Radio Environment Map Reconstruction via Tensor Completion: Bayesian and Semantic Approaches

The radio environment map (REM) is one of the representations of the wireless environments, which consists of the spectrum data and enables the users to understand the electromagnetic situation in temporal, spectral and spatial domains. Generally, the observations of the spectrum data are incomplete due to the insufficient acquisition capability, and even the observed ones could be corrupted by some interferences and white noises. In this paper, we model the REM in all domains using the tensor notation, and propose a Bayesian and a deep-learning approaches to complete the spectrum map from the incomplete and corrupted observed spectrum data. In the first approach, by using the Tucker decomposition on the spectrum tensor, a hierarchical Bayesian framework is modeled to characterize the core tensor, the factor matrices, and the other nuisances. These nodes and their distribution parameters serve as the latent variables in the model. The variational Bayesian method is adopted to compute the posterior probabilities in an iterative manner. Regarding the low-rank property and the correlation of the spectrum, an adaptive compressed tensor decomposition algorithm is proposed to denoise the recovered spectral map in each iteration. In the second approach, the spectrum blanks are initialized by the linear interpolation to obtain the initial complete spectrum tensor. We use the Vision Transformer to solve a semantic segmentation problem in order to identify the semantic regions of the spectrum map in which the power of one emitter dominates. Then, the tensor completion is performed in the individual semantic tensor using the proposed compression algorithm. At last, the simulation results show that both the proposed approaches outperform the existing ones. We further observe that the semantic approach outperforms the Bayesian one for the sparse emitter scenarios while the Bayesian approach exhibits better recovery accuracy as the density of the emitters increases in the normalized mean square error.