{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T12:07:27Z","timestamp":1780488447294,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T00:00:00Z","timestamp":1626566400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571334"],"award-info":[{"award-number":["61571334"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Orthogonal frequency division multiplexing (OFDM) has been widely adopted in underwater acoustic (UWA) communication due to its good anti-multipath performance and high spectral efficiency. For UWA-OFDM systems, channel state information (CSI) is essential for channel equalization and adaptive transmission, which can significantly affect the reliability and throughput. However, the time-varying UWA channel is difficult to estimate because of excessive delay spread and complex noise distribution. To this end, a novel Bayesian learning-based channel estimation architecture is proposed for UWA-OFDM systems. A clustered-sparse channel distribution model and a noise-resistant channel measurement model are constructed, and the model hyperparameters are iteratively optimized to obtain accurate Bayesian channel estimation. Accordingly, to obtain the clustered-sparse distribution, a partition-based clustered-sparse Bayesian learning (PB-CSBL) algorithm was designed. In order to lessen the effect of strong colored noise, a noise-corrected clustered-sparse channel estimation (NC-CSCE) algorithm was proposed to improve the estimation accuracy. Numerical simulations and lake trials are conducted to verify the effectiveness of the algorithms. Results show that the proposed algorithms achieve higher channel estimation accuracy and lower bit error rate (BER).<\/jats:p>","DOI":"10.3390\/s21144889","type":"journal-article","created":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T21:18:52Z","timestamp":1626643132000},"page":"4889","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Bayesian Learning-Based Clustered-Sparse Channel Estimation for Time-Varying Underwater Acoustic OFDM Communication"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2202-4092","authenticated-orcid":false,"given":"Shuaijun","family":"Wang","sequence":"first","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4101-3938","authenticated-orcid":false,"given":"Mingliu","family":"Liu","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8188-9379","authenticated-orcid":false,"given":"Deshi","family":"Li","sequence":"additional","affiliation":[{"name":"Electronic Information School, Wuhan University, Wuhan 430072, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, 129 Luoyu Road, Wuhan 430072, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"795","DOI":"10.3390\/s140100795","article-title":"Underwater Acoustic Wireless Sensor Networks: Advances and Future Trends in Physical, MAC and Routing Layers","volume":"14","author":"Climent","year":"2014","journal-title":"Sensors"},{"key":"ref_2","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_3","unstructured":"Coatelan, S., and Glavieux, A. (1994, January 13\u201316). Design and test of a multicarrier transmission system on the shallow water acoustic channel. Proceedings of the OCEANS\u201994, Brest, France."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhou, S., and Wang, Z. (2014). OFDM for Underwater Acoustic Communications, Wiley Publishing. [1st ed.].","DOI":"10.1002\/9781118693865"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/MCOM.2016.7470947","article-title":"Index modulated OFDM for underwater acoustic communications","volume":"54","author":"Wen","year":"2016","journal-title":"IEEE Commun. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5536","DOI":"10.1109\/TSP.2013.2279771","article-title":"Orthogonal Frequency Division Multiplexing With Index Modulation","volume":"61","author":"Basar","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1109\/JOE.2014.2323365","article-title":"Adaptive Modulation and Coding for Underwater Acoustic OFDM","volume":"40","author":"Wan","year":"2015","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Huang, Y., Wan, L., Zhou, H., Zhou, S., Shen, X., and Wang, H. (2014, January 14\u201319). Adaptive OFDMA for downlink underwater acoustic communications. Proceedings of the 2014 Oceans-St. John\u2019s, St. John\u2019s, NL, Canada.","DOI":"10.1109\/OCEANS.2014.7003120"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1109\/48.895356","article-title":"Signal variability in shallow-water sound channels","volume":"25","author":"Badiey","year":"2000","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1121\/1.1771591","article-title":"Surface wave focusing and acoustic communications in the surf zone","volume":"116","author":"Preisig","year":"2004","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1121\/1.2828055","article-title":"Impact of ocean variability on coherent underwater acoustic communications during the Kauai experiment (KauaiEx)","volume":"123","author":"Song","year":"2008","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2359","DOI":"10.1121\/1.3212925","article-title":"Effect of reflected and refracted signals on coherent underwater acoustic communication: Results from the Kauai experiment (KauaiEx 2003)","volume":"126","author":"Rouseff","year":"2009","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1109\/JOE.2010.2060530","article-title":"Passive Time Reversal Acoustic Communications Through Shallow-Water Internal Waves","volume":"35","author":"Song","year":"2010","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3079","DOI":"10.1109\/TSP.2012.2189769","article-title":"Clustered Adaptation for Estimation of Time-Varying Underwater Acoustic Channels","volume":"60","author":"Wang","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107668","DOI":"10.1016\/j.sigpro.2020.107668","article-title":"Channel prediction based temporal multiple sparse bayesian learning for channel estimation in fast time-varying underwater acoustic OFDM communications","volume":"175","author":"Qiao","year":"2020","journal-title":"Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, S., Li, D., Liu, M., Huang, W., Chen, H., and Cen, Y. (2020, January 21\u201323). Clustered-Sparse Bayesian Learning for Channel Estimation in Underwater Acoustic OFDM Systems. Proceedings of the 2020 