{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T02:19:59Z","timestamp":1778033999160,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,20]],"date-time":"2018-12-20T00:00:00Z","timestamp":1545264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["713567"],"award-info":[{"award-number":["713567"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"publisher","award":["13\/RC\/2077"],"award-info":[{"award-number":["13\/RC\/2077"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has attracted a lot of interest in optical fiber communications due to its simplified digital signal processing (DSP) units, high spectral-efficiency, flexibility, and tolerance to linear impairments. However, CO-OFDM\u2019s high peak-to-average power ratio imposes high vulnerability to fiber-induced non-linearities. DSP-based machine learning has been considered as a promising approach for fiber non-linearity compensation without sacrificing computational complexity. In this paper, we review the existing machine learning approaches for CO-OFDM in a common framework and review the progress in this area with a focus on practical aspects and comparison with benchmark DSP solutions.<\/jats:p>","DOI":"10.3390\/fi11010002","type":"journal-article","created":{"date-parts":[[2018,12,20]],"date-time":"2018-12-20T12:54:36Z","timestamp":1545310476000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Harnessing machine learning for fiber-induced nonlinearity mitigation in long-haul coherent optical OFDM"],"prefix":"10.3390","volume":"11","author":[{"given":"Elias","family":"Giacoumidis","sequence":"first","affiliation":[{"name":"Radio and Optical Laboratory, School of Electronic Engineering, Dublin City University, Glasnevin 9, Dublin D09 Y5N0, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Lin","sequence":"additional","affiliation":[{"name":"Radio and Optical Laboratory, School of Electronic Engineering, Dublin City University, Glasnevin 9, Dublin D09 Y5N0, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinlong","family":"Wei","sequence":"additional","affiliation":[{"name":"Huawei Technologies D\u00fcsseldorf GmbH, European Research Center, Riesstrasse 25, 80992 M\u00fcnchen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7969-3051","authenticated-orcid":false,"given":"Ivan","family":"Aldaya","sequence":"additional","affiliation":[{"name":"Campus S\u00e3o Joao da Boa Vista, State University of S\u00e3o Paulo (UNESP), 13876-750 S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Athanasios","family":"Tsokanos","sequence":"additional","affiliation":[{"name":"Centre for Computer Science and Informatics Research, School of Computer Science, University of Hertfordshire, Hatfield AL10 9AB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liam P.","family":"Barry","sequence":"additional","affiliation":[{"name":"Radio and Optical Laboratory, School of Electronic Engineering, Dublin City University, Glasnevin 9, Dublin D09 Y5N0, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1364\/OPN.26.3.000028","article-title":"Scaling optical fiber networks: Challenges and solutions","volume":"26","author":"Winzer","year":"2015","journal-title":"Opt. Photonics News"},{"key":"ref_2","unstructured":"(2015). Cisco Virtual Networking Index: Forecast and Methodology, 2014\u20132019, CISCO."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1038\/35082518","article-title":"Nonlinear limits to the information capacity of optical fiber communications","volume":"411","author":"Mitra","year":"2001","journal-title":"Nature"},{"key":"ref_4","unstructured":"Agrawal, G.P. (2001). Nonlinear Fiber Optics, Academic Press. [3rd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1126\/science.aab1781","article-title":"Overcoming Kerr-induced capacity limit in optical fiber transmission","volume":"348","author":"Temprana","year":"2015","journal-title":"Science"},{"key":"ref_6","unstructured":"Behrens, C. (2012). Mitigation of Nonlinear Impairments for Advance Optical Modulation Formats. [Ph.D. Thesis, Department of Electronic and Electrical Engineering, University College London]."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1364\/AOP.9.000429","article-title":"Performance limits in optical communications due to fiber nonlinearity","volume":"9","author":"Ellis","year":"2017","journal-title":"Adv. Opt. Photonics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1049\/el:20060561","article-title":"Coherent optical orthogonal frequency division multiplexing","volume":"42","author":"Shieh","year":"2006","journal-title":"Electr. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1109\/JLT.2012.2227942","article-title":"Mid-Span Spectral Inversion for Coherent Optical OFDM Systems: Fundamental Limits to Performance","volume":"31","author":"Morshed","year":"2013","journal-title":"J. Lightw. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1109\/JLT.2015.2408995","article-title":"Demonstration of Phase-conjugated Subcarrier Coding for Fiber Nonlinearity Compensation in CO-OFDM Transmission","volume":"33","author":"Le","year":"2015","journal-title":"J. Lightw. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1109\/LPT.2013.2247753","article-title":"Analytical Evaluation of Practical DBP-Based Intra-Channel Nonlinearity Compensators","volume":"25","author":"Gao","year":"2013","journal-title":"Photonics Technol. