Adaptive Polynomial Chaos Expansion for Uncertainty Quantification of Radio Wave Propagation over Irregular Terrains
Accurate modeling of radio wave propagation over irregular terrains is crucial for designing reliable wireless communication systems in such environments, yet uncertainties in the antenna configuration are not quantified within deterministic models. This paper develops a fixed number of samples adaptive polynomial chaos expansion (APCE) method for uncertainty quantification (UQ) of radio wave propagation over realistic irregular terrains, where the model evaluations are obtained using a two-way parabolic wave equation (PWE) method. The proposed APCE method is designed to construct a compact and stable PCE model from a prescribed and limited set of simulations. The polynomial basis is enriched using an anisotropic basis extension algorithm driven by variance contributions, while validation behavior and the available sample size are used to control basis growth. The convergence analysis shows decreasing validation errors and improved robustness as the sampling budget increases, with lower trial-to-trial variability than the baseline adaptive PCE method, which uses the same variance-driven basis extension strategy. For two realistic terrain profiles, the proposed method accurately predicts the mean and the 5-95 percentile range of the path loss, and improves the estimation of the standard deviation compared with standard and sparse PCE, using only 30 PWE simulations. APCE outperforms standard and sparse PCE, with the largest gains observed for the 5th and 95th percentile estimates, and its construction time is close to that of standard PCE and much lower than that of sparse PCE based on least angle regression. As the sample size increases, APCE maintains low errors with reduced trial-to-trial variability.