{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T13:59:56Z","timestamp":1780927196846,"version":"3.54.1"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"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":["52171339"],"award-info":[{"award-number":["52171339"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Automatic modulation classification (AMC) is an important method for monitoring and identifying any underwater communication interference. Since the underwater acoustic communication scenario is full of multi-path fading and ocean ambient noise (OAN), coupled with the application of modern communication technology, which is usually susceptible to environmental influences, automatic modulation classification (AMC) becomes particularly difficult when it comes to an underwater scenario. Motivated by the deep complex networks (DCN), which have an innate ability to process complex data, we explore DCN for AMC of underwater acoustic communication signals. To integrate the signal processing method with deep learning and overcome the influences of underwater acoustic channels, we propose two complex physical signal processing layers based on DCN. The proposed layers include a deep complex matched filter (DCMF) and deep complex channel equalizer (DCCE), which are designed to remove noise and reduce the influence of multi-path fading for the received signals, respectively. Hierarchical DCN is constructed using the proposed method to achieve better performance of AMC. The influence of the real-world underwater acoustic communication scenario is taken into account; two underwater acoustic multi-path fading channels are conducted using the real-world ocean observation dataset, white Gaussian noise, and real-world OAN are used as the additive noise, respectively. Contrastive experiments show that the AMC based on DCN can achieve better performance than the traditional deep neural network based on real value (the average accuracy of the DCN is 5.3% higher than real-valued DNN). The proposed method based on DCN can effectively reduce the influence of underwater acoustic channels and improve the AMC performance in different underwater acoustic channels. The performance of the proposed method was verified on the real-world dataset. In the underwater acoustic channels, the proposed method outperforms a series of advanced AMC method.<\/jats:p>","DOI":"10.3390\/e25020318","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T02:33:27Z","timestamp":1675996407000},"page":"318","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Automatic Modulation Classification for Underwater Acoustic Communication Signals Based on Deep Complex Networks"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0082-2648","authenticated-orcid":false,"given":"Xiaohui","family":"Yao","sequence":"first","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7611-4192","authenticated-orcid":false,"given":"Honghui","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4242-7427","authenticated-orcid":false,"given":"Meiping","family":"Sheng","sequence":"additional","affiliation":[{"name":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi\u2019an 710060, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yao, X., Yang, H., and Li, Y. 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