{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T16:51:14Z","timestamp":1785430274098,"version":"3.56.0"},"reference-count":24,"publisher":"Optica Publishing Group","issue":"19","license":[{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"<jats:p>Fiber-optic\n\t\t\t\t\tcommunication is an emerging technology that enables high-capacity\n\t\t\t\t\tdata transmission using light waves. However, the inherent\n\t\t\t\t\tnonlinearity of the optical fiber limits the attainable capacity. As a\n\t\t\t\t\tresult, nonlinearity compensation has become a significant focus in\n\t\t\t\t\toptical fiber communication, for which nonlinear frequency-division\n\t\t\t\t\tmultiplexing (NFDM) is an effective solution. The signals generated in\n\t\t\t\t\tan NFDM system are fundamentally optical soliton signals and hence\n\t\t\t\t\tundergo the effect of multi-soliton periodicity. But this results in a\n\t\t\t\t\thigher signal peak-to-average ratio (PAPR) at the receiver front end\n\t\t\t\t\tof NFDM systems, negatively impacting system performance. This paper\n\t\t\t\t\tproposes a phase pre-equalization using optimal phase factors to\n\t\t\t\t\treduce the high PAPR at the receiver. This technique jointly optimizes\n\t\t\t\t\tthe transmitter and receiver, thereby reducing the large PAPR margin.\n\t\t\t\t\tPre-equalization also results in better error performance. Analysis\n\t\t\t\t\tshows that using this technique, the NFDM system is less sensitive to\n\t\t\t\t\tperturbation. A maximum data rate of 24\u00a0Gbps is obtained for\n\t\t\t\t\t1000\u00a0km with a 2-eigenvalue, pre-equalized unilateral spiral\n\t\t\t\t\t8-quadrature amplitude modulation (QAM) NFDM system model, and\n\t\t\t\t\t24.67\u00a0Gbps is obtained for 1000\u00a0km with a 2-eigenvalue,\n\t\t\t\t\tpre-equalized spiral 16-QAM NFDM system model. The maximum\n\t\t\t\t\ttransmission distance extends to 2150\u00a0km for a data rate of\n\t\t\t\t\t10\u00a0Gbps.<\/jats:p>","DOI":"10.1364\/ao.557744","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T12:00:11Z","timestamp":1749124811000},"page":"5444","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Phase optimization approach to control high peak-to-average power ratio in a second-order soliton-based NFDM system"],"prefix":"10.1364","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2075-9917","authenticated-orcid":true,"given":"S.","family":"Sreedevi Nair","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04yn30r61","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.","family":"Vijayakumar","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04yn30r61","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9997-5865","authenticated-orcid":true,"given":"R.","family":"Pradeep","sequence":"additional","affiliation":[{"name":"College of Engineering Trivandrum , APJ Abdul Kalam Technological University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2025,6,25]]},"reference":[{"key":"ao-64-19-5444-R1","doi-asserted-by":"publisher","first-page":"4312","DOI":"10.1109\/TIT.2014.2321143","volume":"60","author":"Yousefi","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ao-64-19-5444-R2","doi-asserted-by":"publisher","first-page":"4329","DOI":"10.1109\/TIT.2014.2321151","volume":"60","author":"Yousefi","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ao-64-19-5444-R3","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/3-540-46629-0_9","article-title":"Nonlinear fiber\n\t\t\t\t\toptics","volume-title":"Nonlinear Science at the Dawn of\n\t\t\t\t\tthe 21st Century","author":"Agrawal","year":"2000"},{"key":"ao-64-19-5444-R4","doi-asserted-by":"publisher","first-page":"4346","DOI":"10.1109\/TIT.2014.2321155","volume":"60","author":"Yousefi","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ao-64-19-5444-R5","first-page":"1","article-title":"Experimental demonstration of nonlinear frequency\n\t\t\t\t\tdivision multiplexed transmission","volume-title":"European Conference on Optical Communication (ECOC)","author":"Aref","year":"2015"},{"key":"ao-64-19-5444-R6","first-page":"1","article-title":"Transmission of waveforms\n\t\t\t\t\tdetermined by 7 eigenvalues with PSK-modulated spectral\n\t\t\t\t\tamplitudes","volume-title":"ECOC 2016; 42nd European\n\t\t\t\t\tConference on Optical Communication","author":"Buelow","year":"2016"},{"key":"ao-64-19-5444-R7","doi-asserted-by":"publisher","first-page":"20286","DOI":"10.1364\/OE.25.020286","volume":"25","author":"Gui","year":"2017","journal-title":"Opt.