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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.10546 |
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| _version_ | 1866913991440203776 |
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| author | Tian, Haotian Lian, Lixiang |
| author_facet | Tian, Haotian Lian, Lixiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unsupervised Deep Equilibrium Model Learning for Large-Scale Channel Estimation with Performance Guarantees Tian, Haotian Lian, Lixiang Signal Processing 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. |
| title | Unsupervised Deep Equilibrium Model Learning for Large-Scale Channel Estimation with Performance Guarantees |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2508.10546 |