{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:33:31Z","timestamp":1781534011221,"version":"3.54.5"},"reference-count":33,"publisher":"Optica Publishing Group","issue":"4","license":[{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:00:00Z","timestamp":1773273600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"China Academy of Information and Communications Technology","award":["QN-2026-009"],"award-info":[{"award-number":["QN-2026-009"]}],"id":[{"id":"https:\/\/ror.org\/038dte259","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["J. Opt. Commun. Netw."],"published-print":{"date-parts":[[2026,4,1]]},"abstract":"<jats:p>Longitudinal power profile estimation (PPE) is an essential forward-sensing technique for optical network monitoring, enabling early detection of abnormal loss and supporting the reliable operation of coherent transmission systems. The conventional least-squares PPE (LS-PPE) method either relies on post-FEC reference symbols, which introduce considerable digital signal processing (DSP) overhead, or employs hard-decision (HD) symbols, which inevitably suffer from a systematic power offset that increases with the pre-FEC bit-error rate (BER). In this paper, we present a comprehensive study of a new, to our knowledge, LS-PPE framework that leverages the pilot symbols (PSs) and training sequence (TS) inherently defined in DSP super-frames. By selectively constructing perturbation matrices from known PS and TS positions while discarding error-prone HD data, the proposed scheme eliminates systematic offset without relying on post-FEC information. Extensive simulations with 130\u00a0GBaud signals across multiple modulation formats and transmission distances demonstrate the robustness of the proposed method under diverse system conditions. Experimental validation on an 80\u00a0GBaud dual-polarization 16QAM transmission over 250\u00a0km standard single-mode fiber confirms estimation accuracy comparable to post-FEC benchmarks and superior robustness over HD-based LS-PPE, highlighting the potential of the PS&amp;TS-based framework for practical deployment.<\/jats:p>","DOI":"10.1364\/jocn.584746","type":"journal-article","created":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T14:00:13Z","timestamp":1771336813000},"page":"B60","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Least-squares longitudinal power profile estimation based on pilot symbols and training sequences in DSP frames"],"prefix":"10.1364","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5819-5782","authenticated-orcid":true,"given":"Du","family":"Tang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/038dte259","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2365-3138","authenticated-orcid":true,"given":"Yingjie","family":"Jiang","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-1673-5564","authenticated-orcid":true,"given":"Hao","family":"Zhou","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7150-9146","authenticated-orcid":true,"given":"Fan","family":"Yang","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yutao","family":"Zhou","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3475-4109","authenticated-orcid":true,"given":"Baoxuan","family":"Quan","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaojun","family":"Qiao","sequence":"additional","affiliation":[{"name":"Beijing University of Posts and Telecommunications"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6978-717X","authenticated-orcid":true,"given":"Hengying","family":"Xu","sequence":"additional","affiliation":[{"name":"Liaocheng University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3790-2652","authenticated-orcid":true,"given":"Chenglin","family":"Bai","sequence":"additional","affiliation":[{"name":"Liaocheng University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junjie","family":"Xie","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/038dte259","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,3,12]]},"reference":[{"key":"jocn-18-4-B60-R1","doi-asserted-by":"publisher","first-page":"3058","DOI":"10.1109\/COMST.2024.3521498","type":"journal-article","volume":"27","author":"Wen","year":"2024","journal-title":"IEEE Commun. Surv. Tutorials"},{"key":"jocn-18-4-B60-R3","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1109\/MCOM.2023.10298069","type":"journal-article","volume":"61","author":"Liu","year":"2023","journal-title":"IEEE Commun. Mag."},{"key":"jocn-18-4-B60-R5","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1038\/s41377-022-01067-1","type":"journal-article","volume":"12","author":"He","year":"2023","journal-title":"Light Sci. Appl."