homodyne olt-onu design for access optical networks

Ph. D. Thesis

Optical Communications GroupDepartment of Signal Theory and Communications

Universitat Politècnica de Catalunya

Homodyne OLT-ONU design for access optical networks

AuthorJosep Mª Fàbrega

AdvisorJosep Prat

Thesis presented in fulfillment of the doctorate program of the signal theory and communications department

March 2010

The work described in this thesis was performed in the Signal Theory and Communications department of the Universitat Politècnica de Catalunya / BarcelonaTech.

Josep Mª FàbregaHomodyne OLT-ONU design for access optical networksSubject 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: 978-84-693-3168-2Reg: 10/53978

”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

UNIVERSITAT POLITECNICA DE CATALUNYA (UPC)

AbstractOptical Communications Group (GCO)

Signal Theory and Communications Department (TSC)

Doctor of Philosophy

by Josep M. Fabrega

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.

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Department or School Web Site URL Here (include http://)

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 Jose Lazaro, Bernhard Schrenk,

Carlos Bock, Joan Gene and Jaume Comellas for their advice and fruitful discussions,

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. Lopez, Mireia Omella, Victor Polo and specially Francesc Bonada,

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-

logical order: Lluıs Vilabru, Joan Miquel Pinol, 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

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

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 frequencydividers . . . . . . . . . . . . . . . . . . . . . . . . . . . 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-Loeve series expansion phase estimation . . . . . . . . . 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

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, withanalog processing . . . . . . . . . . . . . . . . . . . . . . 116

5.2.2 Transceivers based in time-switching phase diversity . . . . . . . . 117

5.2.2.1 Transceiver including phase switch with digital processingand standard balanced detector . . . . . . . . . . . . . . 117

5.2.2.2 Transceiver including phase switch with analog processingand standard balanced detector . . . . . . . . . . . . . . 117

5.2.2.3 Transceiver including direct laser switching with digitalprocessing and standard balanced detector . . . . . . . . 117

5.2.2.4 Transceiver including direct laser switching with analogprocessing 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

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

Contents xiii

Bibliography 181

List of Figures

1.1 Nielsen’s law prediction of bandwidth and data obtained until 2006 (squarepoints). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 thenominal 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 the variance of additive noise (left) and phase noise (right),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 signalsbased 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

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 linewidthevaluated at several main loop delays. . . . . . . . . . . . . . . . . . . . . 58

3.7 OPLL time response for a phase step of 1 rad. Inset figure is a zoombetween 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 spectralwidth 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 firstand second approach) and a lock-in oPLL. . . . . . . . . . . . . . . . . . 77

4.9 Statistical normalized eye-opening (20log) for the I/Q receiver (both firstand 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

List of Figures xvii

4.18 Spectrum after photodetection: Ideal homodyne reception (a) and usingtime-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 to100 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) andIm(t) (NDAD). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.32 Maximum tolerated linewidth per bit rate ratio at BER 10−3 as a functionof 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 polarizationswitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.11 OLT scheme with double fiber and including the FRM based polarizationswitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

6.1 Pure coupler splitting network scheme. . . . . . . . . . . . . . . . . . . . 126

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. Squarepoints are experiments, whereas continuous line is derived from Eqs. 1 and2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 theONU; (c) before electrical filtering at the OLT, and (d) after electricalfiltering 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 andreceived 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 ofreflector currents. (b) Logic stable regions map in function of reflectorcurrents. 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 Iref1 = 22.8 mA and Iref2 = 8.6 mA. (b, c) Wavelengthregion map as a function of both reflector currents for a phase current of1.8 and 2.2 mA, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 162

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) Iref1 = 10.8 mA, Iref2 = 29 mA; (b)Iref1 = 12.4 mA, Iref2 = 8.9 mA; (c) Iref1 = 10.2 mA, Iref2 = 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 workingpoints used to measure the transition between two modes. The white linesdenote such transitions, and the number is used as experiment identifier.(b) Voltage versus time plot of the signals driving reflector sections forexperiment 4 (see table C.1). . . . . . . . . . . . . . . . . . . . . . . . . . 164

C.7 (Id.a) WPT plot: Plot of the wavelength versus time, and power (grayscale) versus both wavelength and time for experiment ’Id’ (see table C.1and/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 (logarithmiccolour scale) versus both wavelength and time for experiment 4. (b) Mainmode 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

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 errorprocess for 1 dB penalty at such BER, and the BER-floor for that standarddeviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Comparison of phase estimation methods. . . . . . . . . . . . . . . . . . 44

3.1 Phase error standard deviation for the optimal configurations as a functionof 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 idealsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.2 Polarization handling methods summary table. . . . . . . . . . . . . . . . 113

5.3 Transceiver architectures summary table. The linewidth tolerance is for 1dB 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-Consecutivemodes in the same super-mode); CS (Consecutive Super-modes); NCS(Non-Consecutive Super-modes); Iph (change in phase current). . . . . . 167

xxi

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

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

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

To my family. . .

xxvii

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

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.


• 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:


• 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.


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


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


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.

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 HomodyneIM-DD ASK FSK PSK ASK PSK

IM-DD - 10/25 dB 13/28 dB 16/31 dB 13/28 dB 19/34 dBASK Het. −10/−25 dB - 3 dB 6 dB 3 dB 9 dBFSK Het. −13/−28 dB −3 dB - 3 dB 0 dB 6 dBPSK Het. −16/−31 dB −6 dB −3 dB - 3 dB 3 dB

ASK Hom. −13/−28 dB −3 dB 0 dB −3 dB - 6 dBPSK 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

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.


• 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 thenominal 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.


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(ω0t+ φS(t)

))(2.1)

eLO(t) =√PLO exp

(j(ω0t+ φLO(t)

))(2.2)


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 ω0t is the nominal wavelength (assuming no mismatch).

Also the complex amplitudes of both signals can be defined as:

ES(t) =√PSe

jφS(t) (2.3)

ELO(t) =√PLOe

jφLO(t) (2.4)

By agreement the optical coupler is assumed to have the following transfer matrix:

S =1√2

[1 1

1 −1

](2.5)

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:

I1(t) = <

∣∣∣∣∣√

1

2

(ES(t) + ELO(t)

)∣∣∣∣∣2

(2.6)

=<2

(PS + PLO) + <√PSPLO cos

(φS(t)− φLO(t)

)(2.7)

I2(t) = <

∣∣∣∣∣√

1

2

(− ES(t) + ELO(t)

)∣∣∣∣∣2

(2.8)

=<2

(PS + PLO)−<√PSPLO cos

(φS(t)− φLO(t)

)(2.9)

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<√PSPLO 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.


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]:

σ2 = σ2S + σ2

T (2.12)

σ2S = 2q

(<(PS + PLO) + ID

)BE (2.13)

σ2T =

(4kBT

RL

)FNBE (2.14)

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.


From this model, the SNR can be calculated when φS(t)−φLO(t) = 0 dividing the average

signal power by the average noise power:

SNR =〈I〉2

σ2(2.15)

=4<2PSPLO

2q(<(PS + PLO) + ID

)BE +

(4kBTRL

)FNBE

(2.16)

Assuming the symbols are equiprobable, the bit error probability Pe can be calculated

as:

Pe =1

2[P (0|180) + P (180|0)] (2.17)

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]:

P (0|180) =1

σ√

2π

∫ 0

−∞exp

(− SNR

2

)dI (2.18)

P (180|0) =1

σ√

2π

∫ ∞0

exp

(SNR

2

)dI (2.19)

and they can be expressed in terms of the complementary error function (erfc):

P (0|180) = P (180|0) =1

2erfc

(√SNR

2

)(2.20)

So, the bit error probability Pe can be calculated as [10]:

Pe =1

2erfc

(√SNR

2

)(2.21)

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].


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<√PSPLO cos

(φd(t) + φe(t)

)(2.22)

φS(t) = φd(t) + φNS(t) (2.23)

φLO(t) = φNLO(t) (2.24)

φe(t) = φNS(t)− φNLO(t) (2.25)

where φNS(t) and φNLO(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:

Pe(φe) =1

2erfc

(√SNR

2cos(φe)

)(2.26)


whereas the average error probability is written as:

Pe =1

2

∫ π

−πp(φe)erfc

(√SNR

2cos(φe)

)dφe (2.27)

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:

Pe =1

2√

2πσ2φe

∫ π

−πe− φ2e

2σ2φe erfc

(√SNR

2cos(φe)

)dφe (2.28)

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


some algebra, such floor is found to be [13]:

Pe =1√

2πσ2φe

∫cosφe<0

e− φ2e

2σ2φe dφe =

2√2πσ2

φe

∫ +∞

π2

e− φ2e

2σ2φe dφe (2.29)

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 equivalent10−9 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 errorprocess 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.


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+I ′ni(t)] cos(φd(t−Tb)−φe(t−Tb))−I ′nq(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:

Y =1

2(I + Ini)(I + I ′ni) + InqI

′nq =

1

2(α2 − β2) (2.32)

where all four noise components are independent identically distributed Gaussian random

variables with zero mean and variance 2σ2. α2 and β2 variables can be expressed as:

α2 = (I + αi)2 + α2

q (2.33)

β2 = β2i + β2

q (2.34)


with

αi =1

2(Ini + I ′ni) (2.35)

αq =1

2(Inq + I ′nq) (2.36)

βi =1

2(Ini − I ′ni) (2.37)

βq =1

2(Inq − I ′nq) (2.38)

Note that αi, αq, βi, βq are zero-mean Gaussian random variables with variance σ2. 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 < β2) = P (β > α) (2.39)

So, it can be calculated in a more direct form as:

Pe =

∫ ∞0

∫ ∞α

pα(α)pβ(β)dαdβ (2.40)

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:

Pe =

∫ ∞0

α

σ2exp

(2α2 + I2

σ2

)I0

(2Iα

σ2

)dα (2.41)

So, making a change of variables by letting λ =√

2α and ν = I/√

2:

Pe =1

2exp

(−I2

2σ2

)∫ ∞0

λ

σ2exp

(λ2 + ν2

2σ2

)I0

(λν

σ2

)dλ (2.42)

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:

Pe =1

2exp

(−I2

2σ2

)=

1

2exp

(−SNR

2

)(2.43)

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


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:

Pe(θ) =1

2exp

(−SNR

2cos2(θ)

)(2.44)

where θ = φe(t0)−φe(t0−Tb), being t0 the optimum sampling time. So, now the average

error probability can be written as:

Pe =1

2

∫ π

−πp(θ) exp

(−SNR

2cos2(θ)

)dθ (2.45)

Regarding θ statistics, the laser phase noise is modeled as a Wiener process [10]:

φe(t) =

∫ t

0

φPN(τ)dτ (2.46)

where φPN(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

0

φPN(τ)dτ −∫ t0−Tb

0

φPN(τ)dτ (2.48)

=

∫ Tb

0

φPN(τ)dτ (2.49)

This means that θ is also a Gaussian process [14] with zero mean and variance σ2θ =

2π∆νTb.


