Dynamic Spectrum Cartography: Reconstructing Spatial-Spectral-Temporal Radio Frequency Map via Tensor Completion

Abstract

Spectrum cartography (SC) aims to construct a global radio-frequency (RF) map across multiple domains, e.g., space, frequency and time, from sparse sensor samples. Recent state-of-the-art SC methods have successfully established the recoverability of $3$-D spatial-spectral RF maps using identifiable models, such as non-negative matrix factorization (NMF) and block-term tensor decomposition (BTD). However, these models do not account for possible time dynamics in RF environment. This work takes a step forward and focuses on a $4$-D spatial-spectral-temporal SC task under time-varying scenarios. From a data recovery viewpoint, the task is highly ill-posed since the degree of freedom (DoF) in a $4$-D map is extremely high. To address this issue, a two-stage methodology is put forth: for stage one, sensor measurements are unraveled into incomplete RF map w.r.t each emitter; for stage two, individual RF maps are completed in parallel and then synthesize the $4$-D map. In this way, DoF in the recovery process is significantly reduced. Two different algorithms are designed, including a basic batch-based one and a full-fledged streaming one enabling on-line SC. From the theory side, recoverability of the proposed approaches is characterized by certain sampling patterns or complexity. Experiments using synthetic, ray-tracing, and real-world data are employed to showcase the effectiveness of the proposed methods.