Rank-Adaptive Bayesian Tensor Ring Completion for Low-Altitude 5D Radio Environment Map Construction

The rapid development of the low-altitude economy demands comprehensive electromagnetic spectrum awareness. However, constructing a comprehensive radio environment map (REM) in this scenario is challenging, as spectrum sensing data collected by unmanned aerial vehicles (UAVs) in complex low-altitude environments is typically sparse, fragmented, and non-uniformly distributed across the high-dimensional space of time, frequency, and 3D space. To address these issues, this study proposes a rank-adaptive Bayesian tensor ring completion (Ra-BTRC) framework. The method models the low-altitude electromagnetic environment as a unified five-dimensional (5D) spectrum tensor. It then employs tensor ring (TR) decomposition to capture latent high-order correlations across all dimensions. To overcome the sensitivity of conventional TR methods to predefined ranks, Ra-BTRC introduces sparsity-inducing priors on the TR core factors, enabling variational Bayesian inference to learn observation uncertainty and infer effective TR ranks from sparse measurements without manually fixing the TR rank. Simulations demonstrate that Ra-BTRC significantly outperforms existing TR-based baselines, achieving more than 10 dB MMSE improvement at a 5% sampling rate while accurately recovering local spectrum structures and temporal dynamics. The proposed approach provides a robust and scalable solution for reliable global low-altitude spectrum cognition under stringent sensing budgets.