Ph. D. Thesis
         Optical Communications Group
 Department of Signal Theory and Communications
       Universitat Pol...
The work described in this thesis was performed in the Signal Theory and Communications
department of the Universitat Poli...
”The most exciting phrase to hear in science, the one that heralds the most discoveries,
is not Eureka! (I found it!) but ...
`
              UNIVERSITAT POLITECNICA DE CATALUNYA (UPC)


                                    Abstract
                ...
Acknowledgements
First of all I want to express my gratitude to my advisor Prof. Josep Prat for having given
to me the opp...
Contents

Abstract                                                                                       v


Acknowledgeme...
Contents                                                                                                             x

  ...
Contents                                                                                                                  ...
Contents                                                                                                                  ...
Contents       xiii

Bibliography   181
List of Figures

 1.1    Nielsen’s law prediction of bandwidth and data obtained until 2006 (square
        points). . . ....
List of Figures                                                                               xvi

   3.2    Lock-In ampli...
List of Figures                                                                              xvii

   4.18 Spectrum after ...
List of Figures                                                                                                         xv...
List of Figures                                                                          xix

   C.4 Plots of the waveleng...
List of Tables

 2.1   Common modulation formats and their SNR differences. . . . . . . . . .                9
 2.2   Compa...
Abbreviations

ADC    Analog to digital converter
AFC    Automatic frequency control
ASK    Amplitude shift keying
AWC    ...
Abbreviations                                                 xxiv

 MZM        Mach-Zehnder modulator
 NRZ        Non ret...
Symbols

          ∆ν    Laser linewidth
          ∆f    Signal bandwidth
          F     Electronic receiver equivalent n...
To my family. . .




      xxvii
Chapter 1

Introduction

More than 40 years have passed since Charles K. Kao publicly demonstrated the pos-
sibility of tr...
Chapter 1. Introduction                                                                    2




    Figure 1.1: Nielsen’s...
Chapter 1. Introduction                                                                  3

   • Total fiber bandwidth (40 ...
Chapter 1. Introduction                                                                  4

   • Allows the use of advance...
Chapter 1. Introduction                                                                   5

1.1     Objectives

The objec...
Chapter 1. Introduction                                                                   6

burst-mode NRZ. A theoretical...
Chapter 1. Introduction                                                                 7

will be described, and a step f...
Chapter 2

State of the art

2.1     Modulation formats

The modulation format to be used in a network is strongly linked ...
Chapter 2. State of the art                                                               10

2.2      Homodyne systems

N...
Chapter 2. State of the art                                                             11

   • The electrical spectrum i...
Chapter 2. State of the art                                                            12

Another approach towards homody...
Chapter 2. State of the art                                                             13

where eS (t) and eLO (t) are t...
Chapter 2. State of the art                                                                14

2.3.1.1   SNR and BER for B...
Chapter 2. State of the art                                                                15

From this model, the SNR ca...
Chapter 2. State of the art                                                             16




      Figure 2.6: Bit error...
Chapter 2. State of the art                                                              17

whereas the average error pro...
Chapter 2. State of the art                                                                    18

some algebra, such floor...
Chapter 2. State of the art                                                                 19

2.3.1.3   SNR and BER for ...
Chapter 2. State of the art                                                                     20

with
                 ...
Chapter 2. State of the art                                                                   21

exhibit different statist...
Chapter 2. State of the art                                                                    22

Continuing the mathemat...
Chapter 2. State of the art                                                               23




                Figure 2....
Chapter 2. State of the art                                                                         24

can interfere in t...
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Homodyne OLT-ONU Design for Access Optical Networks

