Hao Sun

As wireless networks progress toward sixthgeneration (6G), understanding the spatial distribution of directional beam coverage becomes increasingly important for beam management and link optimization. Multiple-input multipleoutput (MIMO) beam map provides such spatial awareness, yet accurate construction under sparse measurements remains difficult due to incomplete spatial coverage and strong angular variations. This paper presents a tensor decomposition approach for reconstructing MIMO beam map from limited measurements. By transforming measurements from a Cartesian coordinate system into a polar coordinate system, we uncover a matrix-vector outer-product structure associated with different propagation conditions. Specifically, we mathematically demonstrate that the matrix factor, representing beam-space gain, exhibits an intrinsic Toeplitz structure due to the shift-invariant nature of array responses, and the vector factor captures distance-dependent attenuation. Leveraging these structural priors, we formulate a regularized tensor decomposition problem to jointly reconstruct line-of-sight (LOS), reflection, and obstruction propagation conditions. Simulation results confirm that the proposed method significantly enhances data efficiency, achieving a normalized mean square error (NMSE) reduction of over 20% compared to state-of-the-art baselines, even under sparse sampling regimes.

This paper proposes a novel structure-aware matrix completion framework assisted by radial basis function (RBF) interpolation for near-field radio map construction in extremely large multiple-input multiple-output (XL-MIMO) systems. Unlike the far-field scenario, near-field wavefronts exhibit strong dependencies on both angle and distance due to spherical wave propagation, leading to complicated variations in received signal strength (RSS). To effectively capture the intricate spatial variations structure inherent in near-field environments, a regularized RBF interpolation method is developed to enhance radio map reconstruction accuracy. Leveraging theoretical insights from interpolation error analysis of RBF, an inverse μ-law-inspired nonuniform sampling strategy is introduced to allocate measurements adaptively, emphasizing regions with rapid RSS variations near the transmitter. To further exploit the global low-rank structure in the near-field radio map, we integrate RBF interpolation with nuclear norm minimization (NNM)-based matrix completion. A robust Huberized leave-one-out cross-validation (LOOCV) scheme is then proposed for adaptive selection of the tolerance parameter, facilitating optimal fusion between RBF interpolation and matrix completion. The integration of local variation structure modeling via RBF interpolation and global low-rank structure exploitation via matrix completion yields a structure-aware framework that substantially improves the accuracy of near-field radio map reconstruction. Extensive simulations demonstrate that the proposed approach achieves over 10% improvement in normalized mean squared error (NMSE) compared to standard interpolation and matrix completion methods under varying sampling densities and shadowing conditions.