Spécialité : Électronique et Communications Ecole doctorale : Informatique, Télécommunications et Electronique de Paris Présentée par Ivan Fernandez de Jauregui Ruiz Pour obtenir le grade de DOCTEUR DE TELECOM SUDPARIS Advanced modulation formats and nonlinear mitigation for spectral efficient optical transmission systems Soutenue le 12 Avril 2018 Devant le jury composé de : Directeur de thèse Prof. Badr-Eddine Benkelfat (Telecom SudParis) Rapporteurs Prof. Alberto Bononi (University of Parma) Prof. Magnus Karlsson (Chalmers University) Examinateurs Prof. Didier Erasme (Télécom ParisTech) Dr. Nicolas Dubreuil (Institute d’Optique Graduate School) Dr. Anne-Laure Billabert (Conservatoire National des Arts et Métiers) Encadrants Dr. Amirhossein Ghazisaeidi (Nokia Bell-Labs France) Prof. Yann Frignac (Telecom SudParis) NNT. <2018TELE0009> 2 “I have heard articulate speech by sunlight! I have heard a ray of the sun laugh and cough and sing! I have been able to hear a shadow and I have even perceived by ear the passage of a cloud across the sun's disk. You are the grandfather of the Photophone and I want to share my delight at my success”. — Alexander Graham Bell, in a letter to his father Alexander Melville Bell, dated February 26, 1880 3 ACKNOWLEDGEMENTS I would like to start by thanking all the members of the jury for the precious time they have taken to read and evaluate my report, as well as for their fruitful advices and comments. It gives me immense pleasure to thank Amirhossein Ghazisaeidi for all his support and continuous guidance during the practical phase of this thesis. I thank him for his astute criticism and for encouraging me to always give my best to present high-quality and meaningful results. I thank him for his patience and for transmitting me part of his immense knowledge. I would also like to express my sincere gratitude to Gabriel Charlet for encouraging me to perform this thesis after my Master’s internship. I thank him for all the practical discussions and for teaching me how to present results in an original and relevant way. I thank him for his guidance, for his trust, and for all his support. I thank Jeremie Renaudier for all his suggestions and help during the final part of this thesis, and which who I would have liked to work more closely since the beginning of my work. I also thank Patrice Tran, Patrick Brindel, Dylan LeGac and Christian Simonneau for having introduced me to the various techniques and tricks in the lab, but specially for your infinite patience on all those hours setting-up, optimizing, and performing all the experiments. I thank also Christian Doriz for all the fruitful discussions and work during the Optoplan project. I specially thank Alexis Carbo, Elie Awwad, Rafael Rios-Müller and Kaoutar Benyahya for all their support, for their friendship, and for their motivation. I thank all my colleagues in the department for their help, and for making my stay at Bell Labs a very pleasant one. It has been a honor and pleasure to be part of this great team. This acknowledge would not be complete without thanking all my family, specially my parents and brothers for all their support, and for encouraging me to always move forward and to search for new limits. I thank them for having educated me with social sense where my work and wellness cannot come at the expense of others. I thank them and my political family for their constant love, encouragement, and moral support. I also thank my friends Ruben Hernandez and Uriel Esparza for their lifetime friendship. Liliana Beltran, Jessica Martinez, Jose Luis Martinez, Daniel Villavicencio,… It would be impossible to tell all the new experiences and good moments that we have lived together. I thank all their support and for always being there for me. Last but not least, I leave these last lines to the most important person in my life, my wife Viridiana. None of this would have been possible without you. You have always been there by my side, encouraging me, motivating me, pushing me. You have not given up in our future no matter how long and difficult the road has been. I thank you for always showing me that good things come with sacrifice, and better do those sacrifices next to the person you love. 5 CONTENTS ACKNOWLEDGEMENTS ......................................................................................................... 5 CONTENTS ............................................................................................................................... 7 ABSTRACT ............................................................................................................................... 9 RESUME ................................................................................................................................. 11 LIST OF ACRONYMS AND SYMBOLS ................................................................................. 15 LIST OF ACRONYMS .................................................................................................... 15 LIST OF SYMBOLS ...................................................................................................... 18 1 COHERENT OPTICAL FIBER TELECOMMUNICATIONS SYSTEMS ....... 21 1.1 TRANSOCEANIC SUBMARINE OPTICAL FIBER SYSTEMS STATUS AND TRENDS ..... 21 1.2 DIGITAL TELECOMMUNICATION SYSTEMS .......................................................... 25 1.2.1 Achievable Information Rates ................................................................. 26 1.2.2 Forward Error Correction Codes ............................................................. 29 1.2.3 Modulation Formats ................................................................................ 30 1.2.4 Pulse Shaping ......................................................................................... 35 1.3 COHERENT OPTICAL COMMUNICATIONS SYSTEMS .............................................. 36 1.3.1 Optical Transmitter .................................................................................. 37 1.3.2 Optical Link ............................................................................................. 38 1.3.3 Optical Coherent Receiver ...................................................................... 50 1.3.4 Standard Digital Signal Processing Blocks ............................................. 52 1.3.5 Nonlinear Digital Signal Processing ........................................................ 56 1.4 PERFORMANCE ANALYSIS ................................................................................ 60 1.4.1 AWGN Channel ....................................................................................... 60 1.4.2 Back-to-back (B2B) Penalties ................................................................. 61 1.4.3 Nonlinear Variance.................................................................................. 62 1.4.4 Theory of Nonlinear Channel .................................................................. 63 1.4.5 Theoretical Limits to Nonlinear Compensation ....................................... 64 1.5 SUMMARY ........................................................................................................ 66 7 2 LOW-COMPLEXITY DIGITAL NONLINEAR COMPENSATION ................. 67 2.1 FILTERED DIGITAL BACKPROPAGATION OPTIMIZATION ........................................ 67 2.1.1 FDBP Parameter Optimization ................................................................ 68 2.1.2 Experimental Validation .......................................................................... 74 2.2 IMPACT OF STOCHASTIC POLARIZATION EFFECTS ON NLC ALGORITHMS .............. 77 2.2.1 Experimental Results .............................................................................. 77 2.2.2 Simulation Results .................................................................................. 85 2.3 PRACTICAL LIMITS OF NLC ALGORITHMS ........................................................... 87 2.3.1 Simulation Set-up .................................................................................... 87 2.3.2 Numerical Results ................................................................................... 89 2.4 SUMMARY ........................................................................................................ 97 3 HIGH-CAPACITY MODULATION FORMATS .............................................. 99 3.1 MODULATION FORMATS COMPARISON ............................................................. 100 3.1.1 Theoretical Performance ....................................................................... 100 3.1.2 Experimental Performance ................................................................... 105 3.2 TRUNCATED PROBABILISTIC CONSTELLATION SHAPING ..................................... 110 3.3 SUMMARY ...................................................................................................... 114 4 TRANSOCEANIC TRANSMISSION RECORDS ........................................ 115 4.1 25.4 TB/S OVER TRANS-PACIFIC DISTANCES USING TPCS-64QAM ................ 115 4.2 HIGH SYMBOL-RATE TRANSOCEANIC TRANSMISSION ......................................... 121 4.2.1 Single-carrier Experiments .................................................................... 122 4.2.2 Dual-carrier Experiments ...................................................................... 125 4.3 65 TB/S LEVERAGED BY PCS-64QAM ............................................................ 128 4.3.1 Experimental Set-up.............................................................................