  1. 1. Ph. D. Thesis Optical Communications Group Department of Signal Theory and Communications Universitat Politècnica de Catalunya Homodyne OLT-ONU design for access optical networks Author Josep Mª Fàbrega Advisor Josep Prat Thesis presented in fulfillment of the doctorate program of the signal theory and communications department March 2010
  2. 2. The work described in this thesis was performed in the Signal Theory and Communications department of the Universitat Politècnica de Catalunya / BarcelonaTech. Josep Mª Fàbrega Homodyne OLT-ONU design for access optical networks Subject headings: Optical communications, fibers and telecomm Copyright © 2010 by Josep Mª Fàbrega All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written consent of the author. Printed in Barcelona, Spain ISBN: 978-84-693-3168-2 Reg: 10/53978
  3. 3. ”The most exciting phrase to hear in science, the one that heralds the most discoveries, is not Eureka! (I found it!) but ’That’s funny...’” Isaac Asimov
  4. 4. ` UNIVERSITAT POLITECNICA DE CATALUNYA (UPC) Abstract Optical Communications Group (GCO) Signal Theory and Communications Department (TSC) Doctor of Philosophy by Josep M. F`brega a Nowadays, when talking about access networks, advanced multimedia applications are changing customer demands, requiring much higher speed connection. Thus, other al- ternatives to deployed Time Division Multiplex Passive Optical Networks (TDM-PONs) are appearing to increase available bandwidth. Wavelength Division Multiplex provides virtual point-to-point connections, so multiplies the effective bandwidth that the fiber can offer. A significant step forward is Ultra-Dense WDM (UD-WDM), where wavelengths are separated by just a few GHz, increasing the number of channels that can be accommo- dated on a single fiber. Following this line, if narrow channel-spacing could be achieved, a new philosophy of Wavelength-To-The-User (λTTU) can be envisaged, multiplying the number of connections as well as maintaining high data rates. One of the enabling technologies for such challenge can be coherent transmission and reception systems. First of all because they allow the use of improved modulation formats (like Phase Shift Keying - PSK), extending the reach of the networks. Secondly, as they use electrical filtering for channel selection, narrow channel spacing can be achieved while maintaining high speed connection. The most promising technology for achieving these performances is homodyne reception. Several novel transceiver architectures, based in homodyne reception, are proposed and experimentally evaluated in this work. The most robust and simple of the considered architectures has been fully developed and prototyped in order to be used in a net- work test-bed. For that prototype, transmission experiments demonstrate a sensitivity of −38.7 dBm sensitivity at 1 Gb/s, while featuring a power budget of 47 dB. Furthermore, different PON architectures are proposed and specifically designed for the proposed transceivers. With the experimental prototype previously developed, network deployment is obtained, capable to serve up to 1280 users at maximum distance of 27 km and featuring a maintained data rate of 1 Gb/s per user.
  5. 5. Acknowledgements First of all I want to express my gratitude to my advisor Prof. Josep Prat for having given to me the opportunity to join the optical communications research group and develop my Ph.D. within it. His guidance and friendship have set the cornerstone of the work presented in this thesis. These investigations would not have been possible without the full support of the optical communications group at UPC. My special thanks to Jos´ L´zaro, Bernhard Schrenk, e a Carlos Bock, Joan Gen´ and Jaume Comellas for their advice and fruitful discussions, e also demonstrating their sincere friendship. A warm hug to thank all the colleagues for making an enjoyable atmosphere everyday during these years. In this aspect I would like to emphasize the support of the remaining members of the Access and Transmission team: Eduardo T. L´pez, Mireia Omella, Victor Polo and specially Francesc Bonada, o for his unvaluable help in the network administration. Also I want to acknowledge the support of those that not belong to GCO: The entire SI-TSC team and our colleagues from i2CAT, with who we shared the same space for many years. Special thanks to Lutz Molle and Ronald Freund, for their valuable support and friend- liness, particularly during my stay at HHI. Thanks to Ahmad ElMardini, Rich Baca and Ricardo Saad, from Tellabs Inc., for their help during the test period of the SCALING contract. Also I would like to mention Marco Forzati and ACREO for bringing us the opportunity of collaboration with them and Syntune. I am very thankful to all master thesis students I supervised and co-supervised. The herewith presented work wouldn’t been possible without their contributions. In chrono- ıs u n ` logical order: Llu´ Vilabr´, Joan Miquel Pi˜ol, Miquel Angel Mestre and Marc Vilalta (almost finishing). On the personal level, I would like to thank all my family for their support, specially the most important person in my live, Vanessa Ortega, for her encouragement and endurance. For financial assistance I am indebted to several public projects and private contracts: COTS contract (Nortel Networks), SCALING contract (Tellabs Inc.), EU-FP7 BONE and SARDANA projects; Spanish MICINN projects TEC2008-01887 (TEYDE), RA4D and RAFOH; EU-FP6/7 E-Photon(+) and EuroFOS networks of excellence, and the MEC PTA-2003-02-00874 grant. vii
  6. 6. Contents Abstract v Acknowledgements vii List of Figures xv List of Tables xxi Abbreviations xxiii Symbols xxv 1 Introduction 1 1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Complementary work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 State of the art 9 2.1 Modulation formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Homodyne systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 PSK receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Homodyne receiver performances . . . . . . . . . . . . . . . . . . 12 2.3.1.1 SNR and BER for BPSK signals . . . . . . . . . . . . . 14 2.3.1.2 Phase errors in homodyne detection of BPSK signals . . 16 2.3.1.3 SNR and BER for DPSK signals . . . . . . . . . . . . . 19 2.3.1.4 Phase errors in homodyne detection of DPSK signals . . 21 2.3.2 oPLL based systems . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.2.1 Additive noise impact in a generic OPLL . . . . . . . . . 23 2.3.2.2 Phase noise impact in a generic OPLL . . . . . . . . . . 25 2.3.2.3 Loop delay impact in a generic OPLL . . . . . . . . . . 26 2.3.2.4 Costas loop . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2.5 Decision-Driven OPLL (DD-OPLL) . . . . . . . . . . . . 30 2.3.2.6 Balanced OPLL . . . . . . . . . . . . . . . . . . . . . . . 33 ix
  7. 7. Contents x 2.3.2.7 Subcarrier modulated OPLL (SCM-OPLL) . . . . . . . 36 2.3.3 Phase and polarization diversity systems . . . . . . . . . . . . . . 38 2.3.3.1 Multiple differential detection . . . . . . . . . . . . . . . 38 2.3.3.2 Wiener filter phase estimation . . . . . . . . . . . . . . . 41 2.3.3.3 M-power law phase estimation with regenerative frequency dividers . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.3.3.4 Viterbi-Viterbi phase estimation . . . . . . . . . . . . . 45 2.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3 Lock-In amplifier OPLL architecture 47 3.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.1.1 Loop analysis and linearization . . . . . . . . . . . . . . . . . . . 48 3.1.2 Noise, dithering and loop delay impacts . . . . . . . . . . . . . . . 52 3.1.3 Acquisition parameters . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.3.1 Hold in range . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.3.2 Pull in range . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.4 Data crosstalk and cycle slipping effects . . . . . . . . . . . . . . 54 3.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2.1 Phase noise simulations . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2.2 Time response simulations . . . . . . . . . . . . . . . . . . . . . . 57 3.2.3 Amplitude of the dithering signal . . . . . . . . . . . . . . . . . . 60 3.2.4 Comparison with other loops . . . . . . . . . . . . . . . . . . . . . 60 3.3 Experiments and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4 Advances in phase and polarization diversity architectures 69 4.1 Full phase diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.1.1 Karhunen-Lo`ve series expansion phase estimation . . . e . . . . . . 70 4.1.1.1 Receiver scheme . . . . . . . . . . . . . . . . . . . . . . 70 4.1.1.2 Phase estimation algorithm . . . . . . . . . . . . . . . . 71 4.1.1.3 Algorithm performances and discussion . . . . . . . . . . 72 4.2 Time switched phase / polarization diversity . . . . . . . . . . . . . . . . 74 4.2.1 Phase diversity combined with differential detection . . . . . . . . 74 4.2.1.1 Expected system performances . . . . . . . . . . . . . . 76 4.2.1.2 Simplified scheme and phase noise analysis . . . . . . . . 77 4.2.1.3 Frequency drift . . . . . . . . . . . . . . . . . . . . . . . 82 4.2.1.4 Channel spacing . . . . . . . . . . . . . . . . . . . . . . 84 4.2.2 Fuzzy data estimation . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.2.1 Receiver scheme . . . . . . . . . . . . . . . . . . . . . . 91 4.2.2.2 Data estimation . . . . . . . . . . . . . . . . . . . . . . 91 4.2.2.3 System performances . . . . . . . . . . . . . . . . . . . . 94 4.2.3 Direct drive time switching . . . . . . . . . . . . . . . . . . . . . . 95 4.2.3.1 Receiver scheme . . . . . . . . . . . . . . . . . . . . . . 95 4.2.3.2 Phase noise analysis . . . . . . . . . . . . . . . . . . . . 98
