HankelKANet: Lightweight Path Loss Estimation via Physics-Inspired Hankel Convolution
Organizations: School of Computer Science and Technology, Anhui University of Technology, Maanshan 243002, China · Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ London, U.K.
Abstract
Accurate path loss (PL) estimation is essential for wireless network planning and optimization. This paper proposes HankelKANet, a lightweight physics-inspired network for PL estimation that structurally embeds electromagnetic propagation characteristics into the neural architecture. Built on a single residual UNet backbone, the proposed model integrates urban layout features with a convolutional Kolmogorov-Arnold network(KAN). Specifically, the convolutional kernels are parameterized by the radial amplitudes of the zeroth- and first-order Hankel functions. This formulation acts as a physics-inspired nonlinear distance encoding, enabling the network to capture dominant attenuation characteristics directly without requiring additional physics-based loss terms. Experimental results demonstrate that HankelKANet achieves state-of-the-art accuracy and efficiency on both the simulated RadioMapSeer dataset and the real-world Huawei RSRPSet. Compared with the leading baseline, PEFNet, it reduces the parameter count by 78% and lowers the RMSE by 16.96% on the simulated data, while further exhibiting robust cross-dataset transferability and high data efficiency during target-domain adaptation. To interpret these empirical gains, we mathematically establish a parameter-conditional spatial gradient bound. Using discrete Dirichlet energy (DDE) and Jacobian sensitivity heatmaps, we empirically verify that this physical encoding intrinsically constrains the network's spatial derivatives. This structural smoothness effectively eliminates non-physical spatial ripples, preventing overfitting to simulator artifacts and serving as the fundamental driver for robust real world generalization.
Figures & tables
| Method | MAE (dB) | RMSE (dB) | |
|---|---|---|---|
| 3GPP TR 36.873 [ 4 ] | 0.2552 | 11.5416 | 14.7590 |
| ray tracing [ 6 ] | 0.8594 | 4.7591 | 6.3250 |
| DTR [ 36 ] | 0.4733 ( 0.0004) | 8.7962 ( 0.0063) | 12.1251 ( 0.0104) |
| KNN [ 37 ] | 0.5808 ( 0.0002) | 7.8994 ( 0.0095) | 10.8649 ( 0.0053) |
| ANN [ 7 ] | 0.6303 ( 0.0034) | 7.4167 ( 0.0027) | 10.1688 ( 0.0029) |
| RadioUNet [ 8 ] | 0.9616 ( 0.0002) | 1.4747 ( 0.0180) | 2.8748 ( 0.0305) |
| Condition | Radio maps | Evaluated pixels | MAE (dB) | RMSE (dB) | |
|---|---|---|---|---|---|
| Overall outdoor test set | 8,000 | 397,944,539 | 0.9849 | 0.7980 | 1.8392 |
| LOS | 8,000 | 125,925,669 | 0.9885 | 0.4614 | 1.3884 |
| NLOS | 8,000 | 272,018,870 | 0.9820 | 1.2583 | 2.2506 |
| Short distance ( m) | 8,000 | 99,342,877 | 0.9910 | 0.3809 | 0.9827 |
| Long distance ( m) | 8,000 | 99,980,657 | 0.9633 | 1.9792 | 3.1182 |
| High building density ( ) | 2,160 | 89,968,345 | 0.9715 | 1.1780 | 2.2229 |
| Budget ( ) | Method | MAE (dB) | RMSE (dB) | |
|---|---|---|---|---|
| Training from Scratch | ||||
| 1% | PEFNet | 0.6448 | 4.7843 | 7.8452 |
| HankelKANet | 0.6896 | 4.4375 | 7.4218 | |
| 5% | PEFNet | 0.7620 | 3.5207 | 6.4211 |
| HankelKANet | 0.7983 | 3.2884 | 5.9126 | |
| 10% | PEFNet | 0.8340 | 2.8129 | 5.3628 |
| Ablation Variant | MAE (dB) | RMSE (dB) | |
|---|---|---|---|
| w/o Physical Branch | 0.6783 | 6.7468 | 9.5872 |
| Hankel replaced by B-spline | 0.8734 | 1.7899 | 2.7958 |
| w/o skip-connected module | 0.9445 | 2.1316 | 4.0146 |
| with non-trainable | 0.8833 | 1.1926 | 2.1594 |
| HankelKANet (Proposed) | 0.9849 | 0.7980 | 1.8392 |
| Representation Choice | Orders ( ) / Mode | RMSE (dB) | FLOPs (G) | Latency (s) | |
|---|---|---|---|---|---|
| Radial Envelope Only (Amplitude) | |||||
| Zeroth-order only | 0.8559 | 3.1025 | 91.48 | 0.95 | |
| First-order only | 0.8352 | 3.6856 | 91.48 | 0.97 | |
| Proposed Variant | 0.9849 | 1.8392 | 91.58 | 1.11 | |
| Second-order added | 0.9851 | 1.8376 | 91.66 | 1.20 | |
| Third-order added | 0.9845 | 1.8662 | 91.78 | 1.29 | |
| Method | Params (M) | FLOPs (G) | Size (MB) | Peak Mem (MB) | Lat. (s) | maps/s |
| RadioUNet | 25.41 | 58.31 | 101.65 | 260 | 1.396 | 0.716 |
| PEFNet | 118.38 | 506.25 | 473.52 | 720 | 1.426 | 0.701 |
| Ours (Net Only) | 26.13 | 91.58 | 104.50 | 260 | 0.812 | 1.232 |
| Hankel Encoding | 0.0005 | N/A a | 0.002 | 120 | 0.285 | 3.509 |
| HankelKANet | 26.13 | 104.50 | 340 | 1.110 | 0.901 |
| Model | Pre-trained | Target Domain Data Budget ( ) | ||||
|---|---|---|---|---|---|---|
| 0% (Zero-shot) | 1% | 5% | 10% | 20% | ||
| Scratch Baseline | No | - | 7.42 | 5.91 | 4.94 | 4.31 |
| PEFNet | Yes | 6.43 | 5.73 | 4.92 | 4.48 | 4.12 |
| HankelKANet | Yes | 5.82 | 5.14 | 4.57 | 4.23 | 3.98 |
Radio Propagation Modeling
Radio Propagation Modeling predicts how electromagnetic signals travel through environments for wireless planning, channel estimation, and sensing.
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