Dynamic spectrum cartography via canonical polyadic tensor decomposition

摘要

Spectrum cartography aims at estimating multidimensional radio map from limited geographical observations. Recovering unobserved elements in a radio map, from sequential spectrum observations over a long period in large geographic areas, poses major challenges to real-time requirement and storage. As historical information from dynamic spectrum observations is not well utilized, traditional spectrum cartography methods, which are statically applied on single or multiple time slots, are not well suitable for time-varying scenarios. To address these challenges, we propose two novel radio map reconstruction algorithms based on tensor canonical polyadic decomposition (CPD), called dynamic window size based CPD (DW-CPD) and incremental CPD (I-CPD). The dynamic window size of DW-CPD is derived based on Kruskal condition of tensor CPD, and I-CPD is derived based on an exponentially weighted least squares criterion. We prove that the solution of I-CPD converges to a stationary point of the tensor completion problem, which validates that the proposed 1-CPD is suitable for applications in estimating dynamic CP factor. Simulations results show that DW-CPD and I-CPD based algorithms have similar estimation performance for dynamic spectrum cartography, and are better than the existing methods. Due to the overall advantage of performance, running time and storage, I-CPD based algorithm is preferable for real-time applications.