Continuing the mathematical development, the average error probability becomes:

Pe =1

2√

2πσ2θ

∫ π

−πe− θ2

2σ2θ exp

(−SNR

2cos2(θ)

)dθ (2.50)

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) = GPC

√PS sin(φe(t)) (2.51)

where phase error is defined as φe(t) = φS(t)− φLO(t), and GPC = RL<√PLO

This leads to the well-known PLL characteristic equation:

dφe(t)

dt=dφS(t)

dt− dφLO(t)

dt=dφS(t)

dt− AG

∫ +∞

−∞sin(φe(τ)

)f(t− τ)dτ (2.52)


Figure 2.10: Optical Phase Locked Loop simplified scheme

where A =√PS; G = GV COGPC , 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:

H(S) =ΦLO(S)

ΦS(S)=

AGF (S)

S + AGF (S)(2.53)

A Proportional-Integral (PI) filter is usually used to act as a PLL regulator. Then F (S)

is:

F (S) =1 + τ2S

τ1S(2.54)

and the OPLL transfer function becomes:

H(S) =2ξωnS + ω2

n

S2 + 2ξS + ω2n

(2.55)

Being ωn =√AG/τ1 the natural frequency of the PLL and ξ = ωnτ2/2 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


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]:

Φe(S) =SΦS(S)

S + AGF (S)− GV COVN(S)F (S)

S + AGF (S)(2.56)

The noise transfer function can be defined as follows:

AS(S) =ΦLO(S)

VN(S)

∣∣∣∣ΦS(S)=0

= −Φe(S)

VN(S)

∣∣∣∣ΦS(S)=0

= − GV COF (S)

S + AGF (S)= − H(S)

AGPC

(2.57)

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

ΦeN(S) = VN(S)AS(S) = −VN(S)H(S)

AGPC

= −VN(S)GV COF (S)

S + AGF (S)(2.59)

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):

σ2AN = 〈φ2

eN(t)〉 (2.60)

=

∫ +∞

−∞SAN(ω)|AS(ω)|2dω

2π(2.61)

=1

A2G2PC

∫ +∞

−∞SAN(ω)|H(ω)|2dω

2π(2.62)

=1

SNR

BN

Be

(2.63)

where the noise equivalent bandwidth of the PLL has been defined asBN =∫ +∞−∞ |H(ω)|2 dω

2π,

and Be is the electrical input bandwidth (typically 0.7 ·Rb).


For the case of a first order loop filter BN can be calculated as [15]

BN =ωn2

(ξ +

1

4ξ2

)(2.64)

2.3.2.2 Phase noise impact in a generic OPLL

It is well known that phase noise is the major limitation on Phase Locked Loops. This

parameter is especially harmful in optical PLL where two lasers (transmitter and local

oscillator) are important sources of this noise. In fact the treatment could be done

equivalently considering all phase noise located at the local oscillator side. The linewidth

imposed is the sum of the one imposed separately for each contribution.

In many cases, the impossibility to find a cost effective laser with low phase noise has

limited the development of optical systems using such device.

The phase error contribution can be separated by superposition due to the linearity of

the system. So, it can be described as follows:

Φ′e(S) = Φ′eD(S) + Φ′eN(S) (2.65)

Φ′eN(S) = ΦN(S)AΦ(S) (2.66)

=ΦN(S)

S + AGF (S)(2.67)

= ΦN(S)[1−H(S)

](2.68)

σ2PN =

∫ +∞

−∞SPN(ω)|AΦ|2

dω

2π(2.69)

=

∫ +∞

−∞SPN(ω)|1−H(ω)|2dω

2π(2.70)

= 2π∆νBPN (2.71)

where SPN = 2π∆ν/ω2 is the phase noise baseband equivalent power spectrum density

(PSD) with lorentzian shape, and BPN =∫ +∞−∞

∣∣∣∣1−H(ω)ω

∣∣∣∣2 dω2πFor the case of a first order loop filter, shown in equation 2.55, BPN can be easily inte-

grated leading to:

BPN =1

2ξωn(2.72)


Note that the phase error variance is inversely proportional to the loop bandwidth (high-

pass), so the performance will be better as this parameter grows. While the additive noise

PLL bandwidth BN is low-pass, the PLL bandwidth for phase noise is high-pass; meaning

that a trade off between them must be selected. If the PLL is optimized for cancelling

the phase noise, then its tolerance against additive noise will be worse, and viceversa.

This is shown in figure 2.11. The loop has been evaluated for ξ = 1/√

2, variable natural

frequency (from 1 kHz to 100 MHz), and a bitrate of 1 Gb/s.

Figure 2.11: Iso-curves of the variance of additive noise (left) and phase noise (right),all for ξ = 1/

√2.

2.3.2.3 Loop delay impact in a generic OPLL

The analysis performed in the previous subsections, has assumed both negligible loop

propagation delay and absolute stability for all closed loop systems. If the assumption of

zero effective time delay is not made then it becomes evident that, for systems of wider

bandwidth, absolute stability may not be guaranteed.

From the phase locked loop linear model a few modifications should be introduced to

characterize the loop propagation delay, and the new OPLL transfer function can be

found:

H(S) =AGF (S)e−τS

S + AGF (S)e−τS(2.73)

Except the new transfer function expression, the phase error variance equation remains

the same as in the negligible delay case. Using the expressions, the standard deviation


Figure 2.12: PLL parameters optimization for 1 ns loop delay and 1 MHz linewidth.

of phase noise can be evaluated as a function of the loop delay, natural frequency and

linewidth. Figure 2.12 shows, for a certain loop delay, that the loop parameters ξ and ωmhave to be optimized, thus changing the optimum natural frequency and the maximum

linewidth allowed, as shown in equation 2.71.

Set ξ to a certain value, increasing ωn produces higher bandwidths, however, over an

optimum value, closed loop response is highly distorted and PLL requirements become

harder. This is clearly shown in [16], where, after a deep analysis, it is demonstrated

that the loop linewidth requirements get relaxed when loop is overdamped (in fact, when

ξ > 2); and stability is achieved for 2ξωn < 1.6.

In order to find a closed form for the loop delay impact on the optical PLL noise,Norimatsu [17]

used a Pad approximation to e−τS. This is an easy way to obtain the analytic solution

for equivalent noise bandwidths. A second order Pad approximation gives only 0.4%

difference respect to numerical calculations from equation 2.73. In this case,

e−τS =12 + 6τS + (τS)2

12− 6τS + (τS)2(2.74)

thus, phase and additive noises can be calculated as

σ2ANτ =

1

x+ 1·

·144 + 36xy2 + 72xy + 144x− x2y4 − 48x2y2 + 72x2y − x3y4 + 6x3y3 − 12x3y2

144− 144y − 12xy3 + 36xy2 − 72xy − x2y4 + 6x2y3 − 12x2y2σ2AN

(2.75)


σ2PNτ =

144− 36x2 + 72xy − x2y4 + 6x2y3 − 12x2y2

144− 144y − 12xy3 + 36xy2 − 72xy − x2y4 + 6x2y3 − 12x2y2σ2PN (2.76)

where ξ =√x/2 and ωnτ = y

√x.

Even they are long expressions, they permit us to calculate directly the influence of the

noises in the presence of a long loop delay.

Using these expressions, the loop delay impact on a generic PLL could be evaluated.

Such evaluation was for ξ = 2, variable natural frequency (from 1 kHz to 100 MHz), and

1 ns loop delay (equivalent to 20 cm of optical fiber). For the σ2AN the bitrate assumed

was 1 Gb/s. Results are shown in figure 2.13. From these results, without a loop delay,

σ2PN and σ2

AN have a behaviour similar to what is depicted in figure 2.11. Nevertheless,

when the loop delay impact is taken into account, an inestability point can be seen near

ωn = 81 MHz.

Figure 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.

2.3.2.4 Costas loop

Several phase locked loops have been developed for microwave applications. Some of

them have been modified and converted to the optical domain as homodyne receivers to

lock the phase of the incoming signal. Costas, Decision driven and Balanced phase locked

loop are the most successful configurations.


The first specific implementation is based on Costas-Loop design. The receiver extracts

both In-phase an Quadrature signals and mixes them in order to eliminate the informa-

tion. This kind of PLL is implemented using a 90 hybrid, capable to extract the In-phase

and Quadrature components after optical mixing. These components are then multiplied,

leading to a an error signal proportional to sin(2φe(t)), which is driven to the loop filter.

Figure 2.14: Costas PLL scheme.

The behaviour of the hybrid can be described by the transfer matrix S:

Eo =

E1

E2

E3

E4

= ¯S · EI =1√2

√

1− k√k√

1− k −√k√

k j√

1− k√k −j

√1− k

·(

ESELO

)(2.77)

where k is the fraction of input power that arrives at each detector (ideally 1/2).

