MIMO Beam Map Reconstruction via Toeplitz-Structured Matrix-Vector Tensor Decomposition
Abstract
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.
Cite
@article{arxiv.2601.04599,
title = {MIMO Beam Map Reconstruction via Toeplitz-Structured Matrix-Vector Tensor Decomposition},
author = {Hao Sun and Junting Chen and Xianghao Yu},
journal= {arXiv preprint arXiv:2601.04599},
year = {2026}
}