International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP49889.2020.9299826"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Enguix, I.F., Egea, M.S., Gonz\u00e1lez, A.G., and Arenas, D. (2018). Acoustic Characterization of Impulsive Underwater Noise Present in Port Facilities: Practical Case in the Port of Cartagena. Proceedings, 4.","DOI":"10.3390\/ecsa-5-05755"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/JOE.2007.906409","article-title":"Estimation of Rapidly Time-Varying Sparse Channels","volume":"32","author":"Li","year":"2007","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Stojanovic, M. (April, January 31). OFDM for underwater acoustic communications: Adaptive synchronization and sparse channel estimation. Proceedings of the 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, USA.","DOI":"10.1109\/ICASSP.2008.4518853"},{"key":"ref_20","unstructured":"Geng, X., and Zielinski, A. (1995, January 9\u201312). An eigenpath underwater acoustic communication channel model. Proceedings of the \u2018Challenges of Our Changing Global Environment\u2019, OCEANS \u201995 MTS\/IEEE, San Diego, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yang, T.C. (2011, January 6\u20139). Characteristics of underwater acoustic communication channels in shallow water. Proceedings of the OCEANS 2011 IEEE\u2013Spain, Santander, Spain.","DOI":"10.1109\/Oceans-Spain.2011.6003411"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4875","DOI":"10.1109\/ACCESS.2018.2793851","article-title":"A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications","volume":"6","author":"Rani","year":"2018","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7229","DOI":"10.1016\/j.jfranklin.2020.04.002","article-title":"Channel estimation strategies for underwater acoustic (UWA) communication: An overview","volume":"357","author":"Khan","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1080\/02564602.2016.1211966","article-title":"A Review on Sparse Channel Estimation in OFDM System Using Compressed Sensing","volume":"34","author":"Uwaechia","year":"2017","journal-title":"IETE Tech. Rev."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1109\/TSP.2009.2038424","article-title":"Sparse Channel Estimation for Multicarrier Underwater Acoustic Communication: From Subspace Methods to Compressed Sensing","volume":"58","author":"Berger","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.acha.2008.07.002","article-title":"CoSaMP Iterative signal recovery from incomplete and inaccurate samples","volume":"26","author":"Needell","year":"2009","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.apacoust.2016.10.021","article-title":"Distributed compressed sensing estimation of underwater acoustic OFDM channel","volume":"117","author":"Zhou","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1540011","DOI":"10.1142\/S0218396X15400111","article-title":"OFDM Demodulation Using Virtual Time Reversal Processing in Underwater Acoustic Communications","volume":"23","author":"Yin","year":"2015","journal-title":"J. Comput. Acoust."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1109\/TSP.2004.831016","article-title":"Sparse Bayesian learning for basis selection","volume":"52","author":"Wipf","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Prasad, R., and Murthy, C.R. (2010, January 6\u201310). Bayesian Learning for Joint Sparse OFDM Channel Estimation and Data Detection. Proceedings of the Global Telecommunications Conference (GLOBECOM 2010), Miami, FL, USA.","DOI":"10.1109\/GLOCOM.2010.5683775"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Prasad, R., Murthy, C.R., and Rao, B.D. (2014). Joint Approximately Sparse Channel Estimation and Data Detection in OFDM Systems Using Sparse Bayesian Learning, IEEE Press.","DOI":"10.1109\/NCC.2014.6811323"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Qiao, G., Song, Q., Ma, L., Liu, S., Sun, Z., and Gan, S. (2018). Sparse Bayesian Learning For Channel Estimation In Time-varying Underwater Acoustic OFDM Communication. IEEE Access, 56675\u201356684.","DOI":"10.1109\/ACCESS.2018.2873406"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1109\/JPROC.2010.2042415","article-title":"Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels","volume":"98","author":"Bajwa","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5033","DOI":"10.1109\/TII.2019.2895469","article-title":"Accelerated Structure-Aware Sparse Bayesian Learning for Three-Dimensional Electrical Impedance Tomography","volume":"15","author":"Liu","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_35","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_36","doi-asserted-by":"crossref","first-page":"23579","DOI":"10.1109\/ACCESS.2019.2899990","article-title":"Deep Neural Networks for Channel Estimation in Underwater Acoustic OFDM Systems","volume":"7","author":"Jiang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_37","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_38","doi-asserted-by":"crossref","unstructured":"Stojanovic, M. (2006, January 18\u201321). Low Complexity OFDM Detector for Underwater Acoustic Channels. Proceedings of the OCEANS 2006, Boston, MA, USA.","DOI":"10.1109\/OCEANS.2006.307057"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1109\/JOE.2008.920471","article-title":"Multicarrier Communication Over Underwater Acoustic Channels With Nonuniform Doppler Shifts","volume":"33","author":"Li","year":"2008","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_40","unstructured":"Kim, B.-C., and Lu, I.T. (2000, January 11\u201314). Parameter study of OFDM underwater communications system. Proceedings of the OCEANS 2000 MTS\/IEEE Conference and Exhibition, (Cat. No.00CH37158), Providence, RI, USA."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1109\/JSTSP.2011.2159773","article-title":"Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning","volume":"5","author":"Zhang","year":"2011","journal-title":"IEEE J. Sel. Top. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4889\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:31:26Z","timestamp":1760164286000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4889"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,18]]},"references-count":41,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21144889"],"URL":"https:\/\/doi.org\/10.3390\/s21144889","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,18]]}}}