ReVeal-MT: A Physics-Informed Neural Network for Multi-Transmitter Radio Environment Mapping

This manuscript has been submitted for peer review and possible publication in an IEEE journal. The content herein represents the version prepared by the authors and may be subject to further revision during the review. Abstract--Accurately mapping the radio environment (e.g., identifying wireless signal strength at specific frequency bands and geographic locations) is crucial for efficient spectrum sharing, enabling Secondary Users (SUs) to access underutilized spectrum bands while protecting Primary Users (PUs). While existing models have made progress, they often degrade in performance when multiple transmitters coexist, due to the compounded effects of shadowing, interference from adjacent transmitters. T o address this challenge, we extend our prior work on Physics-Informed Neural Networks (PINNs) for single-transmitter mapping to derive a new multi-transmitter Partial Differential Equation (PDE) formulation of the Received Signal Strength Indicator (RSSI). We then propose ReV eal-MT (Re-constructor and Visualizer of Spectrum Landscape for Multiple Transmitters), a novel PINN which integrates the multi-source PDE residual into a neural network loss function, enabling accurate spectrum landscape reconstruction from sparse RF sensor measurements. ReV eal-MT is validated using real-world measurements from the ARA wireless living lab across rural and suburban environments, and benchmarked against 3GPP and ITU-R channel models and a baseline PINN model for a single transmitter use-case. Results show that ReV eal-MT achieves substantial accuracy gains in multi-transmitter scenarios, e.g., achieving an RMSE of only 2.66 dB with as few as 45 samples over a 370-square-kilometer region, while maintaining low computational complexity. These findings demonstrate that ReV eal-MT significantly advances radio environment mapping under realistic multi-transmitter conditions, with strong potential for enabling fine-grained spectrum management and precise coexistence between PUs and SUs. I. INTRODUCTION Existing spectrum sharing frameworks, such as those implemented in the TV White Space (TVWS) database and Citizens Broadband Radio Service (CBRS) Spectrum Access System (SAS), rely heavily on traditional statistical models. However, such models struggle to accurately capture the real-world spectrum occupancy and do not generalize well enough to capture shadowing and fading caused by different kinds of terrain and environmental conditions, leading to conservative approaches that over-protect the primary users (PUs) and cause discrepancies in channel availability for spectrum re-use [1]- [3].