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Modeling and Compensation of Polarization Effects in Fiber-Optic

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Modeling and Compensation of Polarization Effects in Fiber-Optic CHALMERS UNIVERSITY OF TECHNOLOGY SE-412 96 Gothenburg, Sweden Telephone: +46 (0)31 772 10 00 www.chalmers.se CRISTIAN B. CZEGLEDI Popular Scientific Summary s3 Data transmission through optical fiBers is the fastest form of digital Modeling and Compensation of Polarization Effects in Fiber-Optic Communication Systems 2018 communication availaBle today and comprises the BackBone of the Internet network. Every time a web page is accessed, an image is Instagrammed, or a YouTuBe video is watched, the data will travel most likely through an optical fiBer at some point on the way to the user. Even though optical fiBers can provide very high-speed communications, the transmitted signal is disturBed along the way By various sources of noise. If the noise is Beyond some acceptaBle levels, the information intended By the transmitter cannot Be “understood” By the receiver, therefore leading s2 to a failed communication attempt. In order to avoid these situations, the transmitter and receiver are designed such that they are aBle to distinguish s Between noise and useful information. 1 Before designing the transmitter and receiver such that they can tolerate more noise, the nature of the noise has to Be understood and modeled mathematically. These mathematical models, often called channel models, have to reflect the Behavior of the noise accurately. On the contrary, designing the transmitter and receiver Based on inaccurate channel models leads to suBoptimal performance. In this thesis, we are concerned with modeling and mitigation of noise related Modeling and Compensation of to polarization effects. We first develop channel models for polarization effects that occur during propagation. These models can Be used in ModelingPolarization and Compensation Effects in of computer-Based simulations to reproduce polarization effects that occur in a fiBer-optic communication system. Simulations offer a greater flexiBility than PolarizationFiber-Optic Effects Communication in Systems experiments and can Be used to predict the Behavior of a system Before setting up time-consuming experiments. Furthermore, we propose various methods that improve the tolerance to polarization effects of fiBer optical Fiber-Optic Communication Systems communication systems, leading to an increased transmission speed and CRISTIAN B. CZEGLEDI improved energy efficiency. The interested reader is referred to page i of the thesis for a technical aBstract summarizing the contriButions. CristianDepartment B. Czegledi of Electrical Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2018 Department of Electrical Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden, 2018 thesis for the degree of doctor of philosophy Modeling and Compensation of Polarization Effects in Fiber-Optic Communication Systems Cristian B. Czegledi Communication Systems Group Department of Electrical Engineering Chalmers University of Technology Gothenburg, Sweden, 2018 Modeling and Compensation of Polarization Effects in Fiber-Optic Communication Systems Cristian B. Czegledi ISBN 978-91-7597-702-7 Copyright c Cristian B. Czegledi,2018,exceptwhere ⃝ otherwise stated. All rights reserved. Doktorsavhandlingar vid Chalmers tekniska högskola Ny serie Nr 4383 ISSN 0346-718X This thesis has been prepared using LATEXandPSTricks. Communication Systems Group Department of Electrical Engineering Chalmers University of Technology SE-412 96 Gothenburg, Sweden Phone: +46 (0)31 772 1000 www.chalmers.se Front cover illustration: Histogram of a random-walk step of the state of polarization illustrated on the Poincaré sphere (see [Paper A] for details). Printed by Chalmers Reproservice Gothenburg, Sweden, February 2018 Abstract Optical communication systems that exploit the orthogonality between two polarizations of light convey information over optical fibers by modulatingdataoverthetwopolariza- tions. In an idealized scenario, the two polarizations propagate through the fiber without interfering. However, this is not the case for practical fibers, which suffer from various imperfections that lead to polarization-related interference between the two polarizations. This thesis is concerned with polarization effects that ariseincommunicationsystems over optical fibers. In particular, we consider modeling and compensation of such effects, and their impact on and improvement of nonlinearity mitigation algorithms. The impact of an impairment on the performance of a transmission system can be understood via a channel model, which should describe the behavior of the channel as accurately as possible. A theoretical framework is introduced to model the stochastic nature of the state of polarization during