Thus, the equations related to this loop are those corresponding to the voltages at each

point of the scheme:

V1(t) = <RLE1(t)E∗1(t)

=1

2<RL

((1− k)PS + kPLO + 2d

√k(1− k)PSPLO cos

(φe(t)

))(2.78)

V2(t) = <RLE2(t)E∗2(t)

=1

2<RL

((1− k)PS + kPLO − 2d

√k(1− k)PSPLO cos

(φe(t)

))(2.79)


V3(t) = <RLE3(t)E∗3(t)

=1

2<RL

((1− k)PS + kPLO − 2d

√k(1− k)PSPLO sin

(φe(t)

))(2.80)

V4(t) = <RLE4(t)E∗4(t)

=1

2<RL

((1− k)PS + kPLO − 2d

√k(1− k)PSPLO sin

(φe(t)

))(2.81)

VI(t) = V1(t)− V2(t)

= 2<RLd√k(1− k)PSPLO cos

(φe(t)

)(2.82)

VQ(t) = V3(t)− V4(t)

= 2<RLd√k(1− k)PSPLO sin

(φe(t)

)(2.83)

Vm(t) = VI(t) · VQ(t)

= 2<2R2Lk(1− k)PSPLO sin

(2φe(t)

)(2.84)

Hence, assuming the loop is in tracking mode (φe(t) 1), and that all the power between

photodetection paths is equally distributed (k = 1/2)

Vm(t) = <2R2LPSPLOφe(t) (2.85)

So, the loop can be linearized, leading to equation 2.53, but with some changes: A should

be substituted by PS, and GPC by R2LPSPLO.

It should be noted that in the Costas loop, phase ranging is performed with more accuracy

than other loops. Since there is no data detection inside the loop, there is no data to

phase error crosstalk.

In order to optimize data detection, power distribution between I-Q paths has to be

optimized. For instance, in [18], a Costas loop was optimized with 22 ns delay and 80

kHz of total laser linewidth, by using a 4:1 splitting ratio for local laser signal, and a 7:1

ratio for received signal. In this case, for data rate of 5 Gb/s they obtained a phase error

variance of 2.9.

2.3.2.5 Decision-Driven OPLL (DD-OPLL)

In this case, the first phase comparator is the well-known Decision-Driven OPLL (DD-

OPLL). This is better than Costas-Loop in terms of linewidth requirements [17, 19], and

its general schematic is depicted in figure 2.15. The main difference with the Costas

loop is that here the influence of the data (BPSK coded, coming from I branch) on the


phase error signal (coming from Q branch) is removed by performing the data decision

and afterwards multiplying with such error signal. Lets see how it can be described

Figure 2.15: Decision driven PLL scheme.

mathematically, in order to better understand its principles. First lets describe the main

optical and electrical signals.

From the transmitter side, the optical field (eS(t)) and its complex amplitude (ES(t)) can

be defined:

eS(t) =√PS exp(j(ωt+ φS(t))) (2.86)

ES(t) =√PS exp(jφS(t)) (2.87)

where the phase is defined as:

φS(t) = φD(t) + φNS(t) (2.88)

φD(t) =

0 d = 1

π d = −1(2.89)

Here φNS(t) is the noise process associated to the transmitter side, and φD(t) is the data

signal.

From the local oscillator side, the optical signals are defined in a similar way:

eLO(t) =√PLO exp(j(ωt+ φLO(t))) (2.90)

ELO(t) =√PLO exp(jφLO(t)) (2.91)

φLO(t) = φC(t) + φNLO(t) (2.92)


being φC(t) the phase introduced by the local loop, and φNLO(t) the noise process of the

local laser.

Thus, after optical combination and further photodetection, the electrical signals after

each balanced detector can be written:

V1(t) = GPC

√PSd sin

(φN(t)− φC(t)

)+ n1(t) (2.93)

V2(t) = GPC

√PSd cos

(φN(t)− φC(t)

)+ n2(t) (2.94)

where the overall phase noise process is φN(t) = φNS(t) + φNLO(t), the shot noise (pho-

todetection and receiver parts) is characterized by n1,2(t), and GPC = RL<√PLO.

As said before, it can be seen in figure 2.15 that the Decision-Driven implementation

must separate perfectly the data from the OPLL operation. In this sense a perfect data

recovery is assumed, which is a good approximation for the usual BER target values (e.g.

10−9). Please note that FEC data encoding is regarded as an additional resource, so at

this stage the target BERs are higher.

m(t) = dV1(t− Tb) = dGPC

√PSd sin

(φN(t)− φC(t)

)+ dn1(t) (2.95)

m(t) = GPC

√PS sin

(φN(t)− φC(t)

)+ n1(t) (2.96)

Data has no influence on the shot noise impact, therefore it can be omitted. As in generic

PLL here it can be assumed a linear operation:

|φN(t− Tb)− φC(t− Tb)| 1 (2.97)

m(t) = GPC

√PS(φN(t)− φC(t)

)+ n1(t) (2.98)

Thus the same phase-detection function than the generic PLL is obtained. Therefore

the analysis is completely equivalent and results obtained in the previous subsections are

applicable to this loop. One difference is the additional bit delay, that may have some

effect when it is not properly optimized, and for very high PLL bandwidths.

Also, another remarkable difference is the fact that it requires a 90 optical hybrid that

is not a simple element. Even though some feasible approaches have been proposed [20],

it is still a complex device. Please note that binary data detection is performed over the

In-phase (I) branch, while Quadrature (Q) branch is kept for phase tracking. So, power

distribution between both photodetection paths should be carefully designed for each

particular case, in order to optimize both, data detection and tracking performances.


2.3.2.6 Balanced OPLL

The third PLL design corresponds on Balanced PLL. This receiver does not try to elimi-

nate the bits influence on the phase ranging; but just considers it as an extra noise which

produces certain penalty. Usually high frequency bits do not represent an important

impact to low bandwidth processes [21].

Figure 2.16: Balanced PLL scheme.

From figure 2.16, the following set of equations can be written, describing the main optical

and electrical signals:



φS(t) = φD(t) + φNS(t) (2.101)



φLO(t) = φC(t) + φNLO(t) (2.104)

φD(t) =π

2+ ϕd(t) (2.105)

φe(t) = φNS(t)− φNLO(t)− φC(t) (2.106)

where ϕ corresponds to the phase deviation between the two different bits d(t) = 1 and

d(t) = −1; being 2ϕ the peak to peak phase deviation. For a better understanding, this

phase is depicted in the phasor scheme of figure 2.17.


Figure 2.17: Balanced PLL phasor scheme.

The 180 hybrid (usually implemented by an optical 50:50 coupler) behaviour can be

described by next matrix:

Eo =1√2

(1 1

1 −1

)·(

ESELO

)(2.107)

So, the equations for the photodetected signals are:

V1(t) =1

2<RL

(PS + PLO + 2

√PSPLO cos

(φS(t)− φLO(t)

))(2.108)

V2(t) =1

2<RL

(PS + PLO − 2

√PSPLO cos

(φS(t)− φLO(t)

))(2.109)

Next, V3(t) can be calculated, and properly rewritten as:

V3(t) = 2<RL

√PSPLO cos

(φS(t)− φLO(t)

)= 2<RL

√PSPLO cos

(π

2+ ϕd(t) + φNS(t)− φC(t) + φNLO(t)

)= 2<RL

√PSPLO sin

(ϕd(t) + φNS(t)− φC(t)− φNLO(t)

)(2.110)


If V3(t) is expanded by using trigonometric identities:

V3(t) = 2<RL

√PSPLO sin(ϕ)d(t) cos

(φNS(t)− φC(t)− φNLO(t)

)+

+ 2<RL

√PSPLO cos(ϕ)d(t) sin

(φNS(t)− φC(t)− φNLO(t)

)(2.111)

where the phase error term can be easily identified as φe(t) = φNS(t)− φNLO(t)− φC(t).

Then, assuming it is small enough, the phase error ranging signal can be obtained. this

phase error signal will be driving the loop filter:

V3(t) ≈ 2<RL

√PSPLO sin(ϕ)d(t) + <RL

√PSPLO cos(ϕ)d(t)φe(t) (2.112)

being the first term the most useful for data, and the second term the one that contains

φe(t) and, thus, the phase error.

This kind of PLL is influenced by phase noise, shot noise and by crosstalk between data-

detection and phase ranging signals. However, this effects can be controled by carefully

adjusting ϕ. It should be noted that ϕ can not be 0 nor 90. Precisely, [22] demonstrates

that for very low linewidth (1 kHz) and 10 Gb/s data rate, the optimum value is ϕ = 85.

Thus, in this case loop behavior in front of noise (additive and phase noise) is affected by

data crosstalk, leading to [22]:

σ2N =

2π∆ν

2ξωn+ 2Tb tan2(ϕ)

ωn(4ξ2 + 1)

8ξ+

q

2<PS cos2(ϕ)

ωn(4ξ2 + 1)

8ξ(2.113)

As an example, the noise variance σ2N was evaluated for several laser linewidth values

(up to 100 MHz) and different ϕ values, from 80 up to 100. The values of the other

parameters used for such calculations where standard ones: 1 Gb/s bitrate (intended for

access networks), photodetector responsivity of 0.8 A/W, PS of 0 dBm, loop damping

factor ξ = 1/√

2, and loop natural frequency of 1 MHz. Results are shown in figure 2.18.

There it is shown that as the laser linewidth increases the noise power also increases, as

expected. As said before, the ϕ value is also important: when it is approaching 90, the

second term of equation 2.112 gets close to 0 and the phase error can not be ranged.

Thus, the phase error variance has a high peak at that point. In order to avoid this, one

should take ϕ of 80 − 85 degrees (or 95 − 100). Then, even the symbols received are

not orthogonal at all, the PLL is capable to track and compensate the phase error.

In summary, although balanced OPLL theoretically has worse behaviour than other kind

of phase locked loops, it must be taken into account due to its simplicity.


Figure 2.18: Noise variance for the balanced PLL scheme.

2.3.2.7 Subcarrier modulated OPLL (SCM-OPLL)

In this loop, a subcarrier is used in order to track phase of the received signal [23]. Such

subcarrier is achieved by modulating the output of the local laser using a Mach-Zehnder

Modulator (MZM) driven by an electrical VCO. There exist several approaches, but in

the present work the analyzed approach is the one based on the Decision-Driven loop, as

it one of the most robust [23]. A scheme is shown in 2.19.

Figure 2.19: General scheme for a subcarrier decision driven optical phase-lockedloop.


In that scheme, the same analysis we did in the previous loops can be done. So, lets start

writing down the equations which describe the optical signals:

eS(t) =√PS exp(j(ωSt+ φS(t))) (2.114)

φS(t) = φD(t) + φNS(t) (2.115)

eLO(t) =√PLO exp(j(ωLOt+ φLO(t))) (2.116)

φLO(t) = φC(t) + φNLO(t) +π

2+π

2cos(ωct) (2.117)

ωc = ωs − ωLO (2.118)

where, in this case, the MZM is properly biased at 90 point and the electrical VCO drives

the MZM with a sinusoidal signal that introduces a 180 phase shift with frequency ωc.

