Holographic MIMO (HMIMO) is being increasingly recognized as a key enabling technology for 6G wireless systems through the deployment of an extremely large number of antennas within a compact space to fully exploit the potentials of the electromagnetic (EM) channel. Nevertheless, the benefits of HMIMO systems cannot be fully unleashed without an efficient means to estimate the high-dimensional channel, whose distribution becomes increasingly complicated due to the accessibility of the near-field region. In this paper, we address the fundamental challenge of designing a low-complexity Bayes-optimal channel estimator in near-field HMIMO systems operating in unknown EM environments. The core idea is to estimate the HMIMO channels solely based on the Stein's score function of the received pilot signals and an estimated noise level, without relying on priors or supervision that is not feasible in practical deployment. A neural network is trained with the unsupervised denoising score matching objective to learn the parameterized score function. Meanwhile, a principal component analysis (PCA)-based algorithm is proposed to estimate the noise level leveraging the low-rank near-field spatial correlation. Building upon these techniques, we develop a Bayes-optimal score-based channel estimator for fully-digital HMIMO transceivers in a closed form. The optimal score-based estimator is also extended to hybrid analog-digital HMIMO systems by incorporating it into a low-complexity message passing algorithm. The (quasi-) Bayes-optimality of the proposed estimators is validated both in theory and by extensive simulation results. In addition to optimality, it is shown that our proposal is robust to various mismatches and can quickly adapt to dynamic EM environments in an online manner thanks to its unsupervised nature, demonstrating its potential in real-world deployment.

翻译：全息MIMO（HMIMO）通过在紧凑空间内部署极大规模天线阵列以充分挖掘电磁信道潜力，正日益被视为6G无线系统的关键使能技术。然而，若缺乏高效的高维信道估计方法，HMIMO系统的优势将无法完全释放——由于近场区域的可达性，信道分布正变得日益复杂。本文致力于解决在未知电磁环境中工作的近场HMIMO系统内，设计低复杂度贝叶斯最优信道估计器这一基础性挑战。其核心思想是仅基于接收导频信号的Stein得分函数与估计的噪声水平来估计HMIMO信道，无需依赖实际部署中不可行的先验信息或监督信号。我们通过无监督去噪得分匹配目标训练神经网络以学习参数化的得分函数。同时，提出一种基于主成分分析（PCA）的算法，利用近场空间相关性的低秩特性来估计噪声水平。基于这些技术，我们以闭式解形式为全数字HMIMO收发器开发了贝叶斯最优的基于得分的信道估计器。通过将最优得分估计器集成到低复杂度消息传递算法中，该方案进一步扩展至混合模数HMIMO系统。所提估计器的（准）贝叶斯最优性在理论上和大量仿真结果中均得到验证。除最优性外，研究表明我们的方案对各类失配具有鲁棒性，并能凭借其无监督特性以在线方式快速适应动态电磁环境，展现了其在现实部署中的潜力。