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Song, M., Pincemin, E., Vgenopoulou, V., Roudas, I., Amhoud, E.M., and Jaou\u00ebn, Y. (2015, January 22). Transmission performances of 400 Gbps coherent 16-QAM multi-band OFDM adopting nonlinear mitigation techniques. Proceedings of the 2015 Tyrrhenian International Workshop on Digital Communications TIWDC, Florence, Italy.","DOI":"10.1109\/TIWDC.2015.7323334"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1109\/LPT.2014.2321434","article-title":"Volterra-Based Reconfigurable Nonlinear Equalizer for Coherent OFDM","volume":"26","author":"Giacoumidis","year":"2014","journal-title":"Photonics Technol. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"30399","DOI":"10.1364\/OE.23.030399","article-title":"Modified phase-conjugate twin wave schemes for fiber nonlinearity mitigation","volume":"23","author":"Yu","year":"2015","journal-title":"Opt. Exp."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yoshida, T., Sugihara, T., Ishida, K., and Mizuochi, T. (2014, January 9\u201313). Spectrally-efficient Dual Phase-Conjugate Twin Waves with Orthogonally Multiplexed Quadrature Pulse-shaped Signals. Proceedings of the Optical Fiber Communication Conference (OFC), San Francisco, CA, USA.","DOI":"10.1364\/OFC.2014.M3C.6"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1016\/S0031-3203(01)00178-9","article-title":"Image processing with neural networks\u2014A review","volume":"35","author":"Handels","year":"2002","journal-title":"Pattern Recognit."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/LWC.2017.2757490","article-title":"Power of Deep Learning for Channel Estimation and Signal Detection in OFDM Systems","volume":"7","author":"Ye","year":"2018","journal-title":"Wirel. Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1038\/s41566-017-0058-3","article-title":"Machine learning under the spotlight","volume":"11","author":"Zibar","year":"2017","journal-title":"Nat. Photonics"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8487","DOI":"10.1038\/s41598-018-26927-y","article-title":"Photonic machine learning implementation for signal recovery in optical communications","volume":"8","author":"Argyris","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1109\/LPT.2014.2375960","article-title":"Artificial Neural Network Nonlinear Equalizer for Coherent Optical OFDM","volume":"27","author":"Jarajreh","year":"2015","journal-title":"Photonics Technol. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5113","DOI":"10.1364\/OL.40.005113","article-title":"Fiber Nonlinearity-Induced Penalty Reduction in Coherent Optical OFDM by Artificial Neural Network based Nonlinear Equalization","volume":"40","author":"Giacoumidis","year":"2015","journal-title":"Opt. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Giacoumidis, E., Mhatli, S., Wei, J., Le, S.T., Aldaya, I., Stephens, M.F., McCarthy, M.E., Ellis, A.D., Doran, N.J., and Eggleton, B.J. (2017, January 19\u201323). Intra and inter-channel nonlinearity compensation in WDM coherent optical OFDM using artificial neural network based nonlinear equalization. Proceedings of the Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, USA.","DOI":"10.1364\/OFC.2017.Th2A.62"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Koike-Akino, T., Millar, D.S., Parsons, K., and Kojima, K. (2018, January 2\u20135). Nonlinearity Equalization with Multi-Label Deep Learning Scalable to High-Order DP-QAM. Proceedings of the Signal Processing in Photonic Communications (SPPCom), Zurich, Switzerland.","DOI":"10.1364\/SPPCOM.2018.SpM4G.1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1007\/s11082-018-1519-8","article-title":"Performance analysis of Wilcoxon-based machine learning nonlinear equalizers for coherent optical OFDM","volume":"50","author":"Kaur","year":"2018","journal-title":"Opt. Quant. Electr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s11082-017-1065-9","article-title":"Application of functional link artificial neural network for mitigating nonlinear effects in coherent optical OFDM","volume":"49","author":"Kaur","year":"2017","journal-title":"Opt. Quant. Electr."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2507","DOI":"10.1109\/LPT.2016.2601901","article-title":"Radial Basis Function Neural Network Nonlinear Equalizer for 16-QAM Coherent Optical OFDM","volume":"28","author":"Ahmad","year":"2016","journal-title":"Photonics Technol. Lett."},{"key":"ref_27","first-page":"1","article-title":"Fiber nonlinearity equalizer based on support vector classification for coherent optical OFDM","volume":"8","author":"Nguyen","year":"2016","journal-title":"Photonics J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1364\/OL.41.002509","article-title":"Comparison of DSP-based nonlinear equalizers for intra-channel nonlinearity compensation in coherent optical OFDM","volume":"41","author":"Giacoumidis","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2391","DOI":"10.1109\/JLT.2017.2678511","article-title":"Reduction of Nonlinear Inter-Subcarrier Intermixing in Coherent Optical OFDM by a Fast Newton-based Support Vector Machine Nonlinear Equalizer","volume":"35","author":"Giacoumidis","year":"2017","journal-title":"J. Lightw. Technol."},{"key":"ref_30","unstructured":"Giacoumidis, E., Le, S.T., MacCarthy, M.E., Ellis, A.D., and Eggleton, B.J. (December, January 29). Record Intrachannel Nonlinearity Reduction in 40-Gb\/s 16QAM Coherent Optical OFDM using Support Vector Machine based Equalization. Proceedings of the ANZCOP\/ACOFT, Adelaide, Australia."