Beam-Delay Domain Channel Estimation for mmWave XL-MIMO Systems

This paper investigates the uplink channel estimation of the millimeter-wave (mmWave) extremely large-scale multiple-input-multiple-output (XL-MIMO) communication system in the beam-delay domain, taking into account the near-field and beam-squint effects due to the transmission bandwidth and array aperture growth. Specifically, we model spatial-frequency domain channels in the beam-delay domain to explore inter-antenna and inter-subcarrier correlations. Within this model, the frequency-dependent hybrid-field beam domain steering vectors are introduced to describe the near-field and beam-squint effects. The independent and non-identically distributed Bernoulli-Gaussian models with unknown prior hyperparameters are employed to capture the sparsity in the beam-delay domain, posing a challenge for channel estimation. Under the constrained Bethe free energy minimization framework, we design different structures and constraints on trial beliefs to develop hybrid message passing (HMP) algorithms, thus achieving efficient joint estimation of beam-delay domain channel and prior hyperparameters. To further improve the model accuracy, the multidimensional grid point perturbation (MDGPP)-based representation is presented, which assigns individual perturbation parameters to each multidimensional discrete grid. By treating the MDGPP parameters as unknown hyperparameters, we propose the two-stage HMP algorithm for MDGPP-based channel estimation, where the output of the initial stage is pruned for the refinement stage to reduce the computational complexity. Numerical simulations demonstrate the significant superiority of the proposed algorithm over benchmarks with both near-field and beam-squint effects.