{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:42:58Z","timestamp":1760118178813,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T00:00:00Z","timestamp":1735257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","award":["62171126","2022A1515140137"],"award-info":[{"award-number":["62171126","2022A1515140137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["62171126","2022A1515140137"],"award-info":[{"award-number":["62171126","2022A1515140137"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we propose a random frequency division multiplexing (RFDM) method for multicarrier modulation in mobile time-varying channels. Inspired by compressed sensing (CS) technology which use a sensing matrix (with far fewer rows than columns) to sample and compress the original sparse signal simultaneously, while there are many reconstruction algorithms that can recover the original high-dimensional signal from a small number of measurements at the receiver. The approach choose the classic sensing matrix of CS\u2013Gaussian random matrix to compress the signal. However, the signal is not sparse which makes the reconstruction algorithms ineffective. We take full account of the great power of deep neural networks (DNN) to detect the signal as it is an underdetermined equation. The proposed RFDM establishes a novel signal modulation and detection method to target better transmission efficiency, and the simulation results show that the proposed method can achieve good BER, offering a new research paradigm to improve the spectrum efficiency of a multi-subcarrier, multi-antenna, multi-user system.<\/jats:p>","DOI":"10.3390\/e27010009","type":"journal-article","created":{"date-parts":[[2024,12,27]],"date-time":"2024-12-27T01:30:42Z","timestamp":1735263042000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Random Frequency Division Multiplexing"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6863-9087","authenticated-orcid":false,"given":"Chanzi","family":"Liu","sequence":"first","affiliation":[{"name":"The School of Electric Engineering and Intelligentization, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianjian","family":"Wu","sequence":"additional","affiliation":[{"name":"The School of Electric Engineering and Intelligentization, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5015-7335","authenticated-orcid":false,"given":"Qingfeng","family":"Zhou","sequence":"additional","affiliation":[{"name":"The School of Electric Engineering and Intelligentization, Dongguan University of Technology, Dongguan 523808, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hadani, R., Rakib, S., Tsatsanis, M., Monk, A., Goldsmith, A.J., Molisch, A.F., and Calderbank, R. (2017, January 19\u201322). Orthogonal time frequency space modulation. Proceedings of the 2017 IEEE Wireless Communications and Networking Conference (WCNC), San Francisco, CA, USA.","DOI":"10.1109\/WCNC.2017.7925924"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8214","DOI":"10.1109\/TWC.2023.3260906","article-title":"Affine frequency division multiplexing for next generation wireless communications","volume":"22","author":"Bemani","year":"2023","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1109\/LWC.2024.3397668","article-title":"Interleave Frequency Division Multiplexing","volume":"13","author":"Chi","year":"2024","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"13734","DOI":"10.1109\/TVT.2023.3277499","article-title":"Restricted search space exploration with refinement for symbol detection in uplink massive mimo","volume":"72","author":"Datta","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Aafreen, R., and Khan, M.Z.A. (2024, January 24\u201327). Low-Complexity Detection Using Channel Dimensionality Reduction in 6G Uplink Systems. Proceedings of the 2024 IEEE 99th Vehicular Technology Conference (VTC2024-Spring), Singapore.","DOI":"10.1109\/VTC2024-Spring62846.2024.10683420"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1109\/LWC.2022.3229002","article-title":"Low-Complexity Suboptimal ML Detection for OFDM-IM Systems","volume":"12","author":"Kim","year":"2023","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2694","DOI":"10.1109\/COMST.2020.3011561","article-title":"When Machine Learning Meets Privacy in 6G: A Survey","volume":"22","author":"Sun","year":"2020","journal-title":"IEEE Commu. Surv. Tutor."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7571","DOI":"10.1109\/TWC.2020.3012785","article-title":"Learning to Search for MIMO Detection","volume":"19","author":"Sun","year":"2020","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2045","DOI":"10.1109\/TVT.2023.3312029","article-title":"Deep Learning Aided LLR Correction Improves the Performance of Iterative MIMO Receivers","volume":"73","author":"Chen","year":"2024","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7235","DOI":"10.1109\/TIT.2011.2161794","article-title":"A Probabilistic and RIPless Theory of Compressed Sensing","volume":"57","author":"Candes","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4003","DOI":"10.1109\/TIP.2019.2959737","article-title":"Sensing Matrix Design for Compressive Spectral Imaging via Binary Principal Component Analysis","volume":"29","author":"Monsalve","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5513","DOI":"10.1109\/JSEN.2023.3243390","article-title":"Compressed Sensing Approach for Physiological Signals: A Review","volume":"23","author":"Lal","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"127362","DOI":"10.1109\/ACCESS.2019.2937490","article-title":"MIMO Signal Multiplexing and Detection Based on Compressive Sensing and Deep Learning","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","unstructured":"(2024, October 30). 3GPP TS 36.211; Version 9.1.0. Release 9. LTE: April 2010. Available online: https:\/\/www.etsi.org\/deliver\/etsi_ts\/136200_136299\/136211\/09.01.00_60\/ts_136211v090100p.pdf."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:01:02Z","timestamp":1760115662000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/1\/9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,27]]},"references-count":14,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["e27010009"],"URL":"https:\/\/doi.org\/10.3390\/e27010009","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,12,27]]}}}