In this paper, we investigate the channel estimation problem for extremely large-scale multi-input and multi-output (XL-MIMO) systems, considering the spherical wavefront effect, spatially non-stationary (SnS) property, and dual-wideband effects. To accurately characterize the XL-MIMO channel, we first derive a novel spatial-and-frequency-domain channel model for XL-MIMO systems and carefully examine the channel characteristics in the angular-and-delay domain. Based on the obtained channel representation, we formulate XL-MIMO channel estimation as a Bayesian inference problem. To fully exploit the clustered sparsity of angular-and-delay channels and capture the inter-antenna and inter-subcarrier correlations, a Markov random field (MRF)-based hierarchical prior model is adopted. Meanwhile, to facilitate efficient channel reconstruction, we propose a sparse Bayesian learning (SBL) algorithm based on approximate message passing (AMP) with a unitary transformation. Tailored to the MRF-based hierarchical prior model, the message passing equations are reformulated using structured variational inference, belief propagation, and mean-field rules. Finally, simulation results validate the convergence and superiority of the proposed algorithm over existing methods.

翻译：本文研究了超大规模多输入多输出（XL-MIMO）系统的信道估计问题，综合考虑了球面波前效应、空间非平稳特性以及双宽带效应。为精确表征XL-MIMO信道，我们首先推导了一种新颖的XL-MIMO系统空频域信道模型，并深入分析了该信道在角度-时延域的统计特性。基于所得信道表示，我们将XL-MIMO信道估计问题构建为贝叶斯推断框架。为充分挖掘角度-时延信道的簇状稀疏特性并捕捉天线间与子载波间的相关性，本文采用基于马尔可夫随机场的分层先验模型。同时，为实现高效信道重构，我们提出了一种基于酉变换近似消息传递的稀疏贝叶斯学习算法。针对该分层先验模型，消息传递方程通过结构化变分推断、置信传播及平均场规则进行了重构。仿真结果验证了所提算法的收敛性及其相对于现有方法的优越性。