High-Fidelity Wireless Signal Reconstruction by Small Language Models with Reinforcement Learning in Low Altitude Wireless Network

Wireless signal reconstruction is essential for RF-based positioning in GPS-denied environments, yet faces fundamental challenges from multipath propagation, shadowing, and non-Gaussian noise. Traditional approaches require extensive site-specific calibration and environment-specific model training, limiting their utility for rapid-deployment scenarios. We present an In-Context Signal Completion (ICSC) framework demonstrating that compact language models fine-tuned with Group Relative Policy Optimization using physics-informed rewards can perform RSSI reconstruction across two complementary tasks: sequential extrapolation (predicting signal strength at future trajectory positions) and spatial interpolation (reconstructing signals at arbitrary locations within measurement constellations). Our 0.5B-parameter model achieves 55% recall within 2 dB on sequential prediction, surpassing GPT-4o (51%) while achieving a Mean Absolute Error (MAE) of 2.85 dB, representing a 49% reduction compared to the untrained baseline. This cross-task transfer provides evidence that the models acquire transferable physical reasoning rather than task-specific patterns. The 0.5B configuration maintains 3 ms inference latency, enabling real-time processing on resource-constrained edge devices. Our approach reduces deployment requirements from weeks of per-site data collection to immediate inference using sequential measurements as context, establishing a new paradigm for adapting foundation models to physical measurement tasks.