Local Low-Rankness and Double Autoregression: A Tensor Completion Framework for Space-Based Radio Environment Mapping

In the field of spectrum situation monitoring, space-based spectrum mapping can overcome the limitations of ground-based monitoring, such as restricted coverage, environmental constraints, and difficulties in equipment deployment. However, current research on radio map reconstruction methods based on space-based satellite data is insufficient. Traditional methods mostly set missing patterns based on the type of data collected on the ground, such as random sampling or strip sampling. These methods can meet the needs of generating spectrum maps for local spectrum monitoring on the ground, but they are hardly adaptable to the task of space-based global spectrum mapping. To address this challenge, we have designed a tensor reconstruction method for radio maps based on local low-rankness. Before conducting global completion, we first identify local regions in the map with more prominent low-rank characteristics for completion. This enables the method to handle radio map reconstruction in the context of space-based wide-area coverage. During the reconstruction phase, targeting the two-dimensional spatial completion problem of space-based spectrum maps, we extend the autoregressive process from the temporal dimension in classical spatiotemporal models to the spatial domain, proposing a low-rank tensor completion model based on dual autoregression (LRTCDAR). By incorporating a dual autoregressive structure to capture spatial correlations and combining it with the inherent low-rank property of radio maps, the model achieves high-precision reconstruction of incomplete radio maps. Extensive experimental results demonstrate that, compared to state-of-the-art methods, the proposed approach effectively reconstructs radio maps under various conditional backgrounds. Notably, LRTCDAR exhibits greater advantages when applied to satellite data acquisition scenarios.