Spatio-Temporal-Frequency Radio Map Inference via Physical Guided Multiscale Bayesian Neural Networks

Abstract

This letter aims to reconstruct spatio-temporal-frequency radio maps from sparse sensor measurements to support proactive wireless resource allocation in low-altitude UAV scenarios. We propose a physically guided multiscale Bayesian neural network (PGM-BNN), which integrates a learnable distance-dependent attenuation prior, multiscale temporal-frequency Fourier encoding, and MAP-based Bayesian regularization. The physical guidance module provides lightweight propagation-related features from sparse reference sensors, while the multiscale Fourier encoding captures slow global trends and rapid local oscillations in the temporal-frequency domain. A MAP-based Bayesian neural network module is further used as a prior-regularized probabilistic regression component for sparse-data inference. Experimental results show that PGM-BNN accurately reconstructs global radio maps using only a few observation points. Compared with DPA, RadioUNet, and SCA, the proposed method achieves the best MSE, RMSE, and MAE values while maintaining competitive MAPE performance.