{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:48:48Z","timestamp":1780512528943,"version":"3.54.1"},"reference-count":22,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T00:00:00Z","timestamp":1687564800000},"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":["52071164"],"award-info":[{"award-number":["52071164"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["KYCX23_3879"],"award-info":[{"award-number":["KYCX23_3879"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["52071164"],"award-info":[{"award-number":["52071164"]}]},{"name":"Postgraduate Research and Practice Innovation Program of Jiangsu Province","award":["KYCX23_3879"],"award-info":[{"award-number":["KYCX23_3879"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The orthogonal time frequency space (OTFS) modulation technique can provide reliable communication in time-varying channels. Due to the dispersive characteristics of underwater acoustic channels, this paper proposes an OTFS-IM underwater acoustic communication system based on Hamming distance optimization to reduce the impact of dispersion in underwater acoustic communication. Firstly, the OTFS-IM underwater acoustic communication system is introduced, which introduces index modulation into the Delay\u2013Doppler (DD) domain to make the OTFS system have stronger anti-Delay\u2013Doppler capability. In contrast, since there is index sequence redundancy in a specific index combination, a Hamming distance optimization model is used to eliminate the redundant combination in the specific index combination sequence and further improve the bit error rate performance of the system. In addition, the Hamming distance optimized OTFS-IM underwater acoustic communication system is verified by simulation analysis. The results show that the proposed Hamming distance optimized OTFS-IM can achieve more reliable bit error rate performance.<\/jats:p>","DOI":"10.3390\/e25070972","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T05:39:13Z","timestamp":1687757953000},"page":"972","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Hamming Distance Optimized Underwater Acoustic OTFS-IM Systems"],"prefix":"10.3390","volume":"25","author":[{"given":"Xiaopeng","family":"Guo","sequence":"first","affiliation":[{"name":"Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9249-3049","authenticated-orcid":false,"given":"Biao","family":"Wang","sequence":"additional","affiliation":[{"name":"Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2720-5199","authenticated-orcid":false,"given":"Yunan","family":"Zhu","sequence":"additional","affiliation":[{"name":"Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zide","family":"Fang","sequence":"additional","affiliation":[{"name":"Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaoyue","family":"Han","sequence":"additional","affiliation":[{"name":"Ocean College, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,24]]},"reference":[{"key":"ref_1","first-page":"685","article-title":"Spatial diversity and combination technology using amplitude and phase weighting method for phase-coherent underwater acoustic communications","volume":"42","author":"Li","year":"2018","journal-title":"Chin. J. Acoust."},{"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","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_4","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_5","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1109\/JOE.2013.2291139","article-title":"Filterbank multicarrier communications for underwater acoustic channels","volume":"40","author":"Amini","year":"2015","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_6","first-page":"38","article-title":"Method of time reversal filter bank multicarrier underwater acoustic communication","volume":"45","author":"Fang","year":"2020","journal-title":"Acta Acust."},{"key":"ref_7","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 IEEE Wireless Communications & Networking Conference, San Francisco, CA, USA.","DOI":"10.1109\/WCNC.2017.7925924"},{"key":"ref_8","first-page":"3145","article-title":"Channel estimation and equalization for orthogonal time frequency space modulation","volume":"17","author":"Mishra","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6033","DOI":"10.1109\/TWC.2021.3071493","article-title":"Performance Analysis of Coded OTFS Systems over High-Mobility Channels","volume":"20","author":"Li","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1109\/MWC.001.2000408","article-title":"Orthogonal Time-Frequency Space Modulation: A Promising Next-Generation Waveform","volume":"28","author":"Wei","year":"2021","journal-title":"IEEE Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hadani, R., Rakib, S., Molisch, A.F., Ibars, C., Monk, A., Tsatsanis, M., Delfeld, J., Goldsmith, A., and Calderbank, R. (2017, January 4\u20139). Orthogonal Time FrequencySpace (OTFS) modulation for millimeter-wave communications systems. Proceedings of the 2017 IEEE MTT-S International Microwave Symposium (IMS), Honololu, HI, USA.","DOI":"10.1109\/MWSYM.2017.8058662"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Feng, X., Esmaiel, H., Wang, J., Qi, J., Zhou, M., Qasem, Z.A., Sun, H., and Gu, Y. (2020, January 6\u20139). Underwater Acoustic Communications Based on OTFS. Proceedings of the 2020 15th IEEE International Conference on Signal Processing (ICSP), Beijing, China.","DOI":"10.1109\/ICSP48669.2020.9320923"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1049\/iet-com.2019.0376","article-title":"Performance of OFDM-based massive MIMO OTFS systems for underwater acoustic communication","volume":"14","author":"Bocus","year":"2020","journal-title":"IET Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1051\/jnwpu\/20213950954","article-title":"A low-complexity orthogonal time frequency space modulation method for underwater acoustic communication","volume":"39","author":"Zhang","year":"2021","journal-title":"J. Northwest. Polytech. Univ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"108386","DOI":"10.1016\/j.apacoust.2021.108386","article-title":"OTFS underwater acoustic communications based on passive time reversal","volume":"185","author":"Jing","year":"2022","journal-title":"Appl. Acoust."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hang, S., and Li, W. (2022, January 17\u201320). OTFS for Underwater Acoustic Communications: Practical System Design and Channel Estimation. Proceedings of the OCEANS 2022, Hampton Roads, VA, USA.","DOI":"10.1109\/OCEANS47191.2022.9977069"},{"key":"ref_17","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":"Poor","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Liang, Y., Li, L., Fan, P., and Guan, Y. (2020, January 25\u201328). Doppler Resilient Orthogonal Time-Frequency Space (OTFS) Systems Based on Index Modulation. Proceedings of the 2020 IEEE 91st Vehicular Technology Conference (VTC2020-Spring), Antwerp, Belgium.","DOI":"10.1109\/VTC2020-Spring48590.2020.9129380"},{"key":"ref_19","first-page":"1984","article-title":"Index Detection for Underwater Acoustic FBMC-IM System Based on Deep Bidirectional Long Short-Term Memory Network","volume":"44","author":"Zhu","year":"2022","journal-title":"Dianzi Yu Xinxi Xuebao\/J. Electron. Inf. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, J., Cui, Y., Liu, L., Ma, S., and Pan, G. (2017, January 22\u201325). Frequency offset estimation for index modulation-based cognitive underwater acoustic communications. Proceedings of the 2017 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xiamen, China.","DOI":"10.1109\/ICSPCC.2017.8242614"},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1109\/JOE.2013.2278787","article-title":"Statistical characterization and computationally efficient modeling of a class of underwater acoustic communication channels","volume":"38","author":"Qarabaqi","year":"2013","journal-title":"IEEE J. Ocean. 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