MIMO Beam Map Reconstruction via Toeplitz-Structured Matrix-Vector Tensor Decomposition

TL;DR

This paper introduces a tensor decomposition method leveraging Toeplitz structure to accurately reconstruct MIMO beam maps from limited measurements, improving data efficiency for 6G beam management.

Contribution

It presents a novel Toeplitz-structured tensor decomposition approach that exploits array response invariances for better beam map reconstruction from sparse data.

Findings

Achieves over 20% NMSE reduction compared to baselines.

Effectively reconstructs LOS, reflection, and obstruction conditions.

Enhances data efficiency in sparse measurement regimes.

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.