Time-Varying Compressed Spectrum Mapping Using Dictionary-Weighted Smoothing

Spectrum mapping plays an increasingly important role in wireless communication applications, such as spectrum sharing and dynamic spectrum allocation. In this paper, we consider the problem of three-dimensional (3D) time-varying spectrum map reconstruction at a low sampling rate. Regarding this problem, we propose a spectrum mapping method based on compressed sensing. First, we obtain the sampling positions by singular value decomposition (SVD) and Householder transformation. Then, in contrast to traditional fixed sparse basis, we propose online k-singular value decomposition (O-KSVD) algorithm for online dictionary learning (ODL) to adaptively update the sparse basis. With the well-learned dictionary, a combine of weighted smoothing regularization (WSR) and sparsity regularization is introduced to restore the spatial structure of the spectrum map. Finally, simulations confirm the superiority of our proposed method in 3D time-varying spectrum mapping tasks.