\n\t\t\t\t\tExpress"},{"key":"ao-64-19-5444-R8","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1109\/50.219570","volume":"11","author":"Hasegawa","year":"1993","journal-title":"J. Lightwave Technol."},{"key":"ao-64-19-5444-R9","first-page":"151","volume":"3","author":"Nair","year":"2014","journal-title":"Int. J.\n\t\t\t\t\tSci. Res."},{"key":"ao-64-19-5444-R10","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1038\/nphoton.2017.118","volume":"11","author":"Le","year":"2017","journal-title":"Nat. Photonics"},{"key":"ao-64-19-5444-R11","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1364\/OPTICA.4.000307","volume":"4","author":"Turitsyn","year":"2017","journal-title":"Optica"},{"key":"ao-64-19-5444-R12","doi-asserted-by":"publisher","first-page":"103473","DOI":"10.1016\/j.yofte.2023.103473","volume":"81","author":"Nair","year":"2023","journal-title":"Opt. Fiber\n\t\t\t\t\tTechnol."},{"key":"ao-64-19-5444-R13","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1016\/S0893-9659(03)00061-2","volume":"16","author":"Wright","year":"2003","journal-title":"Appl. Math.\n\t\t\t\t\tLett."},{"key":"ao-64-19-5444-R14","doi-asserted-by":"publisher","author":"Aref","year":"2016","DOI":"10.48550\/arXiv.1605.06328"},{"key":"ao-64-19-5444-R15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-46064-0","volume-title":"Optical Solitons in Fibers","author":"Hasegawa","year":"2003"},{"key":"ao-64-19-5444-R16","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1109\/JLT.2020.3033624","volume":"39","author":"Gaiarin","year":"2020","journal-title":"J. Lightwave Technol."},{"key":"ao-64-19-5444-R17","first-page":"1","article-title":"Nonlinearity mitigation in\n\t\t\t\t\tradio over fiber network using nonlinear fourier transform based\n\t\t\t\t\toptical fiber link","volume-title":"Second International\n\t\t\t\t\tConference on Next Generation Intelligent Systems (ICNGIS)","author":"Nair","year":"2022"},{"key":"ao-64-19-5444-R18","doi-asserted-by":"publisher","first-page":"2335","DOI":"10.1109\/JLT.2019.2904102","volume":"37","author":"Da Ros","year":"2019","journal-title":"J. Lightwave Technol."},{"key":"ao-64-19-5444-R19","volume-title":"Semiconductor Optical Amplifiers and\n\t\t\t\t\tmm-Wave Wireless Links for Converged Access Networks","author":"Koenig","year":"2014"},{"key":"ao-64-19-5444-R20","volume-title":"Wireless Terahertz Communications:\n\t\t\t\t\tOptoelectronic Devices and Signal Processing","author":"Harter","year":"2021"},{"key":"ao-64-19-5444-R21","volume-title":"An Experimental Approach to CDMA and\n\t\t\t\t\tInterference Mitigation: From System Architecture to Hardware Testing\n\t\t\t\t\tThrough VLSI Design","author":"Fanucci","year":"2004"},{"key":"ao-64-19-5444-R22","first-page":"1","article-title":"NFDMLab:\n\t\t\t\t\tsimulating nonlinear frequency division multiplexing in\n\t\t\t\t\tPython","volume-title":"Optical Fiber Communications\n\t\t\t\t\tConference and Exhibition (OFC)","author":"Brehler","year":"2019"},{"key":"ao-64-19-5444-R23","doi-asserted-by":"publisher","first-page":"5464","DOI":"10.1109\/JLT.2017.2775105","volume":"35","author":"Kamalian","year":"2017","journal-title":"J. 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Lightwave Technol."}],"container-title":["Applied Optics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=ao-64-19-5444&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T15:02:28Z","timestamp":1750863748000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=ao-64-19-5444"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,25]]},"references-count":24,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2025]]},"published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.1364\/ao.557744","relation":{},"ISSN":["1559-128X","2155-3165"],"issn-type":[{"value":"1559-128X","type":"print"},{"value":"2155-3165","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,25]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/AO.557744","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"4 February 2025","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"4 June 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"25 June 2025","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2025 Optica Publishing Group. All rights, including\n\t\t\t\t\tfor text and data mining (TDM), Artificial Intelligence (AI) training,\n\t\t\t\t\tand similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}