  8. 8. Contents xi 4.2.3.3 Frequency drift analysis . . . . . . . . . . . . . . . . . . 101 4.2.3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2.3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . 102 4.2.4 Searching for a polarization diversity . . . . . . . . . . . . . . . . 104 4.3 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5 ONU and OLT architectures 111 5.1 Summary of techniques and issues to take into account . . . . . . . . . . 111 5.1.1 Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.1.2 Polarization mismatch . . . . . . . . . . . . . . . . . . . . . . . . 112 5.1.3 Modulation techniques and Rayleigh backscattering . . . . . . . . 113 5.2 ONU and transceiver architectures . . . . . . . . . . . . . . . . . . . . . 114 5.2.1 Transceivers based in a full phase diversity scheme . . . . . . . . 114 5.2.1.1 Transceiver with 90 degree hybrid and digital processing 114 5.2.1.2 Transceiver with 90 degree hybrid and analog processing 115 5.2.1.3 Transceiver including 90 degree hybrid and PBS, with dig- ital processing . . . . . . . . . . . . . . . . . . . . . . . 115 5.2.1.4 Transceiver including 90 degree hybrid and PBS, with analog processing . . . . . . . . . . . . . . . . . . . . . . 116 5.2.2 Transceivers based in time-switching phase diversity . . . . . . . . 117 5.2.2.1 Transceiver including phase switch with digital processing and standard balanced detector . . . . . . . . . . . . . . 117 5.2.2.2 Transceiver including phase switch with analog processing and standard balanced detector . . . . . . . . . . . . . . 117 5.2.2.3 Transceiver including direct laser switching with digital processing and standard balanced detector . . . . . . . . 117 5.2.2.4 Transceiver including direct laser switching with analog processing and standard balanced detector . . . . . . . . 118 5.2.3 Transceiver based in Optical Phase-Locked Loop . . . . . . . . . . 119 5.2.3.1 Transceiver with OPLL and analog processing . . . . . . 119 5.2.4 Transceiver comparison . . . . . . . . . . . . . . . . . . . . . . . . 120 5.3 OLT architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6 Network topologies 125 6.1 Pure coupler splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.2 Subband WDM tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.3 Advanced: WDM ring-tree SARDANA network . . . . . . . . . . . . . . 127 6.4 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6.4.1 Subband WDM tree PON . . . . . . . . . . . . . . . . . . . . . . 128 6.4.2 Ring-tree ultra-dense WDM PON . . . . . . . . . . . . . . . . . . 130 6.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7 Conclusions and future work 137 7.1 General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
  9. 9. Contents xii 7.2 Future lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7.2.1 Compact coherent transceiver . . . . . . . . . . . . . . . . . . . . 139 7.2.2 Full bidirectionality over a single fiber . . . . . . . . . . . . . . . 139 7.2.3 Spectrum management . . . . . . . . . . . . . . . . . . . . . . . . 140 A Passive optical network solution using a subcarrier multiplex 141 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.2 Receiver scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 A.3 Experiments and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 143 A.3.1 Downstream characterization . . . . . . . . . . . . . . . . . . . . 143 A.3.2 Full-duplex measurements . . . . . . . . . . . . . . . . . . . . . . 145 A.4 Network measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 B Automatic wavelength control design 151 B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 B.2 Loop design and performances . . . . . . . . . . . . . . . . . . . . . . . . 152 B.3 Practical implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 B.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 C Static and dynamic wavelength characterization of tunable lasers 159 C.1 Experiments and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 159 C.1.1 Static characterization: wavelength map . . . . . . . . . . . . . . 160 C.1.1.1 Static characterization setup . . . . . . . . . . . . . . . . 160 C.1.1.2 Static characterization results . . . . . . . . . . . . . . . 160 C.1.2 Dynamic characterization . . . . . . . . . . . . . . . . . . . . . . 162 C.1.2.1 Dynamic characterization setup . . . . . . . . . . . . . . 163 C.1.2.2 Dynamic characterization results . . . . . . . . . . . . . 163 C.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 D Phase noise digital modeling 169 E Lock-In OPLL prototype scheme and printed circuit board 173 F Research publications 177 F.1 Patents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 F.2 Book contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 F.3 Journal publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 F.4 Conference publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 F.5 Submitted publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 F.5.1 Book contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 180 F.5.2 Journal publications . . . . . . . . . . . . . . . . . . . . . . . . . 180 F.5.3 Conference publications . . . . . . . . . . . . . . . . . . . . . . . 180
  10. 10. Contents xiii Bibliography 181
  11. 11. List of Figures 1.1 Nielsen’s law prediction of bandwidth and data obtained until 2006 (square points). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 FTTH access roadmap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Coherent receiver scheme, using balanced photo-detection. . . . . . . . . 10 2.2 Optical spectrum of a wavelength to the user environment. λLO is the nominal wavelength of the local oscillator, for a homodyne case. . . . . . 11 2.3 Comparison between homodyne and heterodyne electrical spectra. . . . . 11 2.4 Generic homodyne receiver. . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 Constellation representation of a BPSK signal in the I and Q plane. . . . 14 2.6 Bit error probabilities for BPSK and DPSK, as a function of SNR. . . . . 16 2.7 BPSK error probability for different phase error standard deviations. . . 17 2.8 BER-floor as a function of φe standard deviation. . . . . . . . . . . . . . 18 2.9 Generic homodyne receiver including a differential decoder. . . . . . . . . 19 2.10 Optical Phase Locked Loop simplified scheme . . . . . . . . . . . . . . . 23 2.11 Iso-curves of √ variance of additive noise (left) and phase noise (right), the all for ξ = 1/ 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.12 PLL parameters optimization for 1 ns loop delay and 1 MHz linewidth. . 27 2.13 Iso-curves of the variance of additive noise and phase noise, all for ξ = 2. (a-b) are for a null loop delay, whereas (c-d) are for a 1 ns loop delay. . . 28 2.14 Costas PLL scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.15 Decision driven PLL scheme. . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.16 Balanced PLL scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.17 Balanced PLL phasor scheme. . . . . . . . . . . . . . . . . . . . . . . . . 34 2.18 Noise variance for the balanced PLL scheme. . . . . . . . . . . . . . . . . 36 2.19 General scheme for a subcarrier decision driven optical phase-locked loop. 36 2.20 Scheme of a phase diversity front end. . . . . . . . . . . . . . . . . . . . . 38 2.21 Schematic of phase and polarization diverse receiver. . . . . . . . . . . . 39 2.22 Scheme of a DPSK detection, in a phase and polarization diversity homo- dyne receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.23 LMS error for a Wiener filter with a lag of 10 symbols. . . . . . . . . . . 43 2.24 Scheme of a phase estimator for polarization multiplexed QPSK signals based in regenerative frequency dividers. . . . . . . . . . . . . . . . . . . 44 3.1 Voltage after balanced detector (V3 (t)) as a function of the phase error (φS (t) − φLO (t)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 xv
  12. 12. List of Figures xvi 3.2 Lock-In amplified oPLL schematic. . . . . . . . . . . . . . . . . . . . . . 49 3.3 Spectral distribution of the terms 3.14, 3.15, and 3.16. . . . . . . . . . . . 50 3.4 Phase noise evolution and phase signal introduced by the loop. Inset (b) is a zoom between 200 ns and 300 ns. . . . . . . . . . . . . . . . . . . . . 56 3.5 Loop natural frequency versus damping factor relationship for optimal con- figurations (transient response and phase noise) with 10 ns main loop delay. 57 3.6 BER-floor for optimal configurations as a function of the laser linewidth evaluated at several main loop delays. . . . . . . . . . . . . . . . . . . . . 58 3.7 OPLL time response for a phase step of 1 rad. Inset figure is a zoom between 500 ns and 550 ns. . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.8 Setting time of the optimal configurations for several loop main delays. . 59 3.9 Rise time of the optimal configurations for several loop main delays. . . . 60 3.10 Maximum overshoot of the optimal configurations for several loop delays. 61 3.11 Phase dithering effect for large loop delays. . . . . . . . . . . . . . . . . . 61 3.12 Phase error deviation evaluated at a loop delay of 10 ns. . . . . . . . . . 62 3.13 Pull in margins of the simulated architectures. . . . . . . . . . . . . . . . 63 3.14 Hold in margins of the simulated architectures. . . . . . . . . . . . . . . . 63 3.15 Experimental Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.16 Electrical power spectrum after photodetection. . . . . . . . . . . . . . . 65 3.17 Electrical power spectrum after photodetection. . . . . . . . . . . . . . . 66 4.1 Scheme for a standard intradyne receiver. . . . . . . . . . . . . . . . . . . 70 4.2 Phase error deviation as a function of time interval squared per spectral width product (T 2 ∆ν). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.3 Block diagram of the phase estimation algorithm. . . . . . . . . . . . . . 73 4.4 Phase error deviation as a function of the spectral width per bitrate ratio. 73 4.5 Time-switched diversity differential homodyne receiver scheme. . . . . . . 75 4.6 Example of the time diversity operation, from scheme shown in figure 4.5. Blue line is Vouti , green line is Voutq and red line is Vout after filtering. . . 76 4.7 I, Q, and I+Q outputs Eye-diagrams, at 50 MHz total laser linewidth. . 77 4.8 Statistical normalized eye opening (20Log) for the I/Q receiver (both first and second approach) and a lock-in oPLL. . . . . . . . . . . . . . . . . . 77 4.9 Statistical normalized eye-opening (20log) for the I/Q receiver (both first and second approach) as a function of the laser frequency drift. . . . . . 78 4.10 Receiver scheme for phase noise analysis. . . . . . . . . . . . . . . . . . . 78 4.11 BER-floor of several cases: theoretical (dashed line), theoretical but includ- ing the penalty due to phase switching (dotted line), numerical simulation (continuous line) and measurements (square points). . . . . . . . . . . . . 80 4.12 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.13 Sensitivity results and output eye-diagram . . . . . . . . . . . . . . . . . 82 4.14 Modeled BER as a function of the laser frequency drift per bitrate ratio. 83 4.15 Measured BER as a function of the laser frequency drift. . . . . . . . . . 84 4.16 Time-Switched Phase-Diversity DPSK receiver for channel spacing study. 85 4.17 g1 (t) and g2 (t) pulse shapes and autocorrelation of g2 (t), R2 (τ ) . . . . . . 86
