{"ID":2882289,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.10546","arxiv_id":"2508.10546","title":"Unsupervised Deep Equilibrium Model Learning for Large-Scale Channel Estimation with Performance Guarantees","abstract":"Supervised deep learning methods have shown promise for large-scale channel estimation (LCE), but their reliance on ground-truth channel labels greatly limits their practicality in real-world systems. In this paper, we propose an unsupervised learning framework for LCE that does not require ground-truth channels. The proposed approach leverages Generalized Stein's Unbiased Risk Estimate (GSURE) as a principled unsupervised loss function, which provides an unbiased estimate of the projected mean-squared error (PMSE) from compressed noisy measurements. To ensure a guaranteed performance, we integrate a deep equilibrium (DEQ) model, which implicitly represents an infinite-depth network by directly learning the fixed point of a parameterized iterative process. We theoretically prove that, under mild conditions, the proposed GSURE-based unsupervised DEQ learning can achieve oracle-level supervised performance. In particular, we show that the DEQ architecture inherently enforces a compressible solution. We then demonstrate that DEQ-induced compressibility ensures that optimizing the projected error via GSURE suffices to guarantee a good MSE performance, enabling a rigorous performance guarantee. Extensive simulations validate the theoretical findings and demonstrate that the proposed framework significantly outperforms various baselines when ground-truth channel is unavailable.","short_abstract":"Supervised deep learning methods have shown promise for large-scale channel estimation (LCE), but their reliance on ground-truth channel labels greatly limits their practicality in real-world systems. In this paper, we propose an unsupervised learning framework for LCE that does not require ground-truth channels. The p...","url_abs":"https://arxiv.org/abs/2508.10546","url_pdf":"https://arxiv.org/pdf/2508.10546v1","authors":"[\"Haotian Tian\",\"Lixiang Lian\"]","published":"2025-08-14T11:35:58Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}