Thus, the signal used for phase ranging becomes:

m(t) = RL<√PLO

√PS ·

· sin(ωSt+ φD(t) + φNS(t)− ωLOt− φC(t)− φNLO(t)− π

2− π

2cos(ωct)

)= RL<

√PLO

√PS ·

· sin(ωSt+ φNS(t)− ωLOt− φC(t)− φNLO(t)

)cos(ωct)

=1

2RL<

√PLO

√PS ·

· sin(φNS(t)− φC(t)− φNLO(t)

)+ sin

(2ωctφNS(t)− φC(t)− φNLO(t)

)(2.119)

Assuming ωc big enough, this signal can be low-pass filtered. Also, the phase error can

be identified as φe(t) = φNS(t)− φNLO(t)− φC(t), and rewrite the expression as:

e(t) =1

2RL<

√PLO

√PS sin

(φe(t)

)(2.120)

With this signal at the input of the loop filter, the loop can be linearized, also leading to

equation 2.53, but taking into account that now:

GPC =1

2RL<

√PLO (2.121)

Please note that this loop has an electrical VCO. Thus, the main advantage of this loop

is that its the performances are expected to be improved in terms of hig-speed phase

tracking and acquisition. Nevertheless, it needs several optical components (MZM, 90

hybrid, quadruple photodetector array), meaning that its cost may be quite high. Also,

it should be noted that in this case the local laser is not running free at all: a wavelength

control loop should be placed in order to keep it close to the received wavelength. In


chapter 3 a comparison with other loops will be shown, when evaluating a novel PLL

approach proposed in this thesis.

2.3.3 Phase and polarization diversity systems

Instead of synchronizing the local laser with the optical incoming carrier by using a

feedback loop, the phase diversity systems do it by means of a feedforward processing

module. Thus a free-running laser is placed at the LO side.

Figure 2.20: Scheme of a phase diversity front end.

In the post-processing module the phase of the received signal is estimated and the optical

impairments are compensated by means of electronic and/or digital signal processing. In

order to allow this stage to work properly, In-Phase and Quadrature components of the

received signal and local oscillator combination have to be present. That is the reason why

a 90 hybrid is the most common way to obtain both optical signal components [20]. This

architecture is based on an intradyne system, using a local oscillator which is nominally

at the same frequency as the incoming signal. The 90 hybrid separates the incoming

optical signal into I and Q components, corresponding to the real and imaginary parts of

a complex signal. An scheme of such a receiver front-end is shown in figure 2.20.

Along a different line, polarization diversity is used and obtained in a similar way, in order

to achieve polarization insensitivity. As commented before, If polarization diversity is also

desired, then the receiver front-end becomes much complex. It is shown in figure 2.21.

Once seen the front-end architectures lets see how they are used to detect PSK or DPSK

signals. Also, some digital signal processing techniques for estimating phase will be shown,

although they are used for detecting multilevel PSK or DPSK signals.

2.3.3.1 Multiple differential detection

The idea of this receiver is to perform an analog processing (differential detection) of

the signals provided at the output of the optical front-end. It was first analyzed and


Figure 2.21: Schematic of phase and polarization diverse receiver.

Figure 2.22: Scheme of a DPSK detection, in a phase and polarization diversityhomodyne receiver.

experimentally demonstrated in [24]. The main advantage of this detection scheme is

its simplicity, and the fact that it can be implemented with simple analog electrical

components.

Figure 2.22, shows the detection scheme for that type of receiver. At the output of each

branch of the diversity front-end, a differential detector (delay and multiply) is placed.

Next, all signals coming from this detectors are added.


Given eS(t) the received signal optical field, and eLO(t) the local oscillator optical field,

for this receiver:

eS(t) =√PS(cos(ϕ)x+ sin(ϕ)e−jθy) exp

(jω0t+ φS(t)

)(2.122)

eLO(t) =√PLO(x+ y) exp

(jω0t+ φLO(t)

)(2.123)

φe(t) = φS(t)− φLO(t) (2.124)

where x and y are the polarization orthogonal components (H,V); and ϕ and θ are the

phases related to the polarization. Since polarization fluctuations are very slow (∼ 1 Hz),

these variables are assumed to be constant during the bit sequence. Please note that

while eS(t) has a random polarization, eLO(t) has a +45 linear polarization.

So, the photodetected voltages are:

VHI(t) = Cd′(t) cos(ϕ) cos(φe(t)

)(2.125)

VV I(t) = Cd′(t) sin(ϕ) cos(φe(t) + θ

)(2.126)

VHQ(t) = Cd′(t) cos(ϕ) sin(φe(t)

)(2.127)

VV Q(t) = Cd′(t) sin(ϕ) sin(φe(t) + θ

)(2.128)

being φe(t) = φS(t)− φLO(t) the phase error; C = 2<RL

√PSPLO the maximum voltage,

d(t) = d′(t) · d′(t− Tb) the detected data.

Then, the output signals at each branch after differential demodulation can be calculated:

VHIo(t) =C2

2d(t) cos2(ϕ) cos

(φe(t)

)cos(φe(t− Tb)

)(2.129)

=C2

2d(t) cos2(ϕ)

(cos(φe(t)− φe(t− Tb)

)+ cos

(φe(t) + φe(t− Tb)

))

VV Io(t) =C2

2d(t) sin2(ϕ) cos

(φe(t) + θ

)cos(φe(t− Tb) + θ

)(2.130)

=C2

2d(t) sin2(ϕ)

(cos(φe(t)− φe(t− Tb)) + cos

(φe(t) + φe(t− Tb) + 2θ

))

VHQo(t) =C2

2d(t) cos2(ϕ) sin

(φe(t)

)sin(φe(t− Tb)

)(2.131)

=C2

2d(t) cos2(ϕ)


)− cos


))


VV Qo(t) =C2

2d(t) sin2(ϕ) sin

(φe(t) + θ

)sin(φe(t− Tb) + θ

)(2.132)

=C2

2d(t) sin2(ϕ)

(cos(φe(t)− φe(t)

)− cos

(φe(t) + φe(t− Tb) + 2θ

))

thus, given Vo(t) = VHIo(t) + VV Io(t) + VHQo(t) + VV Qo(t), and after some algebra:

Vo(t) =C2

2d(t)cos

(φe(t)− φe(t− Tb)

)(2.133)

Now, identifying terms from the values calculated, it is easy to see that:

SNR =4<PSPLO

2q(<(PS + PLO) + ID

)BE +

(4kBTRL

)FNBE

(2.134)

And using equation 2.50 the probability of error for this receiver can be calculated, with

a noisy reference source.

The system works pretty well [24], although the cost is relatively high due to the amount

of components that have to be used.

An alternative version using digital signal processing was proposed for higher order mod-

ulation formats [25]. However, it gets out of the scope of this thesis, since poly-phase

signals are mainly intended for core networks and long-haul transmission systems.

2.3.3.2 Wiener filter phase estimation

In this case polarization issues are disregarded in order to focus on the phase noise

mitigation, and the diversity front-end used is the one depicted in figure 2.20; but with

an analog to digital converter (ADC) at both outputs, Re and Im. After that, a phasor

r(n) describing received signal can be constructed:

r(n) = VI(t0) + jVQ(t0) (2.135)

being t0 the optimum sampling time.

Along a different line, once digitized, laser phase noise can be regarded as an auto-

regressive (AR) process seeded by white noise. This is developed in detail and demon-

strated in appendix D. Taking into account this fact and other noises interacting as white

noise; good phase estimation can be done using well-known linear prediction techniques

by employing a Wiener filter design. This was done in [26], with very good results.


A Lorentzian-shaped laser tone contains phase noise, such that, once digitized:

φ(n) = φ(n− 1) + w(n) (2.136)

where w(n) is a zero-mean Gaussian noise sequence, having a variance of σ2w = 2π∆νTs,

with linewidth ∆ν, and fs = 1/Ts being the sampling rate. Then, the digitized signal

can be reconstructed from the I and Q components, and written as:

r(n) = VI(t0) + jVQ(t0) = d(n) exp(jφ(n)

)+ p(n) (2.137)

where d(n) is the data, and p(n) is the complex additive noise (Gaussian, with variance

σ2p). In order to remove the data modulation r(n) is raised to the Mth power:

s(n) = rM(n) = exp(jMφ(n)

)+Mp′(n) exp

(jMφ(n)

)+ o(p2)

(2.138)

where p′(n) is a different Gaussian noise with the same variance as p(n). Since that the

phase noise is small, a small angle approximation applies:

θ(n) = arg(s(n)

)≈M

(φ(n) + Imp′(n)

)(2.139)

Then, the problem of finding the best estimate of φ(n) (φ(n)) can be stated as Wiener

filter problem:

φ(n) =1

Mθ(n) (2.140)

The Wiener filter can be easily calculated, and, in terms of Z-transform it is [26]:

θ(z) = H(z)θ(z) (2.141)

=1− α

1− αz−1

(αD + (1− α)

D∑k=1

αD−kz−k

)θ(z) (2.142)

where D is the lag number of symbols, and

α =M2σ2

w + 2σ2p −Mσw

√M2σ2

w + 4σ2p

2σ2p

For the particular case of the Wiener filter, the error of the estimator can be easily

calculated and found to be:

e(z) = θ(z)− θ(z) = θ(z)[1−H(z)

](2.143)


Thus, the transfer function of the error can be written as:

He(z) =e(z)

θ(z)= 1−H(z) (2.144)

and the LMS error of this estimator can be calculated [14]:

Ee2(n) =1

2π

∫ π

−π|He(e

jω)|2θ(ejω)dω (2.145)

Given this measure of the estimator’s error, a numerical analysis of a Wiener filter, with

a lag of 10 symbols, has been performed. Results are shown in figure 2.23. There it is

shown how the estimator performances are bounded by the phase noise and the SNR. The

SNR parameter refers to the electrical SNR after photodetection. So, for low linewidths

and low SNR, the estimator error increases. Also, when the linewidth is high enough,

the estimator error is also high for high SNR values. So, from the point of view of the

estimator LMS error, the optimal working zones should be defined for high linewidth

(> 1 MHz) and non-optimal SNR (< 15 dB).

