Sensing Radio Maps via Bayesian Tensor Learning

Spatial-spectral radio map estimation (RME) from sparsely deployed sensors can be viewed as a tensor learning problem. Among tensor models, the block-term decomposition (BTD) model is especially effective for RME, enabling accurate recovery of the radio map as well as emitter-level spatial loss field (SLF) and power spectral density (PSD). However, selecting the appropriate tensor and block-term ranks in the BTD model is crucial yet challenging, as the ranks indicate the number and properties of emitters, which are typically unknown in practice. Inappropriate settings of these ranks leads to overfitting and underfitting of the model. Existing optimization-based BTD learning methods either unrealistically assume that these ranks are known or require parameter tuning. To address these issues, we propose a Bayesian BTD model that incorporates sparsitypromoting priors on the factor matrices for rank learning, eliminating the need for parameter tuning while learning all other parameters. Extensive numerical experiments showcase the effectiveness of the proposed method.