transmission. Themodelgeneralizestheone- dimensional carrier phase noise random walk to higher dimensions, modeling the phase noise and state of polarization drift jointly as rotations oftheelectricfieldandithas been successfully verified using experimental data. Thereafter, the model is extended to account for polarization-mode dispersion and its temporal random fluctuations. Such models will be increasingly important in simulating and optimizing future systems, where sophisticated digital signal processing will be natural parts. The typical digital signal processing solution to mitigate phase noise and drift of the state of polarization consists of two separate blocks that track each phenomenon inde- pendently and have been developed without taking into account mathematical models describing the impairments. Based on the proposed model for the state of polarization, we study a blind tracking algorithm to compensate for these impairments. The algorithm dynamically recovers the carrier phase and state of polarization jointly for an arbitrary modulation format. Simulation results show the effectiveness of the proposed algorithm, having a fast convergence rate and an excellent tolerance to phase and polarization noise. The optical fiber is a nonlinear medium with respect to the intensity of the incident light. This effect leads to nonlinear interference as the intensity of light increases, which made nonlinear interference mitigation techniques to be an intensively studied topic. Typically, these techniques do not take into account polarization-mode dispersion, which becomes detrimental as the nonlinear effects interact with polarization-mode dispersion. We study digital-domain nonlinear interference mitigationalgorithmsthattakeintoac- count polarization-mode dispersion by i) reversing the polarization effects concurrently with reversing the nonlinear effects and by ii) mitigating only the polarization-insensitive nonlinear contributions. These algorithms will be increasingly important in future op- tical systems capable of performing large bandwidth nonlinear interference mitigation, where even small amounts of polarization-mode dispersion become a limiting factor. Keywords: Channel model, model-based, polarization demultiplexing,polarizationdrift, polarization-mode dispersion, PMD, DBP, nonlinear compensation, backpropagation. i ii List of Publications This thesis is based on the following publications: (A) C. B. Czegledi, M. Karlsson, E. Agrell, and P. Johannisson, “Polarization drift channel model for coherent fibre-optic systems,” Nature Scientific Reports,vol.6, art. no. 21217, Feb. 2016. (B) C. B. Czegledi, M. Karlsson, P. Johannisson, and E. Agrell, “Temporal stochastic channel model for absolute polarization state and polarization-mode dispersion,” in Proc. Optical Fiber Communication Conference (OFC),LosAngeles,CA,Mar. 2017, p. Th3F.2. (C) C. B. Czegledi, E. Agrell, M. Karlsson, and P. Johannisson, “Modulation format independent joint polarization and phase tracking for optical communications,” IEEE/OSA Journal of Lightwave Technology,vol.34,no.14,pp.3354–3364,July 2016. (D) C. B. Czegledi, G. Liga, D. Lavery, M. Karlsson, E. Agrell,S.J.Savory,andP. Bayvel, “Polarization-mode dispersion aware digital backpropagation,” in Proc. Eu- ropean Conference on Optical Communication (ECOC),Düsseldorf,Germany,Sept. 2016, pp. 1091–1093. (E) G. Liga, C. B. Czegledi, and P. Bayvel, “A PMD-adaptive DBPreceiverbasedon SNR optimization,” to appear in Proc. Optical Fiber Communication Conference (OFC),SanDiego,CA,Mar.2018. (F) C. B. Czegledi, G. Liga, D. Lavery, M. Karlsson, E. Agrell,S.J.Savory,and P. Bayvel, “Digital backpropagation accounting for polarization-mode dispersion,” Optics Express,vol.25,no.3,pp.1903–1915,Jan.2017. (G) C. B. Czegledi and R. Dar, “Volterra series digital backpropagation accounting for PMD,” in Proc. European Conference on Optical Communication (ECOC),Gothen- burg, Sweden, Sept. 2017, p. W.1.D.1. iii Publications by the author not included in the thesis: (a) C. B. Czegledi, M. R. Khanzadi, and E. Agrell, “Bandlimited power-efficient sig- naling and pulse design for intensity modulation,” IEEE Transactions on Commu- nications,vol.62,no.9,pp.3274–3284,Sept.2014. (b) C. B. Czegledi, M. R. Khanzadi, and E. Agrell, “Bandlimited power-efficient sig- naling for intensity modulation,” in Proc. European Conference on Optical Com- munication (ECOC),Cannes,France,Sept.2014,p.P.3.7. (c) C. B. Czegledi, E. Agrell, and M. Karlsson, “Symbol-by-symbol joint polarization and phase tracking in coherent receivers,” in Proc. Optical Fiber Communication Conference (OFC),LosAngeles,CA,Mar.2015,p.W1E.3. (d) M. Karlsson, C. B. Czegledi, and E. Agrell, “Coherent transmission channels as 4d rotations,” (invited paper) in Proc. Signal Processing in Photonic Communication (SPPCom),Boston,MA,Jul.2015,p.SpM3E.2. (e) C. B. Czegledi,
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