},{"key":"ref_31","unstructured":"Giacoumidis, E., Mhatli, S., Le, S.T., Aldaya, I., McCarthy, M.E., Ellis, A.D., and Eggleton, B.J. (2016, January 18\u201322). Nonlinear Blind Equalization for 16-QAM Coherent Optical OFDM using Support Vector Machines. Proceedings of the ECOC, D\u00fcsseldorf, Germany."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1049\/iet-com.2016.1115","article-title":"A novel SVM robust model Based Electrical Equalizer for CO-OFDM Systems","volume":"11","author":"Mhatli","year":"2017","journal-title":"IET Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1109\/LPT.2018.2832617","article-title":"Unsupervised Support Vector Machines for Nonlinear Blind Equalization in CO-OFDM","volume":"30","author":"Giacoumidis","year":"2018","journal-title":"Photonics Technol. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1049\/iet-com.2017.1212","article-title":"Compensation of filter cascading effects and non-linearities in flexible multi-carrier-based optical networks using a complex-kernel-based support vector machine","volume":"12","author":"Jarajreh","year":"2018","journal-title":"IET Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/JLT.2017.2778883","article-title":"Blind Nonlinearity Equalization by Machine Learning based Clustering for Single- and Multi-Channel Coherent Optical OFDM","volume":"36","author":"Giacoumidis","year":"2018","journal-title":"J. Lightw. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Giacoumidis, E., Aldaya, I., Wei, J.L., Sanchez, C., Mrabet, H., and Barry, L.P. (2018, January 13\u201318). Affinity propagation clustering for blind nonlinearity compensation in coherent optical OFDM. Proceedings of the CLEO, San Jose, CA, USA.","DOI":"10.1364\/CLEO_SI.2018.STh1C.5"},{"key":"ref_37","first-page":"792","article-title":"Impact of Optical Phase Conjugation on the Nonlinear Shannon Limit","volume":"35","author":"Ellis","year":"2017","journal-title":"Opt. Exp."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"20381","DOI":"10.1364\/OE.23.020381","article-title":"Capacity limits of systems employing multiple optical phase conjugators","volume":"23","author":"Ellis","year":"2015","journal-title":"Opt. Exp."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Phillips, I., Tan, M., Stephens, M.F., McCarthy, M., Giacoumidis, E., Sygletos, S., Rosa, P., Fabbri, S., Le, S.T., and Kanesan, T. (2014, January 9\u201313). Exceeding the Nonlinear-Shannon Limit using Raman Laser Based Amplification and Optical Phase Conjugation. Proceedings of the Optical Fiber Communication Conference (OFC), San Francisco, CA, USA.","DOI":"10.1364\/OFC.2014.M3C.1"},{"key":"ref_40","unstructured":"Sanchez, C., Mccarthy, M., Ellis, A.D., Wright, P., and Lord, A. (2015, January 12\u201314). Optical-phase conjugation nonlinearity compensation in Flexi-Grid optical networks. Proceedings of the DNCOCO, Budapest, Hungary."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1038\/nphoton.2013.109","article-title":"Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit","volume":"7","author":"Liu","year":"2013","journal-title":"Nat. Photonics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1109\/JLT.2015.2388854","article-title":"Phase-Conjugated Pilots for Fiber Nonlinearity Compensation in CO-OFDM Transmission","volume":"33","author":"Le","year":"2015","journal-title":"J. Lightw. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1903","DOI":"10.1364\/OE.25.001903","article-title":"Digital backpropagation accounting for polarization-mode dispersion","volume":"25","author":"Czegledi","year":"2017","journal-title":"Opt. Exp."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3956","DOI":"10.1109\/TCOMM.2014.2362534","article-title":"Stochastic digital backpropagation","volume":"62","author":"Irukulapati","year":"2014","journal-title":"Trans. Commun."},{"key":"ref_45","unstructured":"Vgenopoulou, V., Erkilinc, M.S., Killey, R.I., Jaou\u00ebn, Y., Roudas, I., and Tomkos, I. (2016, January 18\u201322). Comparison of Multi-Channel Nonlinear Equalization using Inverse Volterra Series versus Digital Backpropagation in 400 Gb\/s Coherent Superchannel. Proceedings of the 42nd European Conference on Optical Communication (ECOC), Dusseldorf, Germany."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1145\/272991.272995","article-title":"Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudorandom Number Generator","volume":"8","author":"Matsumoto","year":"1998","journal-title":"ACM Trans. Model. Comput. Simul."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/LPT.2017.2755663","article-title":"Applying Neural Networks in Optical Communication Systems: Possible Pitfalls","volume":"29","author":"Eriksson","year":"2017","journal-title":"Photonics Technol. Lett."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"16124","DOI":"10.1364\/OE.16.016124","article-title":"Impact of XPM and FWM on the digital implementation of impairment compensation for WDM transmission using backward propagation","volume":"16","author":"Mateo","year":"2008","journal-title":"Opt. Exp."}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/1\/2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:35:14Z","timestamp":1760196914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/11\/1\/2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,20]]},"references-count":48,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["fi11010002"],"URL":"https:\/\/doi.org\/10.3390\/fi11010002","relation":{},"ISSN":["1999-5903"],"issn-type":[{"value":"1999-5903","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,20]]}}}