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

TL;DR

This paper introduces a self-supervised machine learning-based Bayes-optimal channel estimator for holographic MIMO systems operating in unknown electromagnetic environments, eliminating the need for prior knowledge or extensive training data.

Contribution

It develops a novel self-supervised MMSE channel estimation algorithm using score matching and PCA, suitable for large-scale HMIMO in complex EM environments.

Findings

Approaches oracle MMSE performance with minimal supervision.

Operates effectively without prior channel knowledge.

Maintains low computational complexity.

Abstract

Holographic MIMO (HMIMO) has recently been recognized as a promising enabler for future 6G systems through the use of an ultra-massive number of antennas in a compact space to exploit the propagation characteristics of the electromagnetic (EM) channel. Nevertheless, the promised gain of HMIMO could not be fully unleashed without an efficient means to estimate the high-dimensional channel. Bayes-optimal estimators typically necessitate either a large volume of supervised training samples or a priori knowledge of the true channel distribution, which could hardly be available in practice due to the enormous system scale and the complicated EM environments. It is thus important to design a Bayes-optimal estimator for the HMIMO channels in arbitrary and unknown EM environments, free of any supervision or priors. This work proposes a self-supervised minimum mean-square-error (MMSE) channel estimation algorithm based on powerful machine learning tools, i.e., score matching and principal component analysis. The training stage requires only the pilot signals, without knowing the spatial correlation, the ground-truth channels, or the received signal-to-noise-ratio. Simulation results will show that, even being totally self-supervised, the proposed algorithm can still approach the performance of the oracle MMSE method with an extremely low complexity, making it a competitive candidate in practice.