  The radio environment map (REM) visually displays the spectrum information
over the geographical map and plays a significant role in monitoring,
management, and security of spectrum resources.In this paper, we present an
efficient 3D REM construction scheme based on the sparse Bayesian learning
(SBL), which aims to recovery the accurate REM with limited and optimized
sampling data.In order to reduce the number of sampling sensors, an efficient
sparse sampling method for unknown scenarios is proposed. For the given
construction accuracy and the priority of each location, the quantity and
sampling locations can be jointly optimized.With the sparse sampled data, by
mining the spectrum situation sparsity and channel propagation characteristics,
an SBL-based spectrum data hierarchical recovery algorithm is developed to
estimate the missing data of unsampled locations.Finally, the simulated 3D REM
data in the campus scenario are used to verify the proposed methods as well as
to compare with the state-of-the-art. We also analyze the recovery performance
and the impact of different parameters on the constructed REMs. Numerical
results demonstrate that the proposed scheme can ensure the construction
accuracy and improve the computational efficiency under the low sampling rate.