Figure 2.23: LMS error for a Wiener filter with a lag of 10 symbols.

Given this estimator, a comparison with other methods was carried out by Taylor in [26,

27]. The results obtained for the BPSK case (1.5 Gb/s), and a total laser linewidth of

48 MHz, are summarized in table 2.3. Please note, that for a Gaussian approximation,


a probability of error of 10−9 is achieved for a Q factor of 15.56 dB. Thus, under this

hypothesis, the BER was found for each case and is shown in table 2.3. There the Wiener

filter estimation (with a lag D=10 symbols) is only ∼0.1 dB away from the Maximum a

posteriori (MAP) estimate; which, a priori, is the best possible estimate.

Estimator Q factor (dB) BERWiener filter D=10 8.61 3.5 · 10−3

Wiener filter D=0 6.25 2 · 10−2

PLL 5.88 2.45 · 10−2

MAP 8.66 3.4 · 10−3

Table 2.3: Comparison of phase estimation methods, as seen in [27]. BER is estimatedfrom Q factor and assuming Gaussian statistics.

2.3.3.3 M-power law phase estimation with regenerative frequency dividers

This technique, is another digital signal processing algorithm for phase estimation and it

was proposed in [28]. Here, once I and Q components are photodetected, they are digitized

by high speed ADC. After that, a phasor describing received signal can be constructed

for each orthogonal polarization state detected (XV , XH).

Figure 2.24: Scheme of a phase estimator for polarization multiplexed QPSK signalsbased in regenerative frequency dividers.

After the ADCs, the resulting digitized signal rH,V is raised to the Mth power (M is the

number of different symbols that can be transmitted) and filtered, for cancelling the mod-

ulation. In the example shown in figure 2.24, QPSK modulation format is assumed, for

which M = 4. Next, a low-pass filter is placed in order to eliminate the broadband noise

and high frequency harmonics generated when raising to the Mth power. Afterwards,


the output signal of the filter, drives a stack of regenerative frequency dividers, to divide

the signal frequency by M . In the QPSK case, a couple of them are enough. Finally, the

resulting signal describes a phasor with an estimation of the received signal phase.

The main difference between the present approach and the Wiener filter, is the use of

additional regenerative frequency dividers, that make the algorithm and, thus, the receiver

more complex.

In case a polarization division multiplex is desired, the phasors correspondent to orthog-

onal states rH , rV are each sent to a carrier recovery and demodulation unit, as shown in

figure 2.24. There, the phase-aligned frequency-multiplied carrier signals of both branches

are added before being passed through the low-pass filter and the regenerative frequency

dividers. Finally, after phase cancellation, demodulation is performed. An important

point is that the components of detected data can be correlated with the recovered data

symbols, for compensating polarization fluctuations [28].

In summary, this is an extremely complex frequency estimator. Performances expected

in [28] were achieved in part by its experimental work reported in [29], obtaining a 0.5%

linewidth per bitrate ratio phase noise tolerance at BER-floor of 10−3.

2.3.3.4 Viterbi-Viterbi phase estimation

This technique is also another digital method for carrier phase estimation, which was

first demonstrated for the optical domain in [30]. Perhaps it is the most extensively used

technique for coherent detection of poly-phase optical signals and M-QAM data.

In this case, the received complex samples r(n) are first raised to the Mth power to

remove the M-ary phase modulation. To more accurately estimate the phase error out

of the shot-noise, the raised samples of a block of length N are averaged, and a common

phase error estimate for the block is then obtained by calculating the argument of the

complex sum vector:

θ(n) =1

Marg

(N∑k=1

rM(k)

)(2.146)

To combat the arising M-ary phase ambiguity, differential encoding has to be employed,

and the last symbol of a block has to be corrected after segment changes [31].

A summary of the performances of this estimator was presented in [31], giving a 10−4

linewidth per bitrate ratio phase noise tolerance for 1 dB penalty at BER of 10−4 and

QPSK modulation.


2.4 Chapter summary

This chapter has provided a comprehensive review of optical coherent receivers, and their

evolution all through the years. Therein, special focus has been put on simple optical

phase modulation (BPSK and DPSK) and the influence of phase noise in the reference

optical source. This was used to set up a background level to develop the present thesis.

First, the BPSK and DPSK modulation formats have been introduced, and after they

have been compared to the other formats available, while analyzing detection with noisy

reference signals and showing the need to compensate the phase noise inherent to lasers.

Next, the optical phase-locked loop concept has been introduced as a first solution, some

well-known results for the generic expression have been given for different situations:

Loop linearization plus additive noise, phase noise and loop delay impacts.

Later, the main optical PLLs have been analyzed: Decision driven, Costas, subcarrier

modulated, and balanced. The first three architectures are the more complex as they

use a 90 optical hybrid (plus an amplitude modulator, for the case of the subcarrier

modulated). But they also present the best linewidth tolerances and are very robust

against possible data crosstalk. Nevertheless, their linewidth tolerances are in the order

of the hundreds of kHz. Regarding the balanced OPLL, its simplicity should be high-

lighted, even it has demonstrated very poor performances and being very sensitive to

data crosstalk.

Finally, the phase diversity architecture has been seen. A brief analysis has been provided

and the most popular architectures and algorithms have been analyzed:

1. Analog processing for differential detection

2. Wiener filter phase estimation

3. M-power law phase estimation with regenerative frequency dividers

4. Viterbi-Viterbi phase estimation

Even though the first one is based in a simple concept, nowadays the other ones, especially

the ones based in Wiener filter and Viterbi-Viterbi algorithms, are becoming more popular

due to the improvement of digital signal processors. It should be noted that with such

algorithms one is allowed to use lasers on the order of tens of MHz, for a data rate of 1

Gb/s, representing a big improvement respect the OPLLs.

Chapter 3

Lock-In amplifier OPLL architecture

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 the electrical PLL (used in heterodyne systems) is a well known device, the optical

version (used in homodyne systems) poses several technological problems which have

delayed its development to the general market. As pointed in chapter 2, its three basic

elements are the Phase Comparator, the Electrical Filter and the VCO module (tunable

Laser).

In the present chapter a new OPLL architecture is introduced, aiming to enhance the

phase noise noise tolerance of these devices, while targeting a reduced cost [32, 33]. The

idea is to use simple optics, as in the Balanced OPLL, but improving its phase noise

tolerance [33].

In a homodyne receiver, the phase noise has a Lorentzian spectrum that masks completely

the detected data and the phase error signal (also a baseband signal). Then, an option

is to play with the electrical spectra in order to find a frequency band where the phase

noise spectrum does not mask the phase error signal, improving the PLL performances.

The Lock-In amplifier is a tool widely used in physics that performs this frequency shift

by introducing a dithering at a certain point of the system. Thus, in a Lock-In amplified

OPLL, the main idea (and novelty) is to sinusoidally dither the phase of the local laser

by a small amount (e.g. 50 mrad), enough for achieving a certain phase modulation.

This is done at a frequency above the loop bandwidth and below the bit rate. As the

phase response of a coherent balanced receiver is a cosine (an even function, shown in

figure 3.1), the dithering makes possible the measurement of the phase error by searching

the derivative and removing the inherent positive/negative ambiguity.

Also, the dithering leads to an amplitude modulated phase error signal after the balanced

receiver, which is afterwards filtered and demodulated in a proper way.

47

Chapter 3. Lock-In amplifier OPLL architecture 48

Figure 3.1: Voltage after balanced detector (V3(t)) as a function of the phase error(φS(t)− φLO(t)).

3.1 System model

For a better understanding of this optical PLL, lets proceed with the loop analysis.

There the signals at each point of the loop will be described mathematically, and their

interaction detailed.

3.1.1 Loop analysis and linearization

The phase-locked loop model scheme is depicted in figure 3.2. It is a homodyne balanced

receiver with a Proportional-Integral (PI) loop filter. Dithering is introduced after PI

filter, and just next to photodetection stage the amplitude modulated error signal is

properly filtered and demodulated.

In the scheme presented, the following set of expressions is verified, as a basis for starting

the analysis:



φS(t) = φD(t) + φNS(t) (3.3)



φLO(t) = φC(t) + φNLO(t) +AKV CO

ωcsin(ωct) (3.6)

φLO(t) = φTLO(t) +AKV CO

ωcsin(ωct) (3.7)


where ES is the transmitted optical field, ELO is the local oscillator optical field, PS is

the transmitter optical power, PLO is the local oscillator optical power, φD(t) is the phase

coded data, φNS(t) is the transmitter laser phase noise, φNLO(t) is the local laser phase

noise, φC(t) is the phase introduced by the control loop filter, A is the electrical oscillator

amplitude, KV CO is the local laser constant, and ωc is the dithering frequency.

Figure 3.2: Lock-In amplified oPLL schematic.

For the loop analysis, data φD(t) influence is assumed to be negligible. Afterwards, once

the loop is analyzed and proven to be feasible, data effects on the loop performances will

be evaluated. In order to start, the equations related to the balanced receiver can be

found:

V1(t) =1

2<RL

(PS + PLO − 2

√PSPLO cos(φS(t)− φLO(t))

)(3.8)

V2(t) =1

2<RL

(PS + PLO + 2

√PSPLO cos(φS(t)− φLO(t))

)(3.9)

So the output signal is:

V3(t) = V2(t)− V1(t) (3.10)

= 2<RL

√PSPLO cos

(φS − φTLO(t) +

AKV CO

ωcsin(ωct)

)(3.11)

= 2<RL

√PSPLO · η (3.12)

being η = cos(φS − φTLO(t) + AKV CO

ωcsin(ωct)

).

This voltage V3(t) is the only way to measure the phase error. So, lets pay some special

attention on it. First, the cosine part η can be expanded using the trigonometric identities


related to the sum of arguments:

η = cos(φS(t)− φTLO(t)

)cos(AKV CO

ωcsin(ωct)

)−

− sin(φS(t)− φTLO(t)

)sin(AKV CO

ωcsin(ωct)

)(3.13)

The term AKV COωc

is the dithering amplitude, and it is a parameter to be designed and

optimized. Thus, it can be small enough not to interfere with the phase error, while

keeping the desired amplitude modulation. Also, in tracking mode, the error signal itself

is expected to be low. So, the dithering amplitude can be as low as to assume AKV COωc

1.

