DSP-based Coherent Optical Systems: Receiver Sensitivity and Coding Aspects MIU YOONG LEONG Licentiate Thesis in Physics Stockholm, Sweden 2015 KTH School of Information and Communication Technology TRITA-ICT 2015:03 SE-164 40 Stockholm ISBN 978-91-7595-551-3 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska Högskolan framläg- ges till offentlig granskning för avläggande av teknologie licentiatexamen i fysik onsdagen den 10 juni 2015 klockan 10.00 i Sal C, Electrum 229, Kungl Tekniska Högskolan, Isafjordsgatan 22, Stockholm. © Miu Yoong Leong, juni 2015 Tryck: Universitetsservice US AB iii Abstract User demand for faster access to more data is at a historic high and rising. One of the enabling technologies that makes the information age possible is fiber-optic communications, where light is used to carry information from one place to another over optical fiber. Since the technology was first shown to be feasible in the 1970s, it has been constantly evolving with each new generation of fiber-optic systems achieving higher data rates than its predecessor. Today, the most promising approach for further increasing data rates is digital signal processing (DSP)-based coherent optical transmission with multi-level modulation. As multi-level modulation formats are very suscepti- ble to noise and distortions, forward error correction (FEC) is typically used in such systems. However, FEC has traditionally been designed for additive white Gaussian noise (AWGN) channels, whereas fiber-optic systems also have other impairments. For example, there is relatively high phase noise (PN) from the transmitter and local oscillator (LO) lasers. The contributions of this thesis are in two areas. First, we use a uni- fied approach to analyze theoretical performance limits of coherent optical receivers and microwave receivers, in terms of signal-to-noise ratio (SNR) and bit error rate (BER). By using our general framework, we directly compare the performance of ten coherent optical receiver architectures and five mi- crowave receiver architectures. In addition, we put previous publications into context, and identify areas of agreement and disagreement between them. Second, we propose straightforward methods to select codes for systems with PN. We focus on Bose-Chaudhuri-Hocquenghem (BCH) codes with simple − implementations, which correct pre-FEC BERs around 10 3. Our methods are semi-analytical, and need only short pre-FEC simulations to estimate er- ror statistics. We propose statistical models that can be parameterized based on those estimates. Codes can be selected analytically based on our models. Acknowledgments I would like to thank my main supervisor Assoc. Prof. Sergei Popov. His op- timism and can-do attitude were both encouraging and infectious. He brought a unique perspective, which improved both my understanding and the clarity of my explanations. I would also like to thank my co-supervisor Prof. Gunnar Jacobsen, another optimist. His drive to keep things moving ensured that we made steady progress. He was always accessible, providing me with invaluable opportunities to tap into his wealth of knowledge and experience. Much of this research was conducted in collaboration with the Technical Uni- versity of Denmark (DTU). I would especially like to thank Prof. Knud J. Larsen, whose expertise and well-considered input were vital to the success of this work. I would also like to thank Assoc. Prof. Darko Zibar for his constructive comments. My thanks also to the good people at Aston University. For the opportunity to conduct part of my research there, I would like to thank Dr. Sergey Sergeyev. I would also like to thank Tatiana Kilina for the engaging conversations. A nod to my colleagues at Acreo Swedish ICT and KTH Royal Institute of Tech- nology, especially those at the Networking and Transmission Laboratory (Netlab) at Acreo, for the useful discussions in a pleasant atmosphere. Additionally, I would like to thank my friends, especially Carrie for being sup- portive and dependable through the years. Lastly, I would like to thank my family, especially my father for his quiet love and unrelenting determination to put me through school. v Contents Acknowledgments v List of Publications ix Contributions and Structure of the Thesis xi List of Abbreviations xiii List of Figures xvii List of Tables xix 1 Introduction 1 1.1 HistoricalBackground .......................... 1 1.1.1 The Rise, Demise, and Rebirth of Coherent Optical Systems 1 1.1.2 Forward Error Correction in Coherent Systems . 3 1.2 State-of-the-art and Challenges . 3 2 Coherent Optical Systems 7 2.1 Overview ................................. 7 2.2 Transmitter................................ 7 2.3 Channel.................................. 10 2.3.1 Fiber Losses and Amplification . 10 2.3.2 LaserPhaseNoise ........................ 11 2.3.3 ChromaticDispersion . 12 2.3.4 Polarization-Mode Dispersion . 12 2.3.5 Nonlinear Effects . 13 2.4 Receiver.................................. 14 2.4.1 Optical and Electrical Front-end . 