  13. 13. List of Figures xvii 4.18 Spectrum after photodetection: Ideal homodyne reception (a) and using time-switched phase-diversity (b) . . . . . . . . . . . . . . . . . . . . . . 87 4.19 Complex representation of signal samples including interference. . . . . . 88 4.20 Sensitivity penalty due to channel crosstalk. Square points are experimen- tal data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.21 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.22 Receiver scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.23 IQ plane data plotting without differential decoding (left), and after dif- ferential decoding (right) for a signal corrupted by a phase noise due to 100 kHz of total laser linewidth . . . . . . . . . . . . . . . . . . . . . . . 92 4.24 I and Q components membership functions . . . . . . . . . . . . . . . . . 93 4.25 Data estimation scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.26 BER-floor as a function of the laser linewidth at 1 Gb/s . . . . . . . . . 95 4.27 Generic receiver module . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.28 BER floor versus the linewidth per bitrate ratio . . . . . . . . . . . . . . 97 4.29 Differential BPSK receiver√ scheme . . . . . . . . . . . . . . . . . . . . . . 97 4.30 Bessel coefficients for γ = 2 . . . . . . . . . . . . . . . . . . . . . . . . 99 4.31 Comparison between decision on Id (t) (using delay-and-add, DAD) and Im (t) (NDAD). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.32 Maximum tolerated linewidth per bit rate ratio at BER 10−3 as a function of the gain factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.33 Receiver sensitivity for several configurations. . . . . . . . . . . . . . . . 103 4.34 Experimental setup for the direct drive time-switching. . . . . . . . . . . 104 4.35 SNR factor penalty at 10−3 BER vs gain factor γ. . . . . . . . . . . . . . 105 4.36 SNR factor penalty at 10−3 BER vs frequency drift. . . . . . . . . . . . . 105 4.37 I, Q, H, V time distribution of each bit . . . . . . . . . . . . . . . . . . . 106 4.38 Intradyne differential receiver with polarization and phase diversity. . . . 106 4.39 Alternative implementation for achieving time-switched phase and polar- ization diversities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.1 Transceiver with 90◦ hybrid and digital processing. . . . . . . . . . . . . 114 5.2 Transceiver with 90◦ hybrid and analog processing. . . . . . . . . . . . . 115 5.3 Digital configuration scheme using 90◦ hybrid combined with PBS. . . . . 116 5.4 Analog configuration scheme using 90◦ hybrid combined with PBS. . . . 116 5.5 Digital configuration scheme using phase switch. . . . . . . . . . . . . . . 117 5.6 Analog configuration scheme using phase switch. . . . . . . . . . . . . . . 118 5.7 Digital configuration scheme using standard balanced detector. . . . . . . 118 5.8 Analog configuration scheme using standard balanced detector. . . . . . . 119 5.9 Analogue configuration scheme for the oPLL transceiver prototype. . . . 119 5.10 OLT scheme with double fiber and including the birefringent polarization switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.11 OLT scheme with double fiber and including the FRM based polarization switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.1 Pure coupler splitting network scheme. . . . . . . . . . . . . . . . . . . . 126
  14. 14. List of Figures xviii 6.2 Network scheme and routing profile. . . . . . . . . . . . . . . . . . . . . . 126 6.3 SARDANA network architecture. . . . . . . . . . . . . . . . . . . . . . . 127 6.4 OLT and CPE transmission modules. . . . . . . . . . . . . . . . . . . . . 129 6.5 Up-and Down-stream transmission results. . . . . . . . . . . . . . . . . . 130 6.6 Sensitivity penalty as a function of channel spacing. . . . . . . . . . . . . 130 6.7 Network topology and wavelength plan. . . . . . . . . . . . . . . . . . . . 131 6.8 Central office scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.9 Experimental network testbed . . . . . . . . . . . . . . . . . . . . . . . . 133 6.10 Sensitivity results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 A.1 Half-duplex experimental setup. . . . . . . . . . . . . . . . . . . . . . . . 143 A.2 Low pass equivalent of the mixer’s response for a 5 GHz carrier. . . . . . 144 A.3 Sensitivity results for setup described on figure A.1 . . . . . . . . . . . . 144 A.4 Downstream power penalty at BER 10−10 due to extinction ratio. Square points are experiments, whereas continuous line is derived from Eqs. 1 and 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A.5 Experimental setup for single fibre full-duplex measurements. . . . . . . . 146 A.6 Electrical power spectrums after photo-detection at the receiver side: (a) before electrical filtering at the ONU, (b) after electrical filtering at the ONU; (c) before electrical filtering at the OLT, and (d) after electrical filtering at the OLT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 A.7 Sensitivity results for the proposed OLT and ONU architectures. . . . . . 147 A.8 Scenario 1 schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 A.9 Downstream sensitivity curves for the three different network scenarios. . 148 A.10 Upstream sensitivity curves for the three network scenarios. . . . . . . . 149 A.11 Schematic of scenario 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 A.12 Scheme for scenario 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 B.1 Scheme of the proposed analog frequency estimation loop. . . . . . . . . 152 B.2 Optical SSB-modulation VCO. . . . . . . . . . . . . . . . . . . . . . . . . 152 B.3 Frequency discriminator output vs. frequency difference between LO and received signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 B.4 Loop delay impact on loop setting time. . . . . . . . . . . . . . . . . . . 154 B.5 Error signal variance vs. laser linewidth. . . . . . . . . . . . . . . . . . . 155 B.6 Schematic to be implemented. . . . . . . . . . . . . . . . . . . . . . . . . 155 B.7 Max hold function for the output spectrum of the optical VCO. . . . . . 156 B.8 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 C.1 Experimental setup for stability regions characterization. . . . . . . . . . 160 C.2 (a) Wavelength map: Plot of the wavelength (colour scale) in function of reflector currents. (b) Logic stable regions map in function of reflector currents. The phase current for a) and b) is Iph = 2.4 mA. . . . . . . . . 161 C.3 (a) Plot of the wavelength in function of the phase current. Reflector cur- rents are biased at Iref 1 = 22.8 mA and Iref 2 = 8.6 mA. (b, c) Wavelength region map as a function of both reflector currents for a phase current of 1.8 and 2.2 mA, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 162
  15. 15. List of Figures xix C.4 Plots of the wavelength as a function of the gain current for different re- flector currents (Iph = 2.4 mA): (a) Ir ef 1 = 10.8 mA, Iref 2 = 29 mA; (b) Iref 1 = 12.4 mA, Iref 2 = 8.9 mA; (c) Iref 1 = 10.2 mA, Iref 2 = 11.9 mA. . 162 C.5 Experimental setup for transient response characterization. . . . . . . . . 163 C.6 (a) Stable regions map for Iph = 2.4 mA. The black points denote working points used to measure the transition between two modes. The white lines denote such transitions, and the number is used as experiment identifier. (b) Voltage versus time plot of the signals driving reflector sections for experiment 4 (see table C.1). . . . . . . . . . . . . . . . . . . . . . . . . . 164 C.7 (Id.a) WPT plot: Plot of the wavelength versus time, and power (gray scale) versus both wavelength and time for experiment ’Id’ (see table C.1 and/or figure C.6 (a)). (Id.b) SMSR versus time plot for experiment ’Id’ (see table C.1 and/or figure C.6 (a)). . . . . . . . . . . . . . . . . . . . . 165 C.8 (a) WPT plot: Plot of the wavelength versus time, and power (logarithmic colour scale) versus both wavelength and time for experiment 4. (b) Main mode and secondary mode power versus time (in logarithmic scale). . . . 166 C.9 (a) WPT plot zoom of experiment 5: Plot of the wavelength versus time, and power (logarithmic colour scale) versus both wavelength and time. (b) Wavelength versus time of the main and secondary modes of depicted in (a). (c) Zoom of (b) during the transition between inter-mode (1539.8 nm) and mode 2 (1545.2 nm). . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 D.1 Phase of phase noise spectrum. . . . . . . . . . . . . . . . . . . . . . . . 172 E.1 Printed circuit board outline of the Lock-IN OPLL prototype. . . . . . . 173
  16. 16. List of Tables 2.1 Common modulation formats and their SNR differences. . . . . . . . . . 9 2.2 Comparison between BER values, the standard deviation of the phase error process for 1 dB penalty at such BER, and the BER-floor for that standard deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Comparison of phase estimation methods. . . . . . . . . . . . . . . . . . 44 3.1 Phase error standard deviation for the optimal configurations as a function of linewidth and delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2 Convergence values for setting and rise times, at several loop delays. . . . 60 3.3 Table summarizing results at 10 ns delay. . . . . . . . . . . . . . . . . . . 64 3.4 Measured values of the local oscillator linewidth. . . . . . . . . . . . . . . 64 4.1 Fuzzy logic estimator rules base. . . . . . . . . . . . . . . . . . . . . . . . 93 5.1 Phase noise cancellation techniques summary table. The linewidth toler- ance is for a 10−3 BER-floor, whereas the penalty is respect to an ideal system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.2 Polarization handling methods summary table. . . . . . . . . . . . . . . . 113 5.3 Transceiver architectures summary table. The linewidth tolerance is for 1 dB penalty at 10−10 BER, whereas the penalty is respect to an ideal system.120 6.1 Power budget summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 B.1 Comparison between possible optical VCO approaches. . . . . . . . . . . 156 C.1 The acronyms read in ”kind of transition” column, have a brief explana- tion of the working points location: InM (Inside the same Mode); CM (Consecutive Modes in the same super-mode); NCM (Non-Consecutive modes in the same super-mode); CS (Consecutive Super-modes); NCS (Non-Consecutive Super-modes); Iph (change in phase current). . . . . . 167 xxi
