Tensor-Based Parametric Spectrum Cartography From Irregular Off-Grid Samplings

Tensor-based spectrum cartography (SC) has received increasing interests for recovering multi-dimensional radio map (RM) from sparse measurements. However, existing tensor-based SC methods largely depend on an ideal assumption, that the sparse measurements are regularly located on grids. However, this assumption is largely unrealistic since the RM is continuous in essence, and can be measured at arbitrary positions deviating from the pre-divided grids. This work addresses the problem of parametric SC from irregular off-grid samplings. The main idea is combining interpolation with the multi-linear rank-
$(L,L,1)$
block-term tensor decomposition (LL1). The interpolation is first adopted to guarantee the uniqueness of LL1, under the guidance of the proposed sampling pattern theorem. Then, the power spectrum density (PSD) and spatial loss field (SLF) of each emitter can be smoothly estimated, and SC is completed via the aggregation model. For the whole procedure, the uncertainty derived from interpolation is grid-wisely specified, and imposed as a restriction. Simulations verified that the proposed method outperforms the baselines based on on-grid samplings in harsher environments.