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 extremely large-scale multiple-input multiple-output (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 capture the NF and SnS propagation effects and leverage temporal correlations among multiple pilot symbols for channel prediction. In this model, 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 these 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 angleonly 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 the computational complexity through tensor operations. In the E-step, we develop the bi-layer factor graph representation to isolate the bilinear mixing in the spatial domain induced by SnS propagation, thus facilitating bilayer iterations using approximate inference techniques. In the M-step, we leverage an alternating strategy for hyperparameter learning, with closed-form rules derived by the quadratic approximation of objective functions. Numerical simulations based on the near-practical channel simulator demonstrate the superior channel prediction performance of the proposed algorithm.