},{"key":"jocn-18-4-B60-R6","doi-asserted-by":"publisher","first-page":"4233","DOI":"10.1109\/JLT.2024.3401419","type":"journal-article","volume":"42","author":"Wang","year":"2024","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R7","doi-asserted-by":"publisher","first-page":"041302","DOI":"10.1063\/1.5113955","type":"journal-article","volume":"6","author":"Lu","year":"2019","journal-title":"Appl. Phys. Rev."},{"key":"jocn-18-4-B60-R10","doi-asserted-by":"publisher","first-page":"1853","DOI":"10.1109\/JPROC.2022.3199742","type":"journal-article","volume":"110","author":"Ip","year":"2022","journal-title":"Proc. IEEE"},{"key":"jocn-18-4-B60-R11","doi-asserted-by":"publisher","first-page":"692","DOI":"10.1364\/JOCN.559810","type":"journal-article","volume":"17","author":"Yang","year":"2025","journal-title":"J. Opt. Commun. Netw."},{"key":"jocn-18-4-B60-R12","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1109\/LPT.2023.3307452","type":"journal-article","volume":"35","author":"Zuo","year":"2023","journal-title":"IEEE Photonics Technol. Lett."},{"key":"jocn-18-4-B60-R13","doi-asserted-by":"crossref","DOI":"10.1109\/ICOCN67308.2025.11145413","article-title":"Integrated vibration sensing in DSCM systems under ECLs based on ANN and digital twin","volume-title":"23rd International Conference on Optical Communications and Networks (ICOCN)","author":"Yang","year":"2025"},{"key":"jocn-18-4-B60-R14","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2024.W1B.3","type":"journal-article","article-title":"Recent advances in digital longitudinal monitoring of fiber-optic link","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Sasai","year":"2024"},{"key":"jocn-18-4-B60-R15","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2024.W4A.4","type":"journal-article","article-title":"Digital coherent receiver based optical performance monitoring technology and its application to photonics tomography","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Oda","year":"2024"},{"key":"jocn-18-4-B60-R16","doi-asserted-by":"publisher","first-page":"2726","DOI":"10.1109\/JLT.2020.2984270","type":"journal-article","volume":"38","author":"Tanimura","year":"2020","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R17","doi-asserted-by":"publisher","first-page":"E132","DOI":"10.1364\/JOCN.425494","type":"journal-article","volume":"13","author":"Tanimura","year":"2021","journal-title":"J. Opt. Commun. Netw."},{"key":"jocn-18-4-B60-R18","doi-asserted-by":"crossref","DOI":"10.23919\/OECC\/PSC53152.2022.9850175","type":"journal-article","article-title":"Proposal of linear least squares for fiber-nonlinearity-based longitudinal power monitoring in multi-span link","volume-title":"OptoElectronics and Communications Conference (OECC)","author":"Sasai","year":"2022"},{"key":"jocn-18-4-B60-R19","type":"journal-article","article-title":"Robust longitudinal power profile estimation in optical networks using MMSE with complex scaling factor","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Kim","year":"2023"},{"key":"jocn-18-4-B60-R20","type":"journal-article","article-title":"0.77-dB anomaly loss localization based on DSP-based fiber-longitudinal power estimation using linear least squares","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Sasai","year":"2023"},{"key":"jocn-18-4-B60-R21","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2020.Th1F.1","type":"journal-article","article-title":"Simultaneous detection of anomaly points and fiber types in multi-span transmission links only by receiver-side digital signal processing","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Sasai","year":"2020"},{"key":"jocn-18-4-B60-R22","doi-asserted-by":"publisher","first-page":"3395","DOI":"10.1109\/JLT.2022.3160101","type":"journal-article","volume":"40","author":"Sena","year":"2022","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R23","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2021.M3I.5","type":"journal-article","article-title":"Revealing Raman-amplified power profile and Raman gain spectra with digital backpropagation","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Sasai","year":"2021"},{"key":"jocn-18-4-B60-R24","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2022.Th1C.2","type":"journal-article","article-title":"Location-resolved PDL monitoring with Rx-side digital signal processing in multi-span optical transmission