Sparse Bayesian Learning Based Channel Estimation for SIM-Assisted Near-Field Communications

Accurate acquisition of channel state information is crucial for unlocking the potential of stacked intelligent metasurface (SIM)-assisted communication systems. This paper investigates the channel estimation (CE) problem in SIM-assisted multi-user (MU) millimeter-wave (mmWave) near-field communication systems. We aim to solve the underdetermined problem caused by the large-scale deployment of nearly-passive meta-atoms, where the number of antennas at the base station (BS) is smaller than the number of meta-atoms on the last layer of the SIM. Specifically, we first design a polar-domain transform matrix for uniform planar arrays (UPA) to convert the near-field channel into a polar-domain representation. Moreover, we leverage the channel sparsity in the polar domain and the sparse Bayesian learning (SBL) technique to recover the channel parameters. Additionally, a covariance-free expectation maximization (CoFEM) algorithm is introduced to reduce the computational complexity of the SBL. Numerical simulation results indicate that in SIM-assisted near-field mmWave communications, the algorithms based on the proposed polar-domain transform matrix outperform existing angular-domain approaches. Moreover, the CoFEM algorithm significantly reduces the computational complexity compared to SBL methods.