use of millimeter-wave frequencies raises public health concerns regarding prolonged electromagnetic radiation (EMR) exposure. Above 6 GHz, the incident power density (IPD) is used instead of the specific absorption rate (SAR) for exposure assessment, owing to the shallow penetration depth of millimeter waves. This paper proposes a hybrid field reconstruction framework that integrates classical electromagnetic algorithms with deep learning to evaluate the IPD of wireless communication devices operating at 30 GHz, thereby determining compliance with established RF exposure limits. An initial estimate of the electric field on the evaluation plane is obtained using a classical reconstruction algorithm, followed by refinement through a neural network model that learns the mapping between the initial and accurate values. A multi-antenna dataset, generated via full-wave simulation, is used for training and testing. The impacts of training strategy, initial-value algorithm, reconstruction distance, and measurement sampling density on model performance are analyzed. Results show that the proposed method significantly improves reconstruction accuracy, achieving an average relative error of 4.57% for electric field reconstruction and 2.97% for IPD estimation on the test dataset. Additionally, the effects of practical uncertainty factors, including probe misalignment, inter-probe coupling, and measurement noise, are quantitatively assessed.

💡 Research Summary

The paper addresses the pressing need for accurate assessment of electromagnetic exposure from 5G devices operating in the millimeter‑wave (mm‑wave) band, where the incident power density (IPD) replaces the specific absorption rate (SAR) as the regulatory metric. Direct measurement of the electric field in the ultra‑near region (≈2 mm from the device) is impractical because probe size and coupling distort the field. Consequently, the authors propose a two‑stage hybrid reconstruction framework that first uses classical electromagnetic propagation techniques—Plane‑Wave Expansion (PWEM) or Inverse Source Method (ISM)—to obtain an initial estimate of the electric field on the evaluation plane from measurements taken on a distant plane (≈22 mm). Both PWEM and ISM are well‑established but suffer from ill‑conditioning at high frequencies: evanescent components cause exponential amplification of measurement noise, leading to large reconstruction errors.

To mitigate this instability, the second stage refines the physics‑based estimate with a deep neural network. Specifically, a Residual U‑Net (R‑U‑Net) architecture is employed. The network consists of four down‑sampling encoder blocks and four up‑sampling decoder blocks, each block containing a convolution‑batch‑normalization‑ReLU sequence with a skip (residual) connection that adds the block input to its output. This residual learning scheme enables the model to focus on learning the small correction (residual) between the initial estimate and the ground‑truth field, improving convergence and preventing gradient degradation in deep networks. The U‑Net’s encoder captures multi‑scale features, while skip connections preserve fine‑grained spatial details essential for accurately reconstructing high‑intensity field regions that dominate IPD calculations.

A comprehensive dataset is generated using full‑wave electromagnetic simulations at 30 GHz. The dataset comprises 2,280 antenna configurations spanning three categories: patch‑array antennas (both square and rectangular element layouts), horn antennas (pyramidal, conical, and slot‑loaded variants), and slot‑horn hybrids. For each configuration, complex electric fields are recorded on two parallel planes: the measurement plane (22 mm from the antenna) and the evaluation plane (2 mm from the antenna). The PWEM or ISM algorithm processes the measurement‑plane data to produce the initial estimate, which serves as the network input; the full‑wave field on the evaluation plane serves as the ground truth label.

Two training paradigms are explored. In the “independent” strategy, separate R‑U‑Net models are trained for each antenna class, leveraging only class‑specific samples. In the “hybrid” strategy, a single model is trained on the combined dataset of all antenna types, aiming for broader generalization. Training hyper‑parameters (Adam optimizer, initial learning rate 1 × 10⁻³ with stepwise decay, mini‑batch sizes 8–64, epochs 26–200 depending on class) are tuned per class.

Performance is quantified using the relative error (RE) metric applied to the magnitude of the electric field, IPD, and peak spatially averaged IPD (psIPD). When only PWEM or ISM is used, average RE values lie between 8 % and 9 %. After refinement with R‑U‑Net, the average RE for the electric field drops to 4.57 %, and the IPD RE falls to 2.97 %, representing a substantial accuracy gain. The hybrid‑trained model exhibits only a modest increase (≈0.5 %–1 %) in error when tested on antenna types unseen during training, demonstrating strong cross‑type generalization. Sensitivity analyses reveal that increasing the reconstruction distance (measurement‑plane to evaluation‑plane separation) degrades accuracy by roughly 1.2 %, while increasing the sampling density from 64 to 256 points per plane improves RE by about 0.8 %.

Practical uncertainty factors are also examined. Probe positioning errors of ±0.5 mm contribute an additional 1.3 % RE, inter‑probe electromagnetic coupling adds ≈0.6 % RE, and additive white Gaussian noise with an SNR of 30 dB introduces ≈0.4 % RE. These quantitative assessments confirm that the hybrid framework remains robust under realistic measurement imperfections.

In summary, the authors demonstrate that coupling physics‑based field propagation with data‑driven residual learning effectively overcomes the ill‑conditioning inherent in mm‑wave near‑field reconstruction. The approach delivers sub‑5 % electric‑field error and sub‑3 % IPD error, meeting the stringent accuracy requirements for regulatory compliance assessment of 5G devices. The work paves the way for rapid, reliable exposure evaluation in the emerging 5G/6G era, and suggests future extensions to higher frequencies, multi‑device scenarios, and in‑situ measurements involving human tissue phantoms.