TRASC: Tensor-Based Radio Spectrum Cartography Using Plate Splines and Tensor CP Decomposition

The problem of radio spectrum cartography is addressed based on simultaneous tensor decomposition and interpolation of spatial maps. To this aim, a joint problem of CANDECOMPIPARAFAC (CP) decomposition and thin-plate splines is introduced and solved efficiently. Spectrum cartography is known as estimating power spectrum in any arbitrary location and frequency based on a small subset of sensed locations and frequencies. Tensor-based radio spectrum cartography (TRASC) algorithm is proposed to address spectrum cartography which consists of iterative solutions for two subproblems. The tensor de-composition subproblem models the latent temporal and spectral structure of sources, and the interpolation subproblem takes into the account fine spatial details in order to leverage neighborhood information within a certain vicinity. From mathematical point of view, retrieving non-sensed data from incomplete measurements is an ill-posed inverse problem. We utilize an assumption on rank of tensors and an assumption on smoothness of spatial interpo-lated maps to make the joint problem well-posed. Moreover, the impact of dynamics of the network on the rank of the underlying tensor is studied. The simulation results show applicability of the proposed algorithm in spectrum map estimation in presence of multi-dimensional sensing results over time, frequencies and space. Our experiments indicate that utilizing tensors and spatial interpolation is an effective approach for spectrum cartography.