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

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.

A Tensor-Structured Approach to Dynamic Channel Prediction for Massive MIMO Systems with Temporal Non-Stationarity

In moderate- to high-mobility scenarios, channel state information (CSI) varies rapidly and becomes temporally non-stationary, leading to significant performance degradation in channel reciprocity-dependent massive multiple-input multiple-output (MIMO) transmission. To address this challenge, we propose a tensor-structured approach to dynamic channel prediction (TS-DCP) for massive MIMO systems with temporal non-stationarity, leveraging dual-timescale and cross-domain correlations. Specifically, due to the inherent spatial consistency, non-stationary channels on long-timescales are treated as stationary on short-timescales, decoupling complicated correlations into more tractable dual-timescale ones. To exploit such property, we frame the pilot symbols, capturing short-timescale correlations within frames by Doppler domain modeling and long-timescale correlations across frames by Markov/autoregressive processes. Based on this, we develop the tensor-structured signal model in the spatial-frequency-temporal domain, incorporating correlated angle-delay-Doppler domain channels and Vandermonde-structured factor matrices. Furthermore, we model cross-domain correlations within each frame, arising from clustered scatterer distributions, using tensor-structured upgradations of Markov processes and coupled Gaussian distributions. Following these probabilistic models, we formulate the TS-DCP as the variational free energy (VFE) minimization problem, designing trial belief structures through online approximation and the Bethe method. This yields the online TS-DCP algorithm derived from a dual-layer VFE optimization process, where both outer and inner layers leverage the multilinear structure of channels to reduce computational complexity significantly. Numerical simulations demonstrate the significant superiority of the proposed algorithm over benchmarks in terms of channel prediction performance.