system","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Eto","year":"2022"},{"key":"jocn-18-4-B60-R25","doi-asserted-by":"publisher","first-page":"5866","DOI":"10.1109\/JLT.2024.3407722","type":"journal-article","volume":"42","author":"Takahashi","year":"2024","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R26","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2022.Th1C.3","type":"journal-article","article-title":"Localization of reflection induced multi-path-interference over multi-span transmission link by receiver-side digital signal processing","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Hahn","year":"2022"},{"key":"jocn-18-4-B60-R27","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2024.W1B.2","type":"journal-article","article-title":"Estimation and localization of DGD distributed over multi-span optical link by correlation template method","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Hahn","year":"2024"},{"key":"jocn-18-4-B60-R28","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2024.W1B.4","type":"journal-article","article-title":"Fiber longitudinal monitoring of inter-band-SRS-induced power transition in S+C+L WDM transmission","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Kaneko","year":"2024"},{"key":"jocn-18-4-B60-R29","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2024.Th1F.6","type":"journal-article","article-title":"Nonlinear SNR estimation based on power profile estimation in hybrid Raman-EDFA link","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Kim","year":"2024"},{"key":"jocn-18-4-B60-R30","doi-asserted-by":"publisher","first-page":"1955","DOI":"10.1109\/JLT.2023.3327760","type":"journal-article","volume":"42","author":"Sasai","year":"2023","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R31","doi-asserted-by":"publisher","first-page":"2390","DOI":"10.1109\/JLT.2021.3139167","type":"journal-article","volume":"40","author":"Sasai","year":"2022","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R32","doi-asserted-by":"crossref","DOI":"10.1049\/icp.2023.2539","type":"journal-article","article-title":"Demonstration of longitudinal power profile estimation using commercial transceivers and its practical consideration","volume-title":"European Conference on Optical Communications (ECOC)","author":"Chang","year":"2023"},{"key":"jocn-18-4-B60-R33","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2025.W3E.7","article-title":"Impact of BER on longitudinal power profile estimation and its correction","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Chang","year":"2025"},{"key":"jocn-18-4-B60-R34","doi-asserted-by":"crossref","DOI":"10.1364\/OFC.2025.W3E.6","article-title":"Mitigation of power offset induced by hard-decision-error in fiber longitudinal power profile estimation","volume-title":"Optical Fiber Communication Conference (OFC)","author":"Jiang","year":"2025"},{"key":"jocn-18-4-B60-R37","doi-asserted-by":"publisher","first-page":"3278","DOI":"10.1109\/JLT.2023.3234534","type":"journal-article","volume":"41","author":"Sasai","year":"2023","journal-title":"J. Lightwave Technol."},{"key":"jocn-18-4-B60-R38","doi-asserted-by":"crossref","DOI":"10.1049\/cp.2019.1031","article-title":"Experimental demonstration of a coherent receiver that visualizes longitudinal signal power profile over multiple spans out of its incoming signal","volume-title":"45th European Conference on Optical Communication (ECOC)","author":"Tanimura","year":"2019"},{"key":"jocn-18-4-B60-R39","doi-asserted-by":"publisher","first-page":"5846","DOI":"10.1109\/JLT.2024.3401124","type":"journal-article","volume":"42","author":"Tang","year":"2024","journal-title":"J. Lightwave Technol."}],"container-title":["Journal of Optical Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=jocn-18-4-B60&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T13:59:04Z","timestamp":1778680744000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=jocn-18-4-B60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,12]]},"references-count":33,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/jocn.584746","relation":{},"ISSN":["1943-0620","1943-0639"],"issn-type":[{"value":"1943-0620","type":"print"},{"value":"1943-0639","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,12]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/JOCN.584746","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":"18 November 2025","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"16 February 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"12 March 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}