{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-peaceman-rachford-splitting-approach-with","title":"A Peaceman-Rachford Splitting Approach with Deep Equilibrium Network for Channel Estimation","arxiv_id":"2410.23752","date":"2024-10-31","proceeding":null,"authors":["Dingli Yuan","Shitong Wu","Haoran Tang","Lu Yang","Chenghui Peng"],"abstract":"Multiple-input multiple-output (MIMO) is pivotal for wireless systems, yet its high-dimensional, stochastic channel poses significant challenges for accurate estimation, highlighting the critical need for robust estimation techniques. In this paper, we introduce a novel channel estimation method for the MIMO system. The main idea is to construct a fixed-point equation for channel estimation, which can be implemented into the deep equilibrium (DEQ) model with a fixed network. Specifically, the Peaceman-Rachford (PR) splitting method is applied to the dual form of the regularized minimization problem to construct fixed-point equation with non-expansive property. Then, the fixed-point equation is implemented into the DEQ model with a fixed layer, leveraging its advantage of the low training complexity. Moreover, we provide a rigorous theoretical analysis, demonstrating the convergence and optimality of our approach. Additionally, simulations of hybrid far- and near-field channels demonstrate that our approach yields favorable results, indicating its ability to advance channel estimation in MIMO system.","url_abs":"https://arxiv.org/abs/2410.23752v2","url_pdf":"https://arxiv.org/pdf/2410.23752v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-peaceman-rachford-splitting-approach-with","repo_url":"https://github.com/wushitong1234/PR-DEN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"deq","method_name":"DEQ"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}