Hybrid Near- and Far-Field THz UM-MIMO Channel Estimation: A Sparsifying Matrix Learning-Aided Bayesian Approach

Channel estimation (CE) is a critical challenge in harnessing the potential of Terahertz (THz) ultra-massive multiple-input multiple-output (UM-MIMO) systems. Sparsity-exploiting compressed sensing (CS)-aided CE (CSCE) can enhance THz UM-MIMO CE performance with affordable pilot overhead. However, the near-field propagation region becomes significant in THz UM-MIMO networks due to the large array aperture and high carrier frequency, leading to a more profound coexistence of near- and far-field radiation patterns. This hybrid-field propagation characteristic renders existing CSCE frameworks ineffective due to the lack of an appropriate sparsifying matrix. In this work, we investigate the uplink THz UM-MIMO CE problem, by developing a practical THz UM-MIMO channel model that incorporates near- and far-field paths, molecular absorption, and reflection attenuation. We propose a dictionary learning (DL)-aided Bayesian THz CSCE solution to achieve accurate, robust and pilot-efficient CE, even in ill-posed scenarios. Specifically, we tailor a batch-delayed online DL (BD-ODL) algorithm to generate an appropriate dictionary for the hybrid-field THz UM-MIMO channel model. Furthermore, we propose a Bayesian learning (BL)-enabled CSCE framework to leverage THz sparsity and utilize the learnt dictionary. To establish a lower bound for the mean squared error (MSE), we derive the Bayesian Cramér-Rao bound (BCRB). We also conduct a complexity analysis to quantify the required computational resources. Numerical results show a significant improvement in normalized MSE (NMSE) performance compared to conventional CE and CSCE baselines, and demonstrate rapid convergence.