# Tensor-Structured Bayesian Channel Prediction for Upper Mid-Band XL-MIMO Systems

arXiv: https://arxiv.org/abs/2508.08491 · HTML: https://mlsanity.com/paper/2508.08491/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2025.

## Built on by (most cited first, 1 of 1)

- [Unlocking Symbol-Level Precoding Efficiency Through Tensor Equivariant Neural Network](https://mlsanity.com/paper/2510.02108/) (2025)

## Abstract (arXiv)

The upper mid-band balances coverage and capacity for the future cellular systems and also embraces XL-MIMO systems, offering enhanced spectral and energy efficiency. However, these benefits are significantly degraded under mobility due to channel aging, and further exacerbated by the unique near-field (NF) and spatial non-stationarity (SnS) propagation in such systems. To address this challenge, we propose a novel channel prediction approach that incorporates dedicated channel modeling, probabilistic representations, and Bayesian inference algorithms for this emerging scenario. Specifically, we develop tensor-structured channel models in both the spatial-frequency-temporal (SFT) and beam-delay-Doppler (BDD) domains, which leverage temporal correlations among multiple pilot symbols for channel prediction. The factor matrices of multi-linear transformations are parameterized by BDD domain grids and SnS factors, where beam domain grids are jointly determined by angles and slopes under spatial-chirp based NF representations. To enable tractable inference, we replace environment-dependent BDD domain grids with uniformly sampled ones, and introduce perturbation parameters in each domain to mitigate grid mismatch. We further propose a hybrid beam domain strategy that integrates angle-only sampling with slope hyperparameterization to avoid the computational burden of explicit slope sampling. Based on the probabilistic models, we develop tensor-structured bi-layer inference (TS-BLI) algorithm under the expectation-maximization (EM) framework, which reduces computational complexity via tensor operations by leveraging the bi-layer factor graph for approximate E-step inference and an alternating strategy with closed-form updates in the M-step. Numerical simulations based on the near-practical channel simulator demonstrate the superior channel prediction performance of the proposed algorithm.