  Source localization and radio cartography using multi-way representation of
spectrum is the subject of study in this paper. A joint matrix factorization
and tensor decomposition problem is proposed and solved using an iterative
algorithm. The multi-way measured spectrum is organized in a tensor and it is
modeled by multiplication of a propagation tensor and a channel gain matrix.
The tensor indicates the propagating power from each location and each
frequency over time and the channel matrix links the propagating tensor to the
sensed spectrum. We utilize sparsity and other intrinsic characteristics of
spectrum to identify the solution of the proposed problem. Moreover, The online
implementation of the proposed framework results in online radio cartography
which is a powerful tool for efficient spectrum awareness and utilization. The
simulation results show that our algorithm is a promising technique for dynamic
primary user localization and online radio cartography.
