Investigating Map-Based Path Loss Models: A Study of Feature Representations in Convolutional Neural Networks

Path loss prediction is a beneficial tool for efficient use of the radio frequency spectrum. Building on prior research on high-resolution map-based path loss models, this paper studies convolutional neural network input representations in more detail. We investigate different methods of representing scalar features in convolutional neural networks. Specifically, we compare using frequency and distance as input channels to convolutional layers or as scalar inputs to regression layers. We assess model performance using three different feature configurations and find that representing scalar features as image channels results in the strongest generalization.

💡 Research Summary

This paper investigates how scalar features—specifically carrier frequency and link distance—should be incorporated into convolutional neural network (CNN)‑based path‑loss prediction models that use high‑resolution geographic information system (GIS) maps. Building on prior work that treated every input, including scalar quantities, as separate image channels, the authors compare three configurations: (1) the original model, which feeds both frequency and a 2‑D Euclidean distance map as full‑size channels; (2) the FINE model, which replaces the 2‑D distance map with a single constant‑value channel containing the 3‑D link length while keeping frequency as a channel; and (3) the FLIP model, which supplies both frequency and distance as scalar inputs to the fully‑connected regression head after the convolutional feature extractor.

The datasets consist of measured path‑loss values from six UK cities paired with 1‑m resolution digital surface model (DSM) data. For each link, a DSM slice centered on the direct line‑of‑sight is extracted, interpolated to a fixed 256 × W grid, and combined with a channel representing the direct‑path height. An additional channel encodes the Euclidean distance from the transmitter to every pixel. A separate Canadian test set (≈125 000 measurements across ten regions, covering dense urban, suburban, and rural environments) is used for blind evaluation.

All models share the same CNN backbone (convolution + max‑pooling) followed by a fully‑connected regression block, trained with Adam (lr = 1e‑4, batch = 256) for 200 epochs. In UK cross‑validation, each city is held out while the remaining five are split 80/20 for training/validation, with ten random restarts per holdout. Results (Table II) show that FINE improves RMSE on three holdouts (Merthyr Tydfil, Southampton, Stevenage) but degrades performance on the other three, leading to a higher overall mean RMSE (13.74 dB) and larger variance. FLIP achieves low training error (< 5 dB) but suffers severe over‑fitting, with validation and test RMSE consistently above 10 dB.

To assess generalization beyond the UK, the authors train “no‑holdout” models using all six cities, create ensembles by averaging the outputs of ten independently trained instances, and evaluate on the Canadian data. In this setting (Table III), FINE attains the best overall RMSE of 7.25 dB, slightly better than the original (7.42 dB), while FLIP’s ensemble improves to 10.26 dB but still lags behind the channel‑based approaches. Notably, FLIP performs best in three Canadian cities, suggesting that with larger, more diverse training data the scalar‑only formulation can recover some performance.

To explain FLIP’s mixed results, the authors conduct a city‑level linear regression linking FLIP RMSE to three meta‑features: proportion of line‑of‑sight links (pLOS), mean total obstruction depth (μo), and standard deviation of link distance (σd). The analysis (Table IV) reveals that higher pLOS and greater obstruction depth increase RMSE, whereas larger σd (i.e., more varied link lengths) tends to reduce it. This implies that FLIP excels on non‑LOS, low‑clutter links and on longer links where the path‑loss range is compressed, making predictions easier.

The study concludes that scalar features critical to radio propagation should be introduced as image channels before the convolutional layers, allowing the network to learn spatially aware representations that incorporate frequency‑dependent material interactions and distance‑dependent scaling of obstructions. Feeding these scalars only to the regression head leads to over‑fitting and poorer generalization. The findings provide concrete guidance for designing deep‑learning‑based path‑loss models for 6G and beyond, and suggest future work on integrating additional physical descriptors (terrain elevation, Fresnel‑zone clearance, clutter taxonomy) and exploring multi‑task or ensemble strategies to further boost accuracy without sacrificing robustness.