In this case, sine and cosine terms containing the dithering amplitude can be expanded in

Taylor-McLaurin series and truncated after the first and second term respectively. Hence,

η can be rewritten as:

η =

cos(φS(t)− φTLO(t)

)(1− A2K2

V CO

4ω2c

)+ (3.14)

+A2K2

V CO

4ω2c

cos(φS(t)− φTLO(t)

)cos(2ωct) + (3.15)

+AKV CO

ωcsin(φS(t)− φTLO(t)

)sin(ωct) (3.16)

From that, the term 3.14 is a baseband signal containing the phase error information, but

maintaining the ambiguity inherent to the cosine (even function). The same cos(φS(t)−

φLO(t))

is also present in the term 3.15, now modulated with a carrier centred at 2ωc.

Thus, the only useful term is the last one 3.16, containing a sin(φS(t)−φLO(t)

)modulated

with a carrier running at ωc. The distribution of these terms over the electrical spectrum

is shown in figure 3.3.

-

6

ωωc 2ωc

3.14 3.16 3.15

Figure 3.3: Spectral distribution of the terms 3.14, 3.15, and 3.16.


As φS(t) − φLO(t) is mainly due to the phase noise, its variations can be assumed to be

slower than ωc. i.e. the carrier frequency ωc is higher than the bandwidth of φS(t)−φLO(t).

Additionally, the band-pass filter hf1(t) is designed to filter the term centered at ωc,

eliminating the other components. So, V4(t) can be written as:

V4(t) = 2<RL

√PSPLO · η ∗ hf1(t) (3.17)

After the filter, the only surviving term will be the one running at ωc, and V4(t) can be

then rewritten as:

V4(t) = 2<RL

√PSPLO · γ (3.18)

where

γ = η ∗ hf1(t) =AKV CO

ωcsin(φS(t)− φTLO(t)

)sin(ωct) (3.19)

The next step is to demodulate the amplitude modulated phase error term present in

V4(t). That is the reason why V4(t) is multiplied with a pure tone running at ωc, V5(t).

After multiplication, the component at two times ωc is eliminated by hf2(t), a low pass

filter with square ideal response, giving V6(t):

V6(t) = [V4(t) · V5(t)] ∗ hf2(t) (3.20)

= [2<RL

√PSPLO · γ · A sin(ωct)] ∗ hf2(t) (3.21)

=<RL

√PSPLOA

2KV CO

ωcsin(φS(t)− φLO(t)

)(3.22)

and V5(t) is defined as A sin(ωct).

Next, V6(t) is introduced to the loop filter f(t), a standard proportional-integral control.

Its output is added to the output signal of the 90 phase shift (driven by V5(t)), giving

the voltage V7(t) that drives the local laser:

V7(t) = 2<RL

√PSPLO · γ ∗ hf2(t) ∗ f(t) + A cos(ωct) (3.23)

Ideally, the local laser gives a frequency proportional to V7(t), being φLO(t):

φLO(t) = KV CO

∫V7(t)dt+ φNLO(t) (3.24)

=

∫2KV CO<RL

√PSPLO · γ ∗ hf2(t) ∗ f(t)dt+

AKV CO

ωcsin(ωct) + φNLO(t)

Then, identifying terms, the loop can be closed and its its behavior can be modeled with

the following differential equation:

dφC(t)

dt= K sin(φS(t)− φLO(t)) ∗ f(t) (3.25)


where K =A2<RL

√PSPLOK

2V CO

ωc

Thus, while the local laser is controlled in low-pass response, the deviation measure signal

is in band-pass. An important feature of this technique, is that an increase of the loop

SNR in front of the additive noise is reported by controling the bandwidths of the Lock-In

amplifier filters hf1(t), hf2(t) [34].

Assuming loop is in tracking mode (φS(t) − φLO(t) 1), this loop can be linearized

by approximating the sine by its argument, like the typical PLLs as those analyzed by

several known books as [15]. Then, the loop differential equation can be transformed in

the Laplace domain, and rewritten as it was shown in section 2.3.2:

H(S) =ΦLO(S)

ΦS(S)=

KF (S)

S +KF (S)(3.26)

Hence the expressions deduced for generic linearizable loops are applicable in the Lock-In

amplified loop. The most important ones, when regarding the transceiver performances,

are commented in the following subsections.

3.1.2 Noise, dithering and loop delay impacts

Regarding additive and phase noises, it should be noted that the presented PLL expres-

sions have been linearized, having the same output expressions as when working with a

generic PLL. Then, the same analysis made in sections 2.3.2.1 and 2.3.2.2 can be carried

out, obtaining the same outcome. Just as a reminder, the final results from equations 2.63

and 2.71 are revisited:

σ2AN =

ωn2SNRBe

(ξ +

1

4ξ2

)(3.27)

σ2PN =

2π∆ν

2ξωn(3.28)

Lets now analyze the dithering effects. In fact, a small phase perturbation is introduced

in the phase term of V3(t) and cannot be recovered at all. This perturbation is a sinusoid

with an argument that varies rapidly compared to the loop natural frequency. So, from the

statistical point of view, this argument represents a residual phase that can be regarded

as a random phase process uniformly distributed from −π to +π. Please note that this

process is independent from the additive and phase noises. Also, the variance of a sinusoid

of a random phase with uniform distribution is the half of the squared amplitude [14].

Thus, the phase error variance due to the dithering can be written as:

σ2d =

A2K2V CO

2ω2c

(3.29)


As an example, for a small dithering amplitude of 50 mrad a phase error deviation of 2

is obtained, that has almost no impact on the BER of the proposed receiver.

Hence, as all the noises plus dithering can be regarded as independent processes, the total

standard deviation of the phase error can be written as:

σ =√σ2AN + σ2

PN + σ2d

=

√ωn

2SNRBe

(ξ +

1

4ξ2

)+

2π∆ν

2ξωn+A2K2

V CO

2ω2c

(3.30)

When loop delay is not negligible, performances in tracking mode are the same as for a

general PLL scheme. So, loop stability will be achieved for damping factor ξ higher than

2, and a 2ξωnτ product under 1.6 [16]. Also, the theoretical limit for 1 dB penalty at

BER 10−9 will be of 0.74 for the 2ξωnτ product. This will be shown, when talking about

the loop simulations performed.

3.1.3 Acquisition parameters

3.1.3.1 Hold in range

Presuming that the PLL is locked, the hold in range is defined as the maximum frequency

shift of the received signal with respect to the nominal frequency of the local laser, for

which the PLL is still tracking the received signal.

Since the PLL could be linearized, and the active filter in the loop is of first order, the

hold in range theoretical value is demonstrated to be [35]:

∆ωH = ±KF (0) (3.31)

So, in principle, the hold in range can be made arbitrarily large by increasing the DC

loop gain. Thus, a PLL with a theoretically perfect integrator (F (0) =∞), should have

an infinite hold in range. In practice, the gain is always limited because of saturation

of elements such as amplifiers in the loop and laser tuning range. In the presented case

a proportional-integral control is implemented, searching for a maximum of this limit.

Please note that the assumptions for the hold in range calculation are that the PLL is

locked, i.e. the loop can be linearized.


3.1.3.2 Pull in range

It is the maximum frequency difference between the received signal and the local laser,

for which the PLL, initially not locked, is capable to lock and start tracking the phase of

the received signal.

In a first order loop, the pull in range equals the hold in range [35, 36]. Nevertheless, in

the calculation of the pull in range presumes the loop can be unlocked, having to use the

full loop equation. Thus, for a second order loop (similar to our case) the solution has

to be computed, aided by simulation tools. Precisely, for a generic second order tracking

loop with imperfect integrator, it has been found [36] that the pull in margin can be

approximated by:

∆ωP =8

π

√2ξK − ω2

n (3.32)

And the locking time can be expressed as:

Tp ≈(∆ωp)

2

2ξω3n

(3.33)

Thus, the larger the open loop gain is, the larger the pull in range obtained. Also, another

important point is the loop delay influence on the PLL. As the hold in range is determined

when the loop is locked, loop delay will not cause any effect to the hold in range. However,

the pull in range will be dramatically limited by the loop delay [16]. Nevertheless, the

PLL can be optimized to have a pull in range of ∆ωp = 2/τ in case the control filter

accomplishes [16]:τ1

τ2

= 2ξωnτJ1

(4ξωnτ

π

)(3.34)

where J1 is the Bessel function of first kind and order 1, and τ1, τ2 are the control filter

parameters.

Since for the calculation of the pull in range the unlocked loop is considered, it is obvious

that for our case this will not be exact, as phase ranging and locking will be driven by a

Lock-In amplifier. Nevertheless, such expressions will be used as a theoretical limit.

3.1.4 Data crosstalk and cycle slipping effects

In this loop, cycle slipping influence arises mainly when trying to overcome the effects of

data over the phase ranging signal. In order to avoid these data to phase-lock crosstalk, a

full wave rectifier has to be placed between the balanced receiver and the band-pass filter

of figure 3.2. But this produces a non desired effect: π-periodic slip cycles are observed,

instead of the typical 360 cycle slips. This is due to the fact that the full wave rectifier

doubles the argument of the ranging singal.


In order to avoid the effects of this undesired slip-cycling onto the data signal, differential

coding will be used. Thus, only one erroneous bit will result every time the data signal is

reversed. For the loop delays and laser linewidths considered, the time average between

cycle slips is in the order of years [37]. Time average between π-periodic slip cycles is

expected to be in the same order.

3.2 Simulations

The Lock-In amplified oPLL performances were evaluated by means of computer simula-

tions, aiming to analyze:

• Phase noise cancellation

• Step response performances

• Dithering amplitude optimization

• Comparison with other loops

The first three studies were carried out using Matlab/Simulink, whereas the last one was

performed using VPI systems software tools. By now, only the generic system parameters

are given, as the specific information for each case can be found in the next subsections.