  17. 17. Abbreviations ADC Analog to digital converter AFC Automatic frequency control ASK Amplitude shift keying AWC Automatic wavelength control AWG Arrayed waveguide grating BER Bit error ratio BPF Band pass filter BPSK Binary phase shift keying CO Central office CPE Customer premises equipment DAC Digital to analog converter DD Direct detection DFB Distributed feedback DPSK Differential phase shift keying ECL External cavity laser ER Extinction ratio FEC Forward error correction FRM Faraday rotator mirror FTTH Fiber to the home FWHM Full width half maximum GCSR Grating-coupled sampled reflector GPON Gigabit-capable passive optical network I In-phase IM Intensity modulation LD Laser diode LMS Least Mean Square LPF Low pass filter MAP Maximum a posteriori MG-Y modulated-grating Y-branch (laser) MZI Mach-Zehnder interferometer xxiii
  18. 18. Abbreviations xxiv MZM Mach-Zehnder modulator NRZ Non return to zero OLT Optical line termination ONU Optical network unit OPLL Optical phase-locked loop OSA Optical spectrum analyzer OSNR Optical signal to noise ratio OSRR Optical signal to Rayleigh backscattering ratio PBS Polarization beam splitter PI Proportional integral PLC Planar lightwave circuit PLL Phase-locked loop PM Phase modulator PON Passive optical network PPG Pulse pattern generator PRBS Pseudo-random bit sequence PSD Power spectrum density PSK Phase shift keying Q Quadrature QPSK Quadrature phase shift keying RB Rayleigh backscattering RMS Root mean square RN Remote node RZ Return to zero SCM Sub-carrier modulation SIR Signal to interference ratio SNR Signal to noise ratio SOP State of polarization SSB Single side band TDM Time division multiplexing UD Ultra-Dense VCO Voltage controled oscillator VOA Variable optical attenuator WDM Wavelength division multiplexing
  19. 19. Symbols ∆ν Laser linewidth ∆f Signal bandwidth F Electronic receiver equivalent noise factor Fa Excess noise factor Id Photodiode dark current k Boltzmann constant m Modulation index M Multiplication factor of the APD PS Optical received power from transmitter PLO Optical power from local q Electron charge Photodiode responsivity Rb Bit rate RL Load resistor Rx Receiver part T Room temperature Tb Bit time Tx Transmitter part xxv
  20. 20. To my family. . . xxvii
  21. 21. Chapter 1 Introduction More than 40 years have passed since Charles K. Kao publicly demonstrated the pos- sibility of transmitting information through optical fibers [1]. During this time, optical networks have evolved from being an entelechy to a reality that sustains and makes possi- ble the information society in which we live. In recognition, Kao received the 2009 Nobel prize in physics for the groundbreaking achievements concerning the transmission of light in fibers for optical communication. Actually, the concept of optical access networks is very wide and includes many ap- proaches. One of the most popular is the so-called Passive Optical Network (PON) [2], due to its flexibility and low requirements. Typically a PON has a point to multipoint topology, establishing connection between a remote network terminal (Optical Line Ter- mination, OLT) and the customer premises, where an Optical Network Unit (ONU) is placed. When looking at the tendencies of optical access networks, one can realize that user bit rate demand is expected to be increasing in the near future, mostly due to triple-play services and advanced multimedia applications. Precisely, in 1998 Jakob Nielsen predicted that average bandwidth per user gets incremented in a 50 % per year. Until now it has been accomplished and, in case this law is followed, in 2020 each user will demand to get at home an average bandwidth of 1 Gb/s. This makes completely obsolete the technologies commercially available nowadays, and current Fiber To The Home (FTTH) techniques will may get obsolete in long term, being replaced by emerging FTTH technologies. When looking at the several techniques available to upgrade existing access networks, a roadmap can be drawn, shown in figure 1.2. Under the time point of view, now is the deployment of FTTH, point to point (PtP) or GPON/EPON standards. Neverthe- less, PON standardization bodies are pushing technology towards higher FTTH capacity systems, mostly by increasing the aggregate bit rate. Precisely, the IEEE has recently completed and launched the 10G-EPON P802.3av and the FSAN has the NGPON1 rec- ommendation for 10 Gb/s (also named as XGPON) well advanced. In these systems, the 1
  22. 22. Chapter 1. Introduction 2 Figure 1.1: Nielsen’s law prediction of bandwidth and data obtained until 2006 (square points). guarantied effective bandwidth per user will be about 150-300 Mb/s, as the bit rate is shared among e.g. 32 users. These first next generation PONs only encompass a line rate increase (down/up), not yet deployed, and not much is defined in about using WDM technology, which is left for a longer term generation of PONs (like NGPON2), mainly due to the fact that there are several technical hurdles in WDM technologies for PONs, as the ONU colourlessness, the wavelength stability and the cost. So, by increasing the bit rate to 10 Gb/s, the ONU at the CPE is expected to operate at a very high bit rate in the opto-electronics transceivers just to use a small fraction of it. If that is considered in fast electronics (e.g. in CMOS ASICs) the power consumption is almost proportional to the clock speed, one can infer that there is a huge power inefficiency corresponding to the user bandwidth inefficiency; leading to a substantial global power waste. To reverse this tendency, it is obvious that some new philosophy has to be investigated with the corresponding technology challenges. The answer proposed is to try to exploit the pure WDM dimension while minimizing the electronics speed, and maintaining the global numbers unchanged: • Number of served users per PON (in the order of magnitude of 1000). • Guarantied bandwidth per user. If today’s goal is to serve 100 Mb/s, a next step in longer term it can be up to 1 Gb/s; for example current personal computers are nowadays including a 10/100/1000 MEthernet interface, thus 1GEthernet can be considered a very practical goal.
  23. 23. Chapter 1. Introduction 3 • Total fiber bandwidth (40 nm ≈ 5 THz in C-band); although by leaving save guard- bands, and normal modulation formats, only about 1 Tb/s is used in normal prac- tise. Figure 1.2: FTTH access roadmap. A very ultra dense WDM network, with a few GHz channel spacing (below 5 GHz), would be ideal for the numbers presented. With this very narrow channel spacing, many optical carriers could be accommodated on a single fiber and a large number of users could be connected to the network, each of them having an exclusive wavelength. Nevertheless, the major challenge for such networks are the huge technical requirements listed above. The main enabling technology for the proposed network philosophy, capable to reach the presented goals, is coherent transmission. It received great attention at the late 80s and beginning of the 90s, and after a certain period of latency, it has been resurrected. It presents many advantages with respect to the conventional direct detection systems like its excellent wavelength selectivity, low sensitivity and tunability performances [3]. However, it was mainly focused towards long-haul WDM applications, but not seriously considered to be used in access PONs. As these networks have multiple low capacity channels, a major concern in direct-detection (DD) based systems, is the use of optical filters in order to delimitate these channels mainly because of its low selectivity at the GHz spacing scale. Thus, for a very narrow spaced channels, a coherent receiver using electrical filtering is a promising way to solve the problem. Heterodyne optical receivers can be a first approach [4, 5], but due to its inherent image frequency interference, a best solution is homodyne reception. In such homodyne systems, the reception part has a local laser that oscillates at the same wavelength as the received signal. In a second stage both signals are optically mixed and photo-detected. Afterwards, signal processing (analog or digital) is applied to the electrical signal in order to recover transmitted data. The improvements are clear, with respect to other options:
  24. 24. Chapter 1. Introduction 4 • Allows the use of advanced modulation formats (like Phase Shift Keying - PSK, or OFDM), while extending the reach of the networks. • Uses electrical filtering for channel selection, achieving narrow channel spacing while maintaining high speed connection. • Concurrent detection of light signal’s amplitude, phase and polarization recovering more detailed information to be conveyed and extracted, thereby increasing toler- ance to network impairments (such as chromatic dispersion) and improving system performance. • Linear transformation of a received optical signal to an electrical signal that can then be analyzed using modern DSP technology. • Local laser can be tuneable, allowing colourless operation, and it can be reused as an optical source for data transmission. • An increase of receiver sensitivity by 15 to 20 dB compared to incoherent systems. So, homodyne systems match perfectly the proposed network requirements, though some issues like transceivers’ cost have to be addressed. Summarizing, with a coherent transceiver at both sides of the access link, the capabilities can be extended to: • High density, enabling the connection to a high number of users (more than 1000 users per output fiber), meaning narrow channel spacing. • High transmission speed, guaranteeing a minimum bandwidth of 1 Gb/s per user. • External network totally passive, with no insertion of any type of equipment that could include an electrical supply at the external plant (optical distribution net- work). • High power budget, for maintaining a standard central office output power, a low sensitivity receiver has to be implemented, reaching less than −30 dBm. • Highest ONU bandwidth efficiency, with lowest electronics requirements (1 GHz BW), serving every user with the 1G Ethernet LAN standard. • High optical spectral efficiency, by minimizing the wavelength channel spacing below 5 GHz only. • Low power consumption ONUs, reducing it in about one order of magnitude. • Transparency and Independence among channels, in terms of coding, protocol and bit rate, thus avoiding the complex synchronization and ranging of current PONs.
