This paper presents a comparative analysis of three outdoor wave propagation models—ITU-R P.1546-6, the SUI model, and ITU-R P.452-17—benchmarked against the deterministic Parabolic Equation Modeling (PEM) method at 3.6 GHz and 6 GHz. The evaluation focuses on prediction accuracy (RMSE, MAE, bias, relative error), terrain sensitivity, and computational efficiency. At 3.6 GHz, ITU-R P.1546-6 shows poor terrain responsiveness and high relative errors, while ITU-R P.452-17 demonstrates strong terrain sensitivity and low errors in flat areas, but decreased accuracy over hilly terrain. At 6 GHz, the SUI model consistently underestimates field strength and exhibits weak terrain sensitivity, limiting its use to rough estimations. In contrast, ITU-R P.452-17 maintains good terrain correlation and acceptable accuracy, although it slightly overestimates field strength in complex environments. The results confirm that prediction accuracy, terrain sensitivity, and bias are highly model- and frequency-dependent. ITU-R P.452-17 emerges as the most reliable and computationally efficient alternative to deterministic methods when terrain effects must be considered without significant computational overhead.

This study investigates the sensitivity of radio wave propagation models to terrain sampling density in a 5G New Radio Vehicle-to-Everything downlink scenario at 3.6 GHz. Four widely used models are analysed: the empirical ITU-R P.1546-6, the deterministic Parabolic Equation Method, and the hybrid ITU-R P.1812-6 and ITU-R P.452-16. Real terrain profiles from Hungary are considered at multiple resolutions, allowing a systematic assessment of how accuracy degrades as the representation of terrain becomes coarser. The analysis reveals a consistent ranking across environments: the empirical model is the least affected by resolution changes, while deterministic and hybrid methods are significantly more sensitive. To interpret these differences, the study introduces a spectral complexity measure of terrain profiles and establishes its strong relationship with error growth through regression analysis. This provides a novel framework for explaining and quantifying the impact of terrain detail on model behaviour. The findings highlight both the methodological contribution of linking spectral complexity to propagation accuracy and the practical implications for optimising the trade-off between computational efficiency and prediction reliability in vehicular network planning.

Deterministic radio wave propagation models provide high accuracy in complex outdoor environments but remain computationally impractical for large-scale network planning and spectrum management. In contrast, empirical and hybrid models offer low complexity at the expense of reduced accuracy, systematic bias, and limited terrain sensitivity. This paper proposes a unified delta learning framework that enhances fast baseline propagation models by learning a data-driven correction toward a deterministic Parabolic Equation Modeling (PEM) reference. A key novelty lies in a compact, physics-informed feature representation that replaces the full terrain profile with an 18-dimensional vector combining local geometric descriptors, global terrain characteristics, and baseline responses, enabling accurate correction with low-dimensional input. The study also provides the first systematic investigation of delta-based correction across multiple widely used propagation models. The framework is evaluated for free-space propagation, ITU-R P.1546, ITU-R P.1812, and ITU-R P.452 using ridge regression, kernel ridge regression, gradient boosting regression trees, and a neural network model. Model performance is assessed in terms of error reduction, bias mitigation, robustness across learning algorithms, and profile-level generalization to previously unseen propagation paths within the considered terrain categories. Results show substantial error reduction, with up to twofold improvement for simpler baseline models and consistent gains for hybrid models, while preserving computational efficiency.