{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T14:41:20Z","timestamp":1784126480344,"version":"3.55.0"},"reference-count":23,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T00:00:00Z","timestamp":1714348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basic Research Projects of Science, Education and Industry Integration Pilot Project of Qilu University of Technology","award":["2022JBZ01-02"],"award-info":[{"award-number":["2022JBZ01-02"]}]},{"name":"Basic Research Projects of Science, Education and Industry Integration Pilot Project of Qilu University of Technology","award":["2022PX088"],"award-info":[{"award-number":["2022PX088"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Orthogonal chirp division multiplexing (OCDM) offers a promising modulation technology for shallow water underwater acoustic (UWA) communication systems due to multipath fading resistance and Doppler resistance. To handle the various channel distortions and interferences, obtaining accurate channel state information is vital for robust and efficient shallow water UWA communication. In recent years, deep learning has attracted widespread attention in the communication field, providing a new way to improve the performance of physical layer communication systems. In this paper, the pilot-based channel estimation is transformed into a matrix completion problem, which is mathematically equivalent to the image super-resolution problem arising in the field of image processing. Simulation results show that the deep learning-based method can improve the channel distortion, outperforming the equalization performed by traditional estimator, the performance of Bit Error Rate is improved by 2.5 dB compared to the MMSE method in OCDM system. At the 7.5 to 20 dB region, it achieves better bit error rate performance than OFDM systems, and the bit error rate is reduced by approximately 53% compared to OFDM when the SNR value is 20, which is very useful in shallow water UWA channels with multipath extension and severe time-varying characteristics.<\/jats:p>","DOI":"10.3390\/s24092846","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T04:01:52Z","timestamp":1714449712000},"page":"2846","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Image Super Resolution-Based Channel Estimation for Orthogonal Chirp Division Multiplexing on Shallow Water Underwater Acoustic Communications"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0913-1427","authenticated-orcid":false,"given":"Haoyang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Ocean Technology Sciences, Qilu University of Technology (Shandong Academy of Science), Qingdao 266100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chuanlin","family":"He","sequence":"additional","affiliation":[{"name":"School of Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanting","family":"Yu","sequence":"additional","affiliation":[{"name":"Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Science), Qingdao 266100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiqi","family":"Bai","sequence":"additional","affiliation":[{"name":"Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Science), Qingdao 266100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yufei","family":"Han","sequence":"additional","affiliation":[{"name":"Tangshan Institute of Southwest Jiaotong University, Southwest Jiaotong University, Tangshan 063000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/MCOM.2009.4752682","article-title":"Underwater acoustic communication channels: Propagation models and statistical characterization","volume":"47","author":"Stojanovic","year":"2009","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"19099","DOI":"10.1109\/ACCESS.2018.2818110","article-title":"Low probability of detection for underwater acoustic communication: A review","volume":"6","author":"Diamant","year":"2018","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1145\/1347364.1347370","article-title":"Acoustic propagation considerations for underwater acoustic communications network development","volume":"11","author":"Preisig","year":"2007","journal-title":"ACM SIGMOBILE Mobile Comput. Commun. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jiang, R., Cao, S., Xue, C., and Tang, L. (2017, January 22\u201325). Modeling and analyzing of underwater acoustic channels with curvilinear boundaries in shallow ocean. Proceedings of the IEEE International Conference Signal Processing, Communications and Computing (ICSPCC), Xiamen, China.","DOI":"10.1109\/ICSPCC.2017.8242476"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gopi, E.S. (2021). Machine Learning, Deep Learning and Computational Intelligence for Wireless Communication, Springer. Lecture Notes in Electrical Engineering.","DOI":"10.1007\/978-981-16-0289-4"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108299","DOI":"10.1016\/j.sigpro.2021.108299","article-title":"Time-varying carrier frequency offset estimation in OFDM underwater acoustic communication","volume":"190","author":"Avrashi","year":"2022","journal-title":"Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/TTHZ.2011.2159556","article-title":"THz imaging radar for standoff personnel screening","volume":"1","author":"Cooper","year":"2011","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_8","unstructured":"Ouyang, X., Antony, C., Gunning, F., Zhang, H., and Guan, Y.L. (2015). Discrete Fresnel transform and its circular convolution. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1109\/LSP.2017.2737596","article-title":"Chirp spread spectrum toward the Nyquist signaling rate\u2014Orthogonality condition and applications","volume":"24","author":"Ouyang","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3946","DOI":"10.1109\/TCOMM.2016.2594792","article-title":"Orthogonal chirp division multiplexing","volume":"64","author":"Ouyang","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_11","first-page":"3897","article-title":"Machine Learning and Deep Learning: A Review of Methods and Applications","volume":"10","author":"Sharifani","year":"2023","journal-title":"World Inf. Technol. Eng. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3027","DOI":"10.1109\/TVT.2019.2893928","article-title":"Deep-learning-based millimeter-wave massive MIMO for hybrid precoding","volume":"68","author":"Huang","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1109\/MWC.2019.1900027","article-title":"Deep learning for physical layer 5G wireless techniques: Opportunities, challenges and solutions","volume":"27","author":"Huang","year":"2020","journal-title":"IEEE Wirel. Commun."},{"key":"ref_14","first-page":"132","article-title":"Deep learning based communication over the air","volume":"12","author":"Cammerer","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1109\/TCCN.2017.2758370","article-title":"An introduction to deep learning for the physical layer","volume":"3","author":"Hoydis","year":"2017","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1109\/MWC.2019.1800601","article-title":"Deep learning in physical layer communications","volume":"26","author":"Qin","year":"2019","journal-title":"IEEE Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/LWC.2017.2757490","article-title":"Power of deep learning for channel estimation and signal detection in OFDM systems","volume":"7","author":"Ye","year":"2018","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.apacoust.2019.04.023","article-title":"Deep learning based underwater acoustic OFDM communications","volume":"154","author":"Zhang","year":"2019","journal-title":"Appl. Acoust."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1109\/LWC.2018.2832128","article-title":"Deep learning-based channel estimation for beamspace mmWave massive MIMO systems","volume":"7","author":"He","year":"2018","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1109\/LCOMM.2019.2898944","article-title":"Deep learning-based channel estimation","volume":"23","author":"Soltani","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1109\/LWC.2019.2962796","article-title":"Deep residual learning meets OFDM channel estimation","volume":"9","author":"Li","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_22","first-page":"516","article-title":"Low Complexity Equalization for OCDM Systems in Dual-Select Channels","volume":"45","author":"Ning","year":"2023","journal-title":"J. Electron. Inf. Technol."},{"key":"ref_23","unstructured":"Socheleau, F.X., Pottier, A., and Laot, C. (2016, November 28). Watermark: BCH1 Dataset Description. Available online: https:\/\/hal.science\/hal-01404491\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/9\/2846\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:36:27Z","timestamp":1760106987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/9\/2846"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,29]]},"references-count":23,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["s24092846"],"URL":"https:\/\/doi.org\/10.3390\/s24092846","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,29]]}}}