  25. 25. Chapter 1. Introduction 5 1.1 Objectives The objective of this thesis is to evaluate and propose advanced OLT and ONU archi- tectures based on coherent systems for access network deployments. The idea is not to restrict to the receiver architecture itself, but also evaluate the uplink and downlink per- formances of the network in order to find the most effective solution. Specifically the objectives of the thesis are the following: • Identify current coherent systems architectures. Perform an study of the state of the art analyzing the main coherent technologies that are currently being investigated. • Propose advanced architectures that overcome the limitations of the existing ones and fit with the specifications of passive optical networks. • Evaluate some of the advanced techniques by means of simulations and experiments: – Optical Phase-Locked Loops: Costas, Decision-driven, Balanced subcarrier and Lock-In amplified loops. – Phase diversity receivers with zero intermediate frequency: Phase estimation algorithms and differential receivers. • Implement a fully working transceiver prototype of the most reliable and cost- effective architecture. • Research the published work on advanced access network architectures and propose network reuse scenarios to achieve the desired ultra dense WDM operability. • Experimentally demonstrate the performances of the transceiver prototype in the more promising network schemes. 1.2 Complementary work As a complementary work to the accomplishment of the present thesis, other studies have been carried out: IM-DD transmission systems using subcarrier multiplexing, design and study of an automatic frequency control for coherent systems, and tunable laser transient characterization. These studies are understood to help obtaining a more comprehensive view of the concepts developed in the thesis, even if they are rather outside its scope. For the SubCarrier Multiplexed (SCM) system, the objective is to explore an alternative implementation for future PON deployments. Precisely, it is a bi-directional full-duplex 2.5 Gb/s / 1.25 Gb/s in a SCM single fiber PON. The downstream signal is DPSK coded and up-converted by using a 5 GHz subcarrier, while the upstream data is transmitted in
  26. 26. Chapter 1. Introduction 6 burst-mode NRZ. A theoretical model for SCM downstream is proposed and experimen- tally validated. Furthermore, three different deployment scenarios are evaluated: Large coverage area and low density of users; area with medium density of users; and improved access network, covering as much users as possible. For the last case, the power budget could be increased up to 29 dB, matching clearly the typical values of GPON deploy- ments, and serving up to 1280 users. A more detailed report of the system and the tests performed can be found in appendix A. Regarding the automatic frequency control (AFC), details can be found in appendix B. There it is shown how a simulation model was developed for a Cross Product AFC [6]. Parallel to that, a first prototype design was started and several key components (e.g. optical VCO) were identified and characterized, for building the full prototype. Finally, for assuring that everything was the right way, some proof-of-concept experiments were performed in an 8PSK-RZ 30 Gb/s transmission system. Last but not the least, through the high-resolution wavelength-power-time measurement, the dynamic behaviour of a tunable laser (a modulated-grating Y-branch, MG-Y) while switching between modes has been also characterized. A complete report on these mea- surements can be found in appendix C. The optical spectrum at every instant and its evolution along the tuning transient was obtained. With this, it was easy to identify, not only the wavelength temporal drift, but also the transitory mode hopping or interferences over other wavelength channels. 1.3 Thesis overview All the presented objectives and concepts will be explored and analyzed in the present document, which has been organized in 7 chapters. In chapter 2, the most important coherent technologies, that shape the actual scene, will be introduced. After a brief analysis of the coherent detection of BPSK and DPSK modulation formats, optical phase locked loops will be introduced and their influence on phase modulated signals detection will be evaluated. Next, the phase and polarization diversity concepts will be explained as well as the main techniques used in these receivers. Chapter 3 will put forward a new optical phase locked loop (OPLL), based in the lock- in amplification concept. There, the influence of noise will be analyzed, jointly with its associated penalties for a coherent receiver using phase modulated signals. Also, comparison will be performed between this new OPLL and the schemes presented in the state of the art. Chapter 4 will deal with some advances proposed towards an improved and lower cost phase/polarization diversity receiver. There new digital phase/data estimation methods
  27. 27. Chapter 1. Introduction 7 will be described, and a step forward will be taken by proposing a novel coherent receiver type searching time-switched phase and polarization diversities. Chapter 5 describes a set of possible OLT and ONU designs. Special emphasis is put on the possible transceiver architectures, aiming to use the same design at both sides, OLT and ONU. Chapter 6 will give an overview of standard and advanced topologies for FTTx, driven by the concepts presented in this first chapter and taking into account the transceivers discussed in chapter 5. Afterwards, two case studies are presented demonstrating exper- imentally the two more promising network architectures. Finally, the conclusions chapter will summarize the work and present future research lines to continue developing this topic.
  28. 28. Chapter 2 State of the art 2.1 Modulation formats The modulation format to be used in a network is strongly linked with the fact of how it will be generated at the transmitter side, and the type of reception. As an example, a table can be found, where SNR increments are depicted when switching from one modulation format to another [7]. This is shown in table 2.1. In that table, the modulation format that has better SNR performances is homodyne phase shift keying (PSK). Heterodyne Homodyne IM-DD ASK FSK PSK ASK PSK IM-DD - 10/25 dB 13/28 dB 16/31 dB 13/28 dB 19/34 dB ASK Het. −10/−25 dB - 3 dB 6 dB 3 dB 9 dB FSK Het. −13/−28 dB −3 dB - 3 dB 0 dB 6 dB PSK Het. −16/−31 dB −6 dB −3 dB - 3 dB 3 dB ASK Hom. −13/−28 dB −3 dB 0 dB −3 dB - 6 dB PSK Hom. −19/−34 dB −9 dB −6 dB −3 dB −6 dB - Table 2.1: Common modulation formats and their SNR differences. In the access networks that are being deployed today, the modulation format used is IM/DD due to its simplicity. However, its low SNR performances are a major inconvenient when regarding an extended reach access network. That is the reason why it would be preferable to use a more robust format, like PSK, and a coherent detection scheme. According to table 2.1, a minimum SNR increment of 19 dB is expected when migrating from IM/DD to a PSK with homodyne detection. Of course, it is not a fixed increment, as it also depends on the photodetector type. E.g. if a PIN diode is used, the receiver performances in IM-DD are going to be worse than when using an avalanche photodiode. 9
  29. 29. Chapter 2. State of the art 10 2.2 Homodyne systems Nowadays, optical fibre communications are, in a certain sense, as primitive as radio communications when crystal (galena) radio receivers were used. The reason is that there is no need to recover phase information of the optical carrier. Among all, coherent optical transmission systems were investigated at the late 80s, but abandoned due to electronics limitations and the irruption of the EDFA at the beginning of the 90s. Almost 20 years after, technology is more advanced, allowing a full development of coherent systems. Coherent systems present many advantages with respect to the conventional direct de- tection systems because of its excellent wavelength selectivity and low sensitivity. First, in a WDM environment, when using a coherent receiver, channel selection is done after photo-detection, i.e. is done by an electrical filter (instead of an optical filter); thus, se- lectivity is defined by this filter performances. Regarding sensitivity, coherent reception allows to use PSK and other advanced modulation formats. This fact, combined with the use of a local oscillator, is the reason why they can improve sensitivity in 19 dB up to 34 dB, when compared to an Intensity-Modulation Direct-Detection (IM-DD) system [7]. Figure 2.1: Coherent receiver scheme, using balanced photo-detection. The main difference between DD and coherent systems, is that the received signal is mixed with a local laser in an optical coupler. Afterwards, the resulting combination is photo-detected. This is shown in figure 2.1. Current after photo-detection Ip (t) has all information carried by the received optical field. In this chapter, a review of the synchronous detection technology is presented. Depending on the use of an intermediate frequency stage, coherent systems can be homodyne or heterodyne. In a heterodyne system, incoming signal is downconverted into an intermediate frequency (usually higher than bit rate). Afterwards, in a second stage, signal is mixed with an electrical oscillator, now downconverting into a baseband signal. As signals are electrically synchronized inside intermediate frequency module, it is an interesting implementation of a synchronous receiver. Namely, it avoids the need of very narrow lasers. However, the problems are: • This Intermediate Frequency (IF) is very high, limiting the electronics functionality.
