Tensor-structured bayesian channel prediction for XL-MIMO systems

This paper investigates channel prediction for ex-tremely large-scale multiple-input multiple-output (XL-MIMO) systems under near-field (NF) propagation, where spherical wavefronts and high-dimensional channel representations make both modeling and inference computationally challenging. To fully exploit the correlations in the spatial, frequency, and temporal domains, we develop a tensor-structured channel model and its beam-delay-Doppler (BDD) domain representa-tion, where Doppler-domain features enable physically inter-pretable extrapolation over arbitrary prediction horizons within the stationarity interval. To handle NF propagation without incurring a combinatorial grid explosion, we propose a hybrid beam-domain strategy that discretizes only the angle dimension while treating the NF slope parameters as continuous, learn-able hyperparameters, together with perturbation-based grid refinement to support continuous-valued physical parameters without dense sampling. Building on the resulting Bayesian formulation with a sparse prior, we design an approximate inference algorithm within the generalized approximate message passing (GAMP) framework, where both the mean-type and variance-type matrix-vector multiplications are implemented via mode-wise tensor contractions that exploit the separable Kronecker structure of the transform matrix, thereby avoiding explicit Kronecker matrices and substantially reducing com-plexity. Numerical results using the practical channel simulator QuaDRiGa demonstrate that the proposed approach achieves significantly improved channel prediction performance compared with existing methods.