14 2.4.2 Analog-to-Digital Converter . 23 2.4.3 Digital Signal Processing . 24 2.5 Electrical Front-end in Microwave Systems . 25 2.6 Theoretical Performance Limits . 28 vii viii CONTENTS 3 Forward Error Correction 31 3.1 General Principles . 31 3.2 LinearBlockCodes............................ 34 3.3 CyclicCodes ............................... 35 3.4 BCHCodes................................ 35 3.5 Serially-concatenated Codes . 36 3.6 TurboCodes ............................... 37 3.7 LDPCCodes ............................... 37 3.8 CodedModulation ............................ 37 3.9 Interleaving ................................ 38 4 BCH Codes for Coherent Optical Systems 41 4.1 System Model and General Approach . 41 4.2 BinaryBCHcodes ............................ 42 4.3 RScodes ................................. 48 5 Conclusion and Future Research 51 Bibliography 55 List of Publications Publications included in the thesis I. M. Y. Leong, G. Jacobsen, S. Popov, and S. Sergeyev, “Receiver sensitivity in optical and microwave, heterodyne and homodyne systems,” Journal of Optical Communications, vol. 35, no. 3, pp. 221–229, Mar. 2014. II. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Dimensioning BCH codes for coherent DQPSK systems with laser phase noise and cycle slips,” J. Lightw. Technol., vol. 32, no. 21, pp. 4048–4052, Nov. 2014. III. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Interleavers and BCH Codes for Coherent DQPSK Systems with Laser Phase Noise,” IEEE Photon. Technol. Lett., vol. 27, no. 7, pp. 685–688, Apr. 2015. IV. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Dimensioning RS codes for mitigation of phase noise induced cycle slips in DQPSK systems,” in Proc. Asia Communications and Photonics Conference (ACP), Nov. 2014, ATh4D.4. Related publications not included in the thesis V. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Novel BCH code design for mitigation of phase noise induced cycle slips in DQPSK systems,” in Proc. Conf. Lasers Electro-Opt. (CLEO), Jun. 2014, STu3J.6. VI. M. Y. Leong, S. Popov, G. Jacobsen, and S. Sergeyev, “SNR comparison of coherent optical receivers,” in Proc. Progress in Electromagnetics Research Symposium (PIERS), Aug. 2014, p. 966. VII. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Interleaving to Reduce Code Overhead in DQPSK Systems,” in Proc. Progress in Electromagnetics Research Symposium (PIERS), Jul. 2015, in print. ix Contributions and Structure of the Thesis The contributions of this thesis are in two areas: 1. theoretical performance limits for uncoded systems, and 2. simple methods to select simple Bose-Chaudhuri-Hocquenghem (BCH) codes for coherent optical systems with laser phase noise (PN). The thesis is structured as follows. A brief introduction to the history and state-of-the-art is in Chap. 1. An overview of coherent optical systems is in Chap. 2. This covers the transmitter, channel, and receiver. In addition, coherent optical receivers are compared with microwave receivers. A general introduction to coding is in Chap. 3. In Chap. 4, we describe methods for selecting BCH codes for coherent systems with PN. Finally, in Chap. 5, we conclude and provide suggestions for future research. The research presented in this thesis is supported by results which we have published in the following papers. Journal Papers I. M. Y. Leong, G. Jacobsen, S. Popov, and S. Sergeyev, “Receiver sensitivity in optical and microwave, heterodyne and homodyne systems,” Journal of Optical Communications, vol. 35, no. 3, pp. 221–229, Mar. 2014. In Paper I, we derive theoretical limits of signal-to-noise ratio (SNR) and bit error rate (BER) for various coherent optical and microwave receiver architectures using a unified approach. We consider Gaussian noise sources and uncoded systems in our analysis. Based on our framework, we put previous publications in context, and identify areas of agreement/disagreement between them. The author of this thesis was responsible for the mathematical derivations, the comparisons with previous publications, and writing the manuscript. II. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Dimensioning BCH codes for coherent DQPSK systems with laser phase noise xi xii CONTRIBUTIONS AND STRUCTURE OF THE THESIS and cycle slips,” J. Lightw. Technol., vol. 32, no. 21, pp. 4048–4052, Nov. 2014. In Paper II, we propose a statistical model to describe the bit errors in a differential quadrature phase-shift keying (DQPSK) system with laser PN. We use the model to select binary BCH codes that meet a target post-forward error correction (FEC) BER. The author of this thesis was responsible for the choice of statistical model, developing the method for code selection, verifying the method using simulations, and writing the manuscript. III. M. Y. Leong, K. J. Larsen, G. Jacobsen, S. Popov, D. Zibar, and S. Sergeyev, “Interleavers and BCH Codes for Coherent DQPSK Systems with Laser Phase Noise,” IEEE Photon. Technol. Lett., vol. 27, no. 7, pp. 685–688, Apr. 2015.