Physics-Constrained Synthetic Training for Sub-Terahertz Channel Rainfall Sensing

Technical Summary: Physics-Constrained Synthetic Training for Sub-Terahertz Channel Rainfall Sensing

Problem Statement
Terahertz (THz) channels offer high-capacity communication and fine-resolution sensing capabilities, making them a candidate for Integrated Sensing and Communication (ISAC) in 6G networks. However, rain-induced extinction in THz bands creates a significant reliability challenge while simultaneously offering a mechanism for opportunistic rainfall sensing. Unlike mature rainfall retrieval systems based on satellites, radar, or commercial microwave links (CMLs), which rely on large-scale operational datasets for supervised learning, THz channel rainfall estimation suffers from a critical scarcity of real-world data. Existing studies are limited to controlled artificial-rain experiments or short-term outdoor campaigns, preventing the training of robust deep learning models.

Methodology
To address the data scarcity, the authors propose a physics-constrained synthetic training framework validated by limited outdoor measurements. The methodology consists of three main stages:

1. Channel Characterization and Calibration:

   • Measurement: An outdoor campaign was conducted at the Beijing Institute of Technology using a fixed 41.5 m point-to-point THz link at 140 GHz and 229 GHz. The setup utilized vertical linear polarization and recorded received power variations under clear and rainy conditions.
   • Statistical Modeling: The study established a relationship between the Rician $K$-factor and rainfall rate ($R$) using an independent dataset (BIT-24). This linear relationship ($K$ decreases as $R$ increases) was used to model small-scale fading.
   • Physical Constraints: Rain attenuation was modeled using the ITU-R P.838-3 standard and Mie theory, incorporating four distinct Raindrop Size Distribution (DSD) priors: Marshall-Palmer (M-P), Joss-Widespread (J-W), Joss-Drizzle (J-D), and ITU-R P.838-3.

2. Synthetic Data Generation (BIT-24-Gen):

   • A physics-constrained synthetic dataset was generated to bridge the data gap. For each frequency and DSD prior, 20,000 samples were created.
   • Each sample consists of a 20-second received-power sequence (400 points at 0.05s intervals) paired with a constant rainfall rate label.
   • The generation process combines large-scale rain attenuation (determined by the DSD prior and path length) with small-scale Rician fading (governed by the calibrated $K$-$R$ relation) and bounded stochastic drift.
   • Rainfall rates were sampled from a two-component uniform mixture to reflect the long-tailed nature of rain events (70% light rain, 30% moderate/heavy rain).

3. Network Architecture (RainFormer):

   • A hybrid attention-convolution network, RainFormer, was designed to map short-time received-power sequences to rainfall rates.
   • Architecture: The model employs a 1D convolutional embedding, followed by four stacked hybrid blocks. Each block integrates multi-head self-attention (for long-range temporal dependencies) and depthwise convolutional gated feed-forward layers (for local fluctuation patterns).
   • Physical-Statistical Fusion: A critical design feature is the explicit concatenation of physical-statistical descriptors (mean and standard deviation of the input sequence) with the latent representation before the regression head. This ensures the network directly utilizes dominant attenuation and fluctuation statistics rather than relying solely on the backbone to infer them.

Key Results

• In-Distribution Performance: On the synthetic test set (BIT-24-Gen), RainFormer achieved a Root Mean Square Error (RMSE) of 0.1782 mm/h at 140 GHz (using the ITU prior) and 0.2925 mm/h at 229 GHz (using the M-P prior).
• Ablation Studies: The removal of positional encoding caused the most significant performance degradation (RMSE increased to >1.1 mm/h), followed by the removal of explicit physical-statistical descriptors (RMSE increased to 1.65 mm/h at 229 GHz). This confirms that temporal order and explicit statistical descriptors are the primary drivers of predictive accuracy, while self-attention and convolution act as complementary refinements.
• Baseline Comparison: RainFormer outperformed both a 1D-CNN and a vanilla Transformer. At 140 GHz, it reduced RMSE by ~13% compared to the 1D-CNN and ~40% compared to the Transformer. At 229 GHz, it achieved the lowest Mean Absolute Error (MAE), demonstrating robustness across frequencies.
• Zero-Shot Transfer: When applied directly to the measured BIT-25 dataset (without any training or fine-tuning on real rain data), the models produced rank-consistent estimates. The estimates successfully separated weak from heavy rain, and the spread of predictions across the four DSD priors effectively bounded the uncertainty arising from the unobservable path DSD.

Significance and Claims
The paper claims that DSD-bracketed synthetic training is a viable foundation for THz rainfall sensing in scenarios where operational datasets are unavailable. The key contributions are:

1. Data Scarcity Solution: Demonstrating that physics-constrained synthetic data, calibrated with limited real-world channel statistics, can train models that generalize to real measurements without direct supervision on rainfall labels.
2. Uncertainty Quantification: By training on multiple DSD priors, the approach converts the unobservable path DSD from an unquantified bias into a bounded uncertainty envelope, providing physically interpretable estimates.
3. Hybrid Architecture Validation: Establishing that for THz rainfall sensing, explicit physical-statistical descriptors and temporal-order information are more critical than complex attention mechanisms alone.

The authors conclude that this approach supports the development of opportunistic THz rainfall sensing for 6G ISAC and may assist in cross-calibrating meteorological radar retrievals, though they note that future work requires multi-event campaigns and extension to longer channels.