{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T17:31:01Z","timestamp":1767720661952,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,6,10]],"date-time":"2020-06-10T00:00:00Z","timestamp":1591747200000},"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":["61771417, 51734009, 51804304, 61902404, 61901475"],"award-info":[{"award-number":["61771417, 51734009, 51804304, 61902404, 61901475"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Research &amp; Development Project for Science and Technology of Xuzhou, China","award":["KC18105, KC18068"],"award-info":[{"award-number":["KC18105, KC18068"]}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2018YFC0808301"],"award-info":[{"award-number":["2018YFC0808301"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20180640"],"award-info":[{"award-number":["BK20180640"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Program for \u201cIndustrial IoT and Emergency Collaboration \u201d Innovative Research Team in CUMT","award":["2020ZY002"],"award-info":[{"award-number":["2020ZY002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In traditional underwater wireless sensor networks (UWSNs), it is difficult to establish reliable communication links as the acoustic wave experiences severe multipath effect, channel fading, and ambient noise. Recently, with the assistance of magnetic induction (MI) technique, cooperative multi-input-multi-output (MIMO) is utilized in UWSNs to enable the reliable long range underwater communication. Compared with the acoustic-based UWSNs, the UWSNs adopting MI-assisted acoustic cooperative MIMO are referred to as heterogeneous UWSNs, which are able to significantly improve the effective cover space and network throughput. Due to the complex channel characteristics and the heterogeneous architecture, the connectivity of underwater MI-assisted acoustic cooperative MIMO networks is much more complicated than that of acoustic-based UWSNs. In this paper, a mathematical model is proposed to analyze the connectivity of the networks, which considers the effects of channel characteristics, system parameters, and synchronization errors. The lower and upper bounds of the connectivity probability are also derived, which provide guidelines for the design and deployment of underwater MI-assisted acoustic cooperative MIMO networks. Monte Carlo simulations were performed, and the results validate the accuracy of the proposed model.<\/jats:p>","DOI":"10.3390\/s20113317","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T05:56:27Z","timestamp":1592200587000},"page":"3317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Connectivity on Underwater MI-Assisted Acoustic Cooperative MIMO Networks"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4345-4104","authenticated-orcid":false,"given":"Qingyan","family":"Ren","sequence":"first","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221000, China"}]},{"given":"Yanjing","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221000, China"},{"name":"Xuzhou Engineering Research Center of Intelligent Industry Safety and Emergency Collaboration, Xuzhou 221000, China"},{"name":"School of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"given":"Yu","family":"Huo","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221000, China"}]},{"given":"Liang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221000, China"}]},{"given":"Song","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221000, China"},{"name":"Xuzhou Engineering Research Center of Intelligent Industry Safety and Emergency Collaboration, Xuzhou 221000, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,10]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Underwater Sensor Network Applications: A Comprehensive Survey","volume":"2015","author":"Felemban","year":"2015","journal-title":"Int. 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