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In this scheme, the blind equalization is adopted and no training sequence is required. The adaptive modulation is implemented based on the SMSE of blind equalization. The channel state information doesn\u2019t need to be assumed to know. To better realize the adjustment of modulation mode, the polynomial fitting is used to revise the estimated SNR based on the SMSE. In addition, we also adopted the adjustable tap-length blind equalization detector to obtain the SMSE, which can adaptively adjust the tap-length according to the specific underwater channel profile, and thus achieve better SMSE performance. Simulation results validate the feasibility of the proposed approaches. Simulation results also show the advantages of the proposed scheme against existing counterparts.<\/jats:p>","DOI":"10.1186\/s13638-021-01956-w","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T10:03:18Z","timestamp":1617184998000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Adaptive modulation based on steady-state mean square error for underwater acoustic communication"],"prefix":"10.1186","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9556-1895","authenticated-orcid":false,"given":"Zhiyong","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhoumei","family":"Tan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fan","family":"Bai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"1956_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2010\/590458","volume":"2010","author":"CP Shah","year":"2010","unstructured":"C.P. 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