  30. 30. Chapter 2. State of the art 11 • The electrical spectrum is doubled, thus introducing a 3 dB penalty. This is shown in figure 2.3. • An additional filter should be placed in order to avoid image frequency in a multi- channel environment. Figure 2.2: Optical spectrum of a wavelength to the user environment. λLO is the nominal wavelength of the local oscillator, for a homodyne case. Figure 2.3: Comparison between homodyne and heterodyne electrical spectra. A further simplification, at least at a first glance, is the use of homodyne systems. In such systems intermediate frequency is zero. This avoids image frequency problems and the 3 dB penalty. But it needs to directly synchronize local laser and received signals, entailing some handicaps: • Laser phase noise impact on overall receiver performances. • Penalty due to synchronization loop delay. Optical homodyne systems were presented at the 80s, when one of the main investigation fields was coherent systems. In order to properly synchronize local laser and received signals, early systems used an optical Phase-Locked Loop (OPLL) module. But the optical path between local laser and optical mixer (i.e. optical hybrid + photo-detection stages) introduces a non-negligible loop delay, resulting in a significant penalty. Thus, in order to avoid it, extremely low linewidth lasers had to be used.
  31. 31. Chapter 2. State of the art 12 Another approach towards homodyne reception came later, with the concept of zero- IF/intradyne diversity receivers. The main goal of these type of receivers is to replace the feedback loop (OPLL) by a feedforward processing. So, phase locking is done inside this feedforward processing. 2.3 PSK receivers As shown in the introduction, the main core of a coherent system is the receiver. This subsystem, properly combined with a robust modulation format, improves the optical link as commented. This section is organized as follows: First, homodyne receivers are introduced and ba- sic results are summarized. Next OPLLs are introduced and the existing approaches developed are explained. Finally, optical diversity techniques are discussed. 2.3.1 Homodyne receiver performances In this subsection the basic results of an ideal homodyne receiver will be surveyed. First using Binary PSK modulation and afterwards using differential encoded PSK. Also the phase errors influence (mainly due to laser phase noise) will be theoretically evaluated for both cases. These modulation formats have been chosen because of their simplicity, robustness and high performances, as seen in table 2.1. A generic homodyne receiver can be shown in figure 2.4, for a balanced structure. Figure 2.4: Generic homodyne receiver. From that scheme, the following set of equations can be written [8]: eS (t) = PS exp j ω0 t + φS (t) (2.1) eLO (t) = PLO exp j ω0 t + φLO (t) (2.2)
  32. 32. Chapter 2. State of the art 13 where eS (t) and eLO (t) are the optical field expressions for the received and local oscil- lator signals respectively; φS (t) and φLO (t) are the received and local oscillator phases respectively; and ω0 t is the nominal wavelength (assuming no mismatch). Also the complex amplitudes of both signals can be defined as: ES (t) = PS ejφS (t) (2.3) jφLO (t) ELO (t) = PLO e (2.4) By agreement the optical coupler is assumed to have the following transfer matrix: 1 1 1 S=√ (2.5) 2 1 −1 As the optical combining device is a standard coupler and ideally there is no wavelength mismatch, the resulting currents I1 (t), I2 (t) at the output of each photodetector can be expressed as: 2 1 I1 (t) = ES (t) + ELO (t) (2.6) 2 = (PS + PLO ) + PS PLO cos φS (t) − φLO (t) (2.7) 2 2 1 I2 (t) = − ES (t) + ELO (t) (2.8) 2 = (PS + PLO ) − PS PLO cos φS (t) − φLO (t) (2.9) 2 being the responsivity of the photodiode. Then, the resulting current after the balanced receiver Ip (t) can be written as: Ip (t) = I1 (t) − I2 (t) (2.10) = 2 PS PLO cos φS (t) − φLO (t) (2.11) The signal amplitude at regeneration is highly dependant on the phase mismatch φS (t) − φLO (t) that must be minimized. The most used module to do so is the OPLL. The fluctuation phase error mainly comes from the lasers phase noise.
  33. 33. Chapter 2. State of the art 14 2.3.1.1 SNR and BER for BPSK signals One of the most important advantages of homodyne PSK systems is the increase in receiver sensitivity. For BPSK, the bits are coded into two symbols: 0 and 180. Thus, In-phase and Quadrature components of the coded signal are going to be as shown in figure 2.5. Please note that for the receiver proposed, the decision is made along the real (In-phase) axis. Figure 2.5: Constellation representation of a BPSK signal in the I and Q plane. When making a first analysis, the photodetected signal after balanced detection Ip (t) is going to be low-pass filtered by a matched filter [9] and, next, it enters at the decision and sampling stage. Thus, the bit decision is made upon Ip (t) once filtered. By now, it can be only assumed that the receiver current fluctuates because of photodetector’s shot noise (in case a PIN diode is used) and thermal noise. The variance of those current fluctuations is obtained by adding the two contributions [10]: σ 2 = σS + σT 2 2 (2.12) 2 σS = 2q (PS + PLO ) + ID BE (2.13) 2 4kB T σT = FN BE (2.14) RL where ID is the dark current of the photodiode (almost negligible), q is the electron charge, BE is the most limiting electrical bandwidth, kB is the Boltzmann’s constant, T is the temperature in K, FN is the noise figure of the electrical stage, and RL is the impedance of the electrical part.
  34. 34. Chapter 2. State of the art 15 From this model, the SNR can be calculated when φS (t)−φLO (t) = 0 dividing the average signal power by the average noise power: I 2 SNR = (2.15) σ2 2 4 PS PLO = (2.16) 4kB T 2q (PS + PLO ) + ID BE + RL FN BE Assuming the symbols are equiprobable, the bit error probability Pe can be calculated as: 1 Pe = [P (0◦ |180◦ ) + P (180◦ |0◦ )] (2.17) 2 where P (0◦ |180◦ ) is the probability of deciding 0◦ when 180◦ is received, and P (180◦ |0◦ ) is the probability of deciding 180◦ when 0◦ is received. As shown in figure 2.5, the only change between 0◦ and 180◦ is the sign along the real axis, whereas the modulus remains constant. Thus, the optimum decision threshold is going to be 0 [10]. Simplifying the development and assuming Gaussian statistics, the conditioned probabilities can be written as [9]: 0 1 SNR P (0◦ |180◦ ) = √ exp − dI (2.18) σ 2π −∞ 2 ∞ ◦ ◦ 1 SNR P (180 |0 ) = √ exp dI (2.19) σ 2π 0 2 and they can be expressed in terms of the complementary error function (erfc): 1 SN R P (0◦ |180◦ ) = P (180◦ |0◦ ) = erfc (2.20) 2 2 So, the bit error probability Pe can be calculated as [10]: 1 SNR Pe = erfc (2.21) 2 2 Figure 2.6 shows how the error probability varies with the SNR. Usually, the receiver sensitivity corresponds to the average optical power for which SNR = 15.6 dB, being Pe = 10−9 . Another SNR useful value is 9.8, that corresponds to a Pe = 10−3 because if Forward Error Correction (FEC) codes are used, errors can be corrected after data decision, and this 10−3 can be turned on to 10−9 or lower [11].
  35. 35. Chapter 2. State of the art 16 Figure 2.6: Bit error probabilities for BPSK and DPSK, as a function of SNR. 2.3.1.2 Phase errors in homodyne detection of BPSK signals In this subsubsection the phase noise influences on the BPSK ideal receiver are going to be evaluated. It is assumed that there is a phase tracking and/or estimation/cancellation in order to keep the phase errors sufficiently small. To start such analysis, the received photocurrent has to be redefined as: Ip (t) = 2 PS PLO cos φd (t) + φe (t) (2.22) φS (t) = φd (t) + φN S (t) (2.23) φLO (t) = φN LO (t) (2.24) φe (t) = φN S (t) − φN LO (t) (2.25) where φN S (t) and φN LO (t) are the noise contributions to the phases of the received and local oscillator signals respectively, and φd (t) is a signal containing data ideal pulses (0◦ -180◦ ). Obviously, the phase error term (φe (t)) is modeled as a random variable. For the BPSK case, its statistical properties depend on the phase tracking method. Previously, the error probability has been found in terms of SNR. The expression used assumes a perfect phase match, but usually there is a certain amount of phase error. As there is a phase tracking, it can be assumed that φe (t) varies at a speed much lower than data. i.e. it remains constant during the symbol interval [12]. In this case, the conditional error probability in terms of the sampled phase error φe is: 1 SNR Pe (φe ) = erfc cos(φe ) (2.26) 2 2
  36. 36. Chapter 2. State of the art 17 whereas the average error probability is written as: π 1 SNR Pe = p(φe )erfc cos(φe ) dφe (2.27) 2 −π 2 being p(φe ) the probability density function of the phase error. The statistic of the phase is usually approximated by a Gaussian distribution with zero mean. In this case the average error probability becomes: π φ2e 1 − 2σ 2 SNR Pe = e φe erfc cos(φe ) dφe (2.28) 2 2 2πσφe −π 2 In figure 2.7 the error probability is plotted versus the SNR for several phase error stan- dard deviation values. As can be seen, the fact of having a phase error deviation different from zero gives an error floor, i.e., the error probability limit is a finite value. A useful example can be that the standard deviation of phase error must be less than 10◦ in order to maintain less than 0.5 dB power penalty at 10−9 BER. Figure 2.7: BPSK error probability for different phase error standard deviations. In the limit case of infinite SNR, equation 2.28 gives the floor value of the probability of error. It only depends on the variance of the phase error, and gives the limit value. After
