GSURE-Based Unsupervised Deep Equilibrium Model Learning for Large-Scale Channel Estimation
Haotian Tian, Lixiang Lian · 2024
Recently, many supervised deep learning-based methods have been investigated for large-scale MIMO channel estimation. However, the supervised methods require a large amount of ground truth channel as labeled data, which are difficult to obtain in practice. In this paper, we propose to learn the large-scale MIMO channel from compressed noisy measurements without any ground truth channel by introducing a loss function based on Generalized Stein’s Unbiased Risk Estimate (GSURE), which is an unbiased estimate of the projected mean-squared error (PMSE). Furthermore, we adopt deep equilibrium model (DEQ) to directly learn the equilibrium point of an iterative algorithm through an infinite-depth network, therefore it inherits the convergence performance of the underlying algorithm. We show that when using DEQ networks, employing GSURE for unsupervised learning can achieve performance close to that of supervised learning using MSE. Experiments demonstrate that the proposed GSURE-based unsupervised DEQ showcases superior channel estimation performance compared to various baselines when ground-truth channel is unavailable.