The system was designed to operate at a dithering frequency of 700 MHz assuming a

maximum phase error bandwidth of 200 MHz, avoiding the phase noise masking effects

described in the introduction of the present chapter. Also the amplitude used was around

50 mrad (2.86), introducing an additional error phase deviation of 2. So, in order to

obtain 11 of total error phase deviation (< 1 dB penalty at BER of 10−9), a maximum

of 10.82 from noise influence was allowed.

Filters used (bandpass and lowpass) were based on Butterworth approximations because

of their narrow transition band and flat modulus band-pass response. However, they

introduce a variable delay (2.5 ns as total average) in addition to the loop main delay. A

Bessel filter was also studied, because of its flat delay. Nevertheless, as they have very

long transition bands, they were discarded. The filter f(t) was a PI control, leading to

a second order Phase-Locked Loop. So, design parameters to optimize were damping

factor, natural frequency, and loop delay.

3.2.1 Phase noise simulations

This subsection presents the simulation of several configurations (damping factor and

natural frequency) in order to determine the Lock-In loop limitations for minimizing the


phase noise. Also these simulations determined the optimal parameters for the loop, only

considering laser phase noise. Several sweeps of damping factor and natural frequency

were made for different loop main delays (1 ns, 5 ns and 10 ns) and laser linewidths (from

100 kHz to 10 MHz). Details on how the phase noise was digitally modeled in Matlab

environment can be found on appendix D.

A sample of these simulations is shown in figure 3.4. There it can be seen the time

evolution of the phase noise (1 MHz linewidth) and the phase signal introduced by the

OPLL. Figure 3.4(b) corresponds to a zoom of figure 3.4(a) between 200 ns and 300 ns,

for showing the dithering introduced by the loop.

Figure 3.4: Phase noise evolution and phase signal introduced by the loop. Inset (b)is a zoom between 200 ns and 300 ns.

The results obtained practically have the same behavior as a decision-driven architecture,

which is shown in [16, 17]. E.g. 11.39 phase error deviation is obtained for 1 MHz total

laser linewidth and a 3.5 ns loop delay optimum PLL; which fits perfectly with the results

in [17] (see figure 5). At a fixed linewidth and loop delay, phase noise cancellation is in

the same grade at the several optimal configurations, as it is shown in figure 3.5.

So, a priori, there are multiple optimal configurations with damping factors over 2. Since

all optimal configurations for a given loop (same laser linewidth and delay) have similar

phase error RMS values, they have been reproduced in table 3.1 and the BER-floor for

each one was plotted as shown in figure 3.6.

Regarding table 3.1, it should be noted that for 1 MHz linewidth and 1 ns loop delay

a standard deviation of 11.74 was obtained, very close to the limit for operating with

less than 1 dB power penalty at a BER of 10−9 (see sections 2.3.1.2 and 2.3.1.3). For a

BER of 10−3 (FEC limit, phase error deviation < 19), the 1 dB penalty points are near

2 MHz with 1 ns delay and 1 MHz with 5 ns.

BER-floor was obtained by applying the resulting error phase deviation to the expression

deduced by [13] for PSK signals (i.e. infinite SNR is assumed), as in sections 2.3.1.2


Figure 3.5: Loop natural frequency versus damping factor relationship for optimalconfigurations (transient response and phase noise) with 10 ns main loop delay.

Linewidth 1 ns delay 5 ns delay 10 ns delay1 MHz 11.74 15.05 18.23

2 MHz 17.93 23.35 28.24

3 MHz 23.98 28.34 35.08

4 MHz 28.29 34.69 40.35

5 MHz 32.23 36.42 53.82

Table 3.1: Phase error standard deviation for the optimal configurations as a functionof linewidth and delay.

and 2.3.1.3). Note that 10−9 floor can be achieved with 1 MHz laser linewidth and a

loop main delay near 4.5 ns. This means that the loop is at 1 dB penalty for a BER

of 4.86 · 10−6, that with FEC codes can be tolerated. Searching for the limit of FEC

codes, the loop can be at 1 dB penalty of a 10−3 BER, with its equivalent BER-floor of

2.04 · 10−6. For this case 2 MHz can be tolerated with 1 ns loop delay. Conversely, for a

large loop delay of 10 ns, a 1 MHz linewidth is allowed.

3.2.2 Time response simulations

When a PLL is optimized for a better cancellation of the phase noise, its loop bandwidth

is maximized, as seen in section 2.3.2.2. Thus the optimum system for phase noise

cancellation is very similar to the optimal one in step response: it will have minimum rise

and setting times, while keeping a tolerable overshoot.


Figure 3.6: BER-floor for optimal configurations as a function of the laser linewidthevaluated at several main loop delays.

However, there may be some differences. In order to quantify these differences, several

computer simulations were made for evaluating the step response without noise. The

step introduced in all the cases was a phase step of 1 rad. Here also several sweeps of

damping factor and natural frequency were performed for different loop main delays; as

in the previous subsection. Parameters measured were 10%-90% rise and setting times,

and maximum overshoot.

A sample of these simulations is shown in figure 3.7. There it can be seen the time response

of the loop for the proposed phase step of 1 rad. The inset of the figure corresponds to

a zoom between 500 ns and 550 ns, showing the dithering introduced by the proposed

OPLL.

After the proposed sweeps, results confirm the behavior expected: when maximizing the

loop bandwidth, phase noise is minimized successfully (minimum phase error deviation)

and the step response has an optimum setting time. The behavior of the optimal settings

is the same demonstrated in [16] for a decision-driven oPLL limited by its loop delay.

This is shown in figure 3.5 for a 10 ns main loop delay.

When an optimal configuration is achieved with high damping factor, the setting time

and the rise time are very close (see figures 3.8 and 3.9). So, the loop has better time

response. Also, for damping factors over 3 the setting time and the rise time converge to

a certain value. This is shown in table 3.2.

These loops are optimized implementations for phase noise cancellation by using a 2.86

(50 mrad) amplitude of dithering signal.


Figure 3.7: OPLL time response for a phase step of 1 rad. Inset figure is a zoombetween 500 ns and 550 ns.

Figure 3.8: Setting time of the optimal configurations for several loop main delays.

For configurations with a small damping factor and minimum setting time, the maximum

overshoot becomes larger. As it is a very narrow overshoot, it does not affect too much

the loop frequency response and phase noise can be successfully cancelled.

As shown in figure 3.10, the maximum overshoot converges to a minimum value for

damping factors over 3 and optimal loop configurations (minimum setting time). So, in

maximum overshoot terms, it is desirable to use damping factors over 3 as well.


Figure 3.9: Rise time of the optimal configurations for several loop main delays.

Loop delay Setting time Rise time10 ns 49.8 ns 45.2 ns5 ns 31.6 ns 28.9 ns1 ns 19.6 ns 18.6 ns

Table 3.2: Convergence values for setting and rise times, at several loop delays.

3.2.3 Amplitude of the dithering signal

Effects of amplitude of dithering signal variation on phase noise cancellation were also

studied. Since dithering and phase noise are independent processes, degradation intro-

duced by dithering amplitude itself is very low when phase error deviation tends to be

high. So, for large loop delays, dithering impact is mostly on the loop gain, as shown

in figure 3.11. However, loop gain can be optimized by modifying damping factor per

natural frequency product, as in the previous subsections.

For the other cases, it introduces an additional error phase deviation of 2, limiting the

noise influence tolerance to a maximum of 10.82.

3.2.4 Comparison with other loops

The Lock-In amplified oPLL performances were compared to other oPLL architectures:

Balanced, Costas, and Sub-Carrier Modulated loops.

The four oPLL configurations were simulated, estimating their phase noise cancellation.

Several configurations of damping factor, natural frequency and dithering amplitude have


Figure 3.10: Maximum overshoot of the optimal configurations for several loop delays.

Figure 3.11: Phase dithering effect for large loop delays.

been simulated in order to determine the loop limitations when cancelling the phase noise.

Precisely, for each loop, the damping factor now was set to 9, assuring an overdamped

performance, since it has been demonstrated to be optimum when designing loops with

large delay [16]. This is the case for the Lock-In loop implemented, using non-integrated

off the shelf components.

In each case, the loop natural frequency was optimized in terms of output phase error.

These simulations determined the optimal designs for each loop type. So, several sweeps


of damping factor and natural frequency were made for different loop delays and laser

linewidths.

Since 10 ns (equivalent to 20 cm of optical fiber) is an easily implementable delay when

regarding a laboratory prototype, results for optimal configurations at 10 ns loop delay

are shown in figure 3.12.

Figure 3.12: Phase error deviation evaluated at a loop delay of 10 ns.

From the results, it can be seen that at low linewidths (below 1 MHz at 10 ns loop

delay), the Lock-In amplified loop mostly has an intermediate performance between the

Costas loop and the balanced loop. Thus when using the Lock-In amplified loop, for a

11 maximum phase error deviation the maximum linewidth limit is of 675 kHz, near

the balanced loop limit. When using PSK modulation, that phase error of 11 limits to

operate at a 1 dB penalty for BER of 10−9, as shown in sections 2.3.1.2 and 2.3.1.3.

On the other hand, if FEC codes are used, a BER of 10−3 is operable. Then, its 1 dB

penalty point (19 of phase error deviation) can be found at a linewidth of 3.1 MHz. In

this case, the Lock-In amplified loop clearly outperfoms the most advanced loops, such

as the sub-carrier modulated loop.

This behaviour is due to the inclusion of the Lock-In amplifier in the loop. At low

linewidths, it is mostly limited by the dithering amplitude, so its performances are near

the balanced loop. However, at high linewidths, when the dithering amplitude is relatively

negligible, the loop performances are improved by the Lock-In amplifier, that ensures a

better phase ranging. For proper comparison between loops, the values of the most

important points of figure 3.12 have been written in table 3.3.

After phase noise cancellation simulations, other important parameters were also evalu-

ated: hold in and pull in ranges. The results are shown in figures 3.13 and 3.14.


Figure 3.13: Pull in margins of the simulated architectures.

Figure 3.14: Hold in margins of the simulated architectures.

In these figures, it is depicted that the Lock-In amplified loop has low pull in and hold in

ranges. This is its main drawback. Precisely, at 10 ns loop delay, the pull in range is found

to be around 20 MHz in front of the 176 MHz achieved by the subcarrier architecture.

