  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.