  37. 37. Chapter 2. State of the art 18 some algebra, such floor is found to be [13]: φ2e +∞ − φ2e 1 − 2σ 2 2 2σ 2 Pe = e φe dφe = e φe dφe (2.29) 2 2 π 2πσφe cosφe <0 2πσφe 2 Evaluating this integral, the BER-floor value can be easyly plotted and see how the BER is limited by phase tracking errors. This is depicted in figure 2.8, showing that a BER of 10−9 cannot be achieved when σφe is higher than 14.9◦ . Figure 2.8: BER-floor as a function of φe standard deviation. BER Standard deviation for 1 dB penalty BER-floor equivalent 10−9 11◦ 2.31 · 10−16 10−3 19◦ 2.04 · 10−6 4.86 · 10−6 14.9◦ 10−9 2.54 · 10−1 28◦ 10−3 Table 2.2: Comparison between BER values, the standard deviation of the phase error process for 1 dB penalty at such BER, and the BER-floor for that standard deviation. This BER-floor will be useful for evaluating the architectures to be discussed during the present thesis. Thus, it is appropriate to represent in table 2.2 a set of values that will be used later. The idea is to have the floor values (easy to find) and search the equivalent BER, for 1 dB penalty. For example, a BER of 10−9 has the 1 dB penalty point at a phase error standard deviation of 11◦ , which corresponds to a BER-floor of 2.31 · 10−16 .
  38. 38. Chapter 2. State of the art 19 2.3.1.3 SNR and BER for DPSK signals In the case of differentially encoded PSK signals, the coherent detector becomes slightly different, as shown in figure 2.9. In some books it is referred as differentially coherent detector [12]. Special emphasis must be put on the multiplier used, as it should be a four quadrant multiplier. Also, the local oscillator does not have to be tracking the received signal phase, since this kind of detection is more robust against phase mismatch. Figure 2.9: Generic homodyne receiver including a differential decoder. As now the receiver front-end is the same as used in the previous subsection, the SNR expression is the same of equation 2.16. Nevertheless in this case the inputs to the multiplier during the kth bit interval are: Ip (t) + n(t) = [I + Ini (t)] cos(φd (t) − φe (t)) − Inq (t) sin(φe (t)) (2.30) Ip (t−Tb )+n(t−Tb ) = [I +Ini (t)] cos(φd (t−Tb )−φe (t−Tb ))−Inq (t) sin(φe (t−Tb )) (2.31) The low-pass filter then removes the high-frequency terms from the product, leaving at the input of the decision circuit the decision variable amplitude Y . In case the phase error difference between consecutive symbols is negligible (φe (t) ≈ φe (t − Tb )), Y can be written as: 1 1 Y = (I + Ini )(I + Ini ) + Inq Inq = (α2 − β 2 ) (2.32) 2 2 where all four noise components are independent identically distributed Gaussian random variables with zero mean and variance 2σ 2 . α2 and β 2 variables can be expressed as: α2 = (I + αi )2 + αq 2 (2.33) 2 β = βi2 + 2 βq (2.34)
  39. 39. Chapter 2. State of the art 20 with 1 αi = (Ini + Ini ) (2.35) 2 1 αq = (Inq + Inq ) (2.36) 2 1 βi = (Ini − Ini ) (2.37) 2 1 βq = (Inq − Inq ) (2.38) 2 Note that αi , αq , βi , βq are zero-mean Gaussian random variables with variance σ 2 . There- fore, α has a Rician probability density function, whereas β has a Rayleigh probability density function [14]. The average probability of error is found to be when Y < 0, in the case that the consec- utive symbols (ak , ak−1 ) are equal: Pe = P (Y < 0|ak = ak−1 ) = P (α2 < β 2 ) = P (β > α) (2.39) So, it can be calculated in a more direct form as: ∞ ∞ Pe = pα (α)pβ (β)dαdβ (2.40) 0 α where pα (α) and pβ (β) are the probability density functions of α and β respectively. Calculating the inner integral (β), the probability of error becomes: ∞ α 2α2 + I 2 2Iα Pe = exp I0 dα (2.41) 0 σ2 σ2 σ2 √ √ So, making a change of variables by letting λ = 2α and ν = I/ 2: ∞ 1 −I 2 λ λ2 + ν 2 λν Pe = exp exp I0 dλ (2.42) 2 2σ 2 0 σ2 2σ 2 σ2 Now, the integrand is exactly the same function as the Rician probability function, with a total area equal to unity. Hence, the final result becomes: 1 −I 2 1 −SNR Pe = exp = exp (2.43) 2 2σ 2 2 2 Just for comparing both signaling cases, figure 2.6 shows the two error probabilities (BPSK and DPSK) as a function of SNR. Even for a Gaussian noise assumption, they
  40. 40. Chapter 2. State of the art 21 exhibit different statistics when calculating Pe . Nevertheless, note that at 10−9 the dif- ference between them is of only 0.5 dB. 2.3.1.4 Phase errors in homodyne detection of DPSK signals Just following what has been shown for the BPSK case, the expression reported in equa- tion 2.22 can also be used. For the DPSK case, φe statistical properties depend on the phase noise source. If it is only coming from the lasers’ phase noise, it can be assumed that φe (t) varies at a speed much lower than data. i.e. it remains constant during the symbol interval. Please, remember that phase noise is always of the order of MHz, while data is supposed to be of the order of Gb/s (3 orders of magnitude difference). In this case, the conditional error probability in terms of phase error is: 1 −SNR Pe (θ) = exp cos2 (θ) (2.44) 2 2 where θ = φe (t0 ) − φe (t0 − Tb ), being t0 the optimum sampling time. So, now the average error probability can be written as: π 1 −SNR Pe = p(θ) exp cos2 (θ) dθ (2.45) 2 −π 2 Regarding θ statistics, the laser phase noise is modeled as a Wiener process [10]: t φe (t) = φP N (τ )dτ (2.46) 0 where φP N (t) is a white Gaussian process with variance 2π∆ν, where ∆ν is the total laser spectral width (also known as Full Width Half Maximum - FWHM). Thus, assuming Tb t0 : θ = φe (t0 ) − φe (t0 − Tb ) (2.47) t0 t0 −Tb = φP N (τ )dτ − φP N (τ )dτ (2.48) 0 0 Tb = φP N (τ )dτ (2.49) 0 2 This means that θ is also a Gaussian process [14] with zero mean and variance σθ = 2π∆νTb .
  41. 41. Chapter 2. State of the art 22 Continuing the mathematical development, the average error probability becomes: π θ2 1 − 2σ 2 −SNR Pe = e θ exp cos2 (θ) dθ (2.50) 2 2 2πσθ −π 2 Please note that this expression is almost the same that has been found in the previous subsection (equation 2.28). Thus, figure 2.7 is also valid for the DPSK case, except that now the phase error standard deviation is known. The 0.5 dB penalty point found before (10◦ phase error standard deviation), now means that Rb = 1/Tb should be higher than π∆ν/50. Similarly to what was shown before, in the limit case of infinite SNR, equation 2.50 gives the floor value of the probability of error. Thus, equation 2.29 also gives the BER-floor values for DPSK case. 2.3.2 oPLL based systems A phase locked loop is a feedback system in which the feedback signal is used to lock the output frequency and phase of the input signal. Phase locked loops in electrical domain have been one of the most frequently used com- munications circuits. Several applications like filtering, frequency synthesis, motor speed control, signal detection, etc. are common users of such device. While electrical PLL (used in heterodyne systems) is a well known device, optical version (used in homodyne systems) offers several technological problems which have delayed its development to the general market. Next figure 2.10 shows the basic components for a simplified OPLL when no noise influence is considered. The three basic elements are the phase comparator, the electrical filter and the VCO module. In our case, the phase comparator is comprised by the optical coupler and the photodetection front end, while the VCO module is a tunable laser. After filtering DC terms and high frequency terms at the output of phase comparator, the signal remaining is: V (t) = GP C PS sin(φe (t)) (2.51) √ where phase error is defined as φe (t) = φS (t) − φLO (t), and GP C = RL PLO This leads to the well-known PLL characteristic equation: +∞ dφe (t) dφS (t) dφLO (t) dφS (t) = − = − AG sin φe (τ ) f (t − τ )dτ (2.52) dt dt dt dt −∞
  42. 42. Chapter 2. State of the art 23 Figure 2.10: Optical Phase Locked Loop simplified scheme √ where A = PS ; G = GV CO GP C , f (t) is the loop filter transfer function, and GV CO is the VCO gain in [rad/sV]. Although the PLL is not linear because the phase detector is non-linear, it can be accu- rately modelled as a linear device when the phase difference between the phase-detector input signals is small. For the linear analysis, it is assumed that the phase detector output is a voltage which is a linear function of the difference in phase between its inputs. This offers an easy way to study its behaviour by means of Laplace transformation, being the OPLL transfer function: ΦLO (S) AGF (S) H(S) = = (2.53) ΦS (S) S + AGF (S) A Proportional-Integral (PI) filter is usually used to act as a PLL regulator. Then F (S) is: 1 + τ2 S F (S) = (2.54) τ1 S and the OPLL transfer function becomes: 2 2ξωn S + ωn H(S) = (2.55) S 2 + 2ξS + ωn2 Being ωn = AG/τ1 the natural frequency of the PLL and ξ = ωn τ2 /2 the loop damping coefficient. 2.3.2.1 Additive noise impact in a generic OPLL Phase Locked Loop’s target is to match input signal phase. However this objective can be limited by several parameters which affect the receiver performance. Additive noise
  43. 43. Chapter 2. State of the art 24 can interfere in the phase locked loop behaviour. In fact this noise produces an additional phase error that reduces the system’s functionality. In order to show a simplified model, a unique additive noise source (VN (t)) has been considered, added after the phase comparator module, and coming from the input shot noise plus electronic noise. Thus, the resulting characteristic equation for this case, in the Laplace domain, is found to be [15]: SΦS (S) GV CO VN (S)F (S) Φe (S) = − (2.56) S + AGF (S) S + AGF (S) The noise transfer function can be defined as follows: ΦLO (S) Φe (S) GV CO F (S) H(S) AS (S) = =− =− =− (2.57) VN (S) ΦS (S)=0 VN (S) ΦS (S)=0 S + AGF (S) AGP C The phase error is given by the contribution of the signal and the contribution of shot noise. In steady state the characteristic equation is linear and the superposition principle can be applied. Then, Φe (S) can be decomposed into two contributions (signal and noise): Φe (S) = ΦeS (S) + ΦeN (S) (2.58) where H(S) GV CO F (S) ΦeN (S) = VN (S)AS (S) = −VN (S) = −VN (S) (2.59) AGP C S + AGF (S) The interesting parameter is the phase error variance. Assuming φeN (t) is a white Gaus- sian process, and that VN (t) has as a power spectrum density SAN (ω): 2 σAN = φ2 (t) eN (2.60) +∞ dω = SAN (ω)|AS (ω)|2 (2.61) −∞ 2π +∞ 1 dω = 2 G2 SAN (ω)|H(ω)|2 (2.62) A PC −∞ 2π 1 BN = (2.63) SNR Be +∞ where the noise equivalent bandwidth of the PLL has been defined as BN = −∞ |H(ω)|2 dω , 2π and Be is the electrical input bandwidth (typically 0.7 · Rb ).

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