{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:43:19Z","timestamp":1760150599691,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,17]],"date-time":"2023-12-17T00:00:00Z","timestamp":1702771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications","award":["NY223137","61772287","62271426","GDNRC[2023]24"],"award-info":[{"award-number":["NY223137","61772287","62271426","GDNRC[2023]24"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NY223137","61772287","62271426","GDNRC[2023]24"],"award-info":[{"award-number":["NY223137","61772287","62271426","GDNRC[2023]24"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Program of Marine Economy Development Special Foundation of Department of Natural Resources of Guangdong Province","award":["NY223137","61772287","62271426","GDNRC[2023]24"],"award-info":[{"award-number":["NY223137","61772287","62271426","GDNRC[2023]24"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Orthogonal frequency division multiplexing with index modulation (OFDM-IM) has great potential for the implementation of high spectral-efficiency underwater acoustic (UWA) communications. However, general receivers consisting of the optimal maximum likelihood detection suffer from high computational load, which prohibits real-time data transmissions in underwater scenarios. In this paper, we propose a detection based on a vector approximate message passing (VAMP) algorithm for UWA OFDM-IM communications. Firstly, a VAMP framework with a non-loopy factor graph for index detection is formulated. Secondly, by utilizing the sparsity inherently existing in OFDM-IM symbols, a novel shrinkage function is derived based on the minimum mean square error criterion, which guarantees better posterior estimation. To reduce the errors from estimated non-existing indices, one trick is utilized to search the elements from the look-up table with the minimal Euclidean distance for the replacement of erroneously estimated indices. Experiments verify the advantages of the proposed detector in terms of low complexity, robustness and effectiveness compared with the state-of-art benchmarks.<\/jats:p>","DOI":"10.3390\/e25121667","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T03:59:24Z","timestamp":1702871964000},"page":"1667","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Vector Approximate Message Passing Based OFDM-IM Detection for Underwater Acoustic Communications"],"prefix":"10.3390","volume":"25","author":[{"given":"Xiao","family":"Feng","sequence":"first","affiliation":[{"name":"School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Key Laboratory of Southeast Coast Marine Information Intelligent Perception and Application, Ministry of Natural Resources, Zhangzhou 363099, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Key Laboratory of Southeast Coast Marine Information Intelligent Perception and Application, Ministry of Natural Resources, Zhangzhou 363099, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2799-8491","authenticated-orcid":false,"given":"Mingzhang","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Southeast Coast Marine Information Intelligent Perception and Application, Ministry of Natural Resources, Zhangzhou 363099, China"},{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8249-1197","authenticated-orcid":false,"given":"Haixin","family":"Sun","sequence":"additional","affiliation":[{"name":"Key Laboratory of Southeast Coast Marine Information Intelligent Perception and Application, Ministry of Natural Resources, Zhangzhou 363099, China"},{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeyad A. H.","family":"Qasem","sequence":"additional","affiliation":[{"name":"School of Electronic and Computer Engineering, Peking University, Shenzhen 518005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,17]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1109\/LCOMM.2015.2474863","article-title":"Low-complexity ML detector and performance analysis for OFDM with in-phase\/quadrature index modulation","volume":"19","author":"Zheng","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1109\/LCOMM.2015.2514278","article-title":"Low complexity OFDM-IM detector by encoding all possible subcarrier activation patterns","volume":"20","author":"Siddiq","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_4","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":"2022","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"16806","DOI":"10.1109\/ACCESS.2018.2814214","article-title":"A semidefinite relaxation approach to OFDM-IM detection in rapidly time-varying channels","volume":"6","author":"Zheng","year":"2018","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7859","DOI":"10.1109\/ACCESS.2016.2615266","article-title":"Compressed sensing improves the performance of subcarrier index-modulation-assisted OFDM","volume":"4","author":"Zhang","year":"2016","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9607","DOI":"10.1109\/TVT.2021.3101894","article-title":"Approximate message passing algorithms for low complexity OFDM-IM detection","volume":"70","author":"Sui","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"133410","DOI":"10.1109\/ACCESS.2019.2941233","article-title":"Approximate message passing-aided iterative channel estimation and data detection of OFDM-IM in doubly selective channels","volume":"7","author":"Wei","year":"2019","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"18914","DOI":"10.1073\/pnas.0909892106","article-title":"Message-passing algorithms for compressed sensing","volume":"106","author":"Donoho","year":"2009","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2156","DOI":"10.1109\/TWC.2014.2382098","article-title":"Multiuser detection in massive spatial modulation MIMO with low-resolution ADCs","volume":"14","author":"Wang","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2906","DOI":"10.1109\/TCOMM.2020.2973080","article-title":"Factor graph based message passing algorithms for joint phase-noise estimation and decoding in OFDM-IM","volume":"68","author":"Shi","year":"2020","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","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_13","doi-asserted-by":"crossref","first-page":"46975","DOI":"10.1109\/ACCESS.2021.3067878","article-title":"Fully Quadrature Subcarrier-Index Shift Keying for Efficient Underwater Acoustic Communications","volume":"9","author":"Hussein","year":"2021","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Guo, X., Wang, B., Zhu, Y., Fang, Z., and Han, Z. (2023). Hamming Distance Optimized Underwater Acoustic OTFS-IM Systems. Entropy, 25.","DOI":"10.3390\/e25070972"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6664","DOI":"10.1109\/TIT.2019.2916359","article-title":"Vector approximate message passing","volume":"65","author":"Rangan","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1109\/TVT.2021.3130061","article-title":"Message passing-based impulsive noise mitigation and channel estimation for underwater acoustic OFDM communications","volume":"71","author":"Feng","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","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":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2908","DOI":"10.1109\/LCOMM.2021.3093672","article-title":"Double Interpolation-Based Linear Fitting for OMP Channel Estimation in OFDM Systems","volume":"25","author":"Qiao","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_20","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 Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1667\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:40:22Z","timestamp":1760132422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1667"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,17]]},"references-count":20,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["e25121667"],"URL":"https:\/\/doi.org\/10.3390\/e25121667","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,12,17]]}}}