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Holographic MIMO (HMIMO) has recently been recognized as a promising enablerfor future 6G systems through the use of an ultra-massive number of antennas ina compact space to exploit the propagation characteristics of theelectromagnetic (EM) channel. Nevertheless, the promised gain of HMIMO couldnot be fully unleashed without an efficient means to estimate thehigh-dimensional channel. Bayes-optimal estimators typically necessitate eithera large volume of supervised training samples or a priori knowledge of the truechannel distribution, which could hardly be available in practice due to theenormous system scale and the complicated EM environments. It is thus importantto design a Bayes-optimal estimator for the HMIMO channels in arbitrary andunknown EM environments, free of any supervision or priors. This work proposesa self-supervised minimum mean-square-error (MMSE) channel estimation algorithmbased on powerful machine learning tools, i.e., score matching and principalcomponent analysis. The training stage requires only the pilot signals, withoutknowing the spatial correlation, the ground-truth channels, or the receivedsignal-to-noise-ratio. Simulation results will show that, even being totallyself-supervised, the proposed algorithm can still approach the performance ofthe oracle MMSE method with an extremely low complexity, making it acompetitive candidate in practice.

Learning Bayes-Optimal Channel Estimation for Holographic MIMO in Unknown EM Environments