Concerning the hold in range, the exact data is 896 MHz for the Lock-In amplified loop,

and up to 7.68 GHz for the subcarrier.


Balanced Costas SCM Lock-In amplifiedLinewidth tolerance BER 10−9 420 kHz 1.15 MHz 1.35 MHz 675 kHzLinewidth tolerance BER 10−3 1.2 MHz 2.65 MHz 2.75 MHz 3.1 MHz

Pull in margin 19 MHz 72 MHz 176 MHz 20 MHzHold in margin 1.28 GHz 2.55 GHz 7.68 GHz 896 MHz

Table 3.3: Table summarizing results at 10 ns delay.

3.3 Experiments and discussion

A laboratory prototype of the proposed PLL was developed and assembled into an ex-

perimental setup (Figure 3.15).

Figure 3.15: Experimental Setup.

An external cavity tunable laser was placed at the transmitter (Tx) side, while at the

receiver side (as local oscillator) there was a standard DFB laser (Panasonic LNFE03)

running at 1544.07 nm, with a measured sensitivity of 1.4 GHz/V. The local oscillator

laser linewidth was measured by using a self-homodining technique [38]. Results are

shown in table 3.4. The optimum point was found to be 120 mA, giving a laser linewidth

of 833 kHz. As the linewidth specification of the external cavity laser was of 150 kHz,

the total linewidth for the operating OPLL was of 983 kHz.

Laser current Linewidth Laser current Linewidth30 mA 1.66 MHz 150 mA 1 MHz50 mA 1 MHz 165 mA 1 MHz70 mA 916 kHz 175 mA 1 MHz90 mA 916 kHz 200 mA 1 MHz100 mA 833 kHz 225 mA 1.1 MHz120 mA 833 kHz 250 mA 1.17 MHz135 mA 916 kHz 300 mA 1.36 MHz

Table 3.4: Measured values of the local oscillator linewidth.


Figure 3.16: Electrical power spectrum after photodetection.

The Rx laser output was fusion spliced with the optical coupler and the photodetector (a

standard PIN diode). The balanced detector was substituted by a single photodetector

because of the need to monitor optical signals and also achieve relative low loop delay.

A printed circuit board was fully engineered and prototyped, containing the electrical

parts of the OPLL: bandpass and lowpass filters, electrical oscillator (VCO), electronic

phase shifter, RF mixer and PI filter.

The parameters for the Lock-In amplified loop prototype were optimized for the 700 MHz

dithering frequency. Filters placed inside PLL board were designed and implemented to

introduce the same delay as in simulations (around 3 ns). Finally, the total loop delay

was measured using a vectorial network analyzer, and found to be 10 ns.

Locking was observed by tuning one of the lasers until the main beat signal was about

20 MHz, in agreement with the pull in range simulation results. Concerning the hold in

range, it was found to be 868.24 MHz, also in agreement with the simulations.

Figures 3.16 and 3.17 depict the spectra at the output of the photodetector before and

after the phase-locking is achieved. In figure 3.16 it is clearly shown that the peak due

to the frequency difference between the local oscillator generates a replica modulated at

the frequency of the electrical VCO.

Nevertheless, the most interesting spectrum is the one depicted in figure 3.17. From this

spectrum, the phase error standard deviation could be calculated using the procedure

described in [39]. Using Matlab, the photodetected spectrum could be integrated up to

200 MHz, and afterwards divided by the proposed constant of <RLPSPLO. As all these

values where known, it was easy to find the phase error deviation. Precisely, it was of


Figure 3.17: Electrical power spectrum after photodetection.

11.49, for a measurement bandwidth of 200 MHz. This value fits perfectly into the

Lock-In amplfied loop curve of figure 3.12, confirming again the theoretical calculations.

So a BER near 10−9 could be achieved when working with this configuration.

3.4 Chapter summary

In this chapter a novel OPLL concept was introduced and demonstrated, based in Lock-In

amplification of optical phase error. This architecture uses simple optical components,

being especially indicated for low linewidth DFB commercial lasers, and avoiding the use

of the phase-critical optical 0/90 hybrids. While phase noise swings quite slowly, phase

governing band can fill under DFB laser FM response dip and dithering will be above it.

After a theoretical analysis, simulations and experiments were performed: Loop was opti-

mized in front of phase noise, taking into account the time response, dithering amplitude

effects, acquisition parameters, and comparison with other loops.

At first glance (theoretically) its phase noise performances are similar as the Decision-

Driven optical PLL: With a main delay over 4.5-5 ns, the 10−9 BER 1 dB penalty point

cannot be achieved for linewidths worse than 1 MHz.

Nevertheless, after advanced simulations confirmed by experimental results, it was found

that with a more realistic delay value of 10 ns this loop can achieve a 10−9 BER with

675 kHz linewidth. In case FEC codes are used, a BER of 10−3 can be tolerated, en-

hancing the linwidth tolerance up to 3.1 MHz and clearly outperforming the other loops


(Decision driven, balanced, costas and subcarrier modulated). Regarding the acquisiton

parameters, pull in and hold in ranges were found to be 20 MHz and 868.24 MHz, respec-

tively. Thus, a very low range guarantees acquisiton, whereas a much wider is ensuring

the PLL tracking.

Finally, it should be noted that the unique characteristics of such loop make it easy to

embed it onto an integrated semiconductor optical circuit. In that case, the loop delay

can be dramatically reduced, thus improving OPLL performances.

Chapter 4

Advances in phase and polarization

diversity architectures

Even though the PLL proposed in chapter 3 has shown good performances against the

loop delay and laser linewidth, its achievements are very poor for being used with the

majority of commercially available lasers (linewidths in the order of tens of MHz). Thus,

the need to explore the phase diversity techniques was found, as a solution to the phase

noise problem. Nevertheless, the architectures proposed until now (shown in section 2.3.3)

need a full 90 hybrid, which is still a fairly complex device.

Nevertheless, in this chapter two main approaches will be enhanced for achieving the

phase diversity: Full phase diversity and time-switched phase diversity.

First the full phase diversity scheme (using a 90 hybrid) will be improved, proposing a

novel algorithm for phase estimation based in the Karhunen-Loeve series expansion [40],

clearly outperforming the Wiener filter estimation seen in section 2.3.3.2.

Secondly a new phase diversity technique based in time switching is proposed, using more

simple optical devices [41, 42]. The idea is to divide each bit into two time slots: one for

detecting the I component and the other one for detecting the I component. As it is a

concept with enough novelty, it has been patented [43, 44].

For this second approach a first implementation based on differential detection will be

experimentally demonstrated [41], while using a phase modulator (driven by the recovered

data clock) after the local oscillator for achieving the time switching diversity.

Furthermore, two variations of this time switching phase diversity will be analyzed: one

based in Fuzzy logic data estimation and another one simplifying the receiver architecture.

For the first one, a heuristic data estimation method based on Fuzzy logic will be intro-

duced and extensive simulations will be performed, showing a phase noise robustness near

the Wiener filter performances [45]. Regarding the simplified receiver approach, the idea

is to drive the local laser directly with the filtered data clock to achieve the time switching

69

Chapter 4. Advances in phase and polarization diversity architectures 70

diversity [46]. Also, simulations and proof-of-concept experiments will be performed for

this case.

Finally, the natural extension of the time switching concept to the polarization diversity

will be theoretically analyzed, showing its feasibility [47].

4.1 Full phase diversity

4.1.1 Karhunen-Loeve series expansion phase estimation

In chapter 2, the phase and polarization diversity architectures were introduced and

several algorithms (including differential detection) for phase estimation have been seen.

The most remarkable are the ones based in Wiener filter and Viterbi-Viterbi algorithms,

that are becoming more popular due to the improvement of digital signal processors.

With such algorithms one is allowed to use lasers on the order of tens of MHz, for a data

rate of 1 Gb/s, representing a big improvement respect the OPLLs.

Here a phase estimation method based on Karhunen-Loeve series expansion is presented.

It can be implemented using standard DSP devices, since its complexity is not very high.

Also, it clearly outperforms the Wiener filter algorithm.

4.1.1.1 Receiver scheme

A scheme of the receiver to be used is a typical intradyne architecture, shown in figure 4.1.

There, the optical input signal is interfered with a free-running optical local laser in a

2x4 90 hybrid. The output signals of the hybrid are then detected by two balanced de-

tectors, and the I and Q outputs are digitized by an Analog-to-Digital Converter (ADC).

Finally, a Digital Signal Processing (DSP) module performs the phase estimation and

data detection.

Figure 4.1: Scheme for a standard intradyne receiver.


4.1.1.2 Phase estimation algorithm

In section 2.3.1.4 is shown that laser phase noise characterized by a certain spectral width

(∆ν) can be modeled as a Wiener process (w(t)). As a random process, the Wiener process

can be expanded into a Karhunen-Loeve (KL) series form:

w(t) =∞∑n=1

cnϕn(t) (4.1)

where ϕn(t) is a set of orthonormal functions (eigenfunctions) in the interval (0, T ), and

cn are the series coefficents, being random variables. For the Wiener process case, it is

shown that [14]:

ϕn(t) =

√2

Tsin(ωnt) (4.2)

cn =

√2

T

∫ T

0

w(t) sin(ωnt) (4.3)

where ωn =√

2π∆νλn

= (2n+1)π2T

being the eigenvalues defined as the variance of the series coefficients:

λn = Ec2n =

8T 2∆ν

(2n+ 1)2π(4.4)

Since larger eigenvalues are those of lower n, the series can be truncated at a relatively

short number of terms, M . Precisely, it can be easily shown that λ1 is almost 20 times

λ5, then truncating at M = 5 should be enough. Please note that for M = 5 and M = 15

the output phase error deviation of the estimator is almost the same, independently of

the time interval squared per spectral width product. This is shown in figure 4.2, for the

proposed performances evaluation.

In order to estimate and cancel the laser phase noise, what is proposed is to process the

received phase block by block. Thus, a priori, the observable interval length T is known,

and the eigenfunctions can be easily calculated. Consequently, the phase noise can be

estimated as:

w(t) = c>ϕ =(c1 c2 c3 . . . cn

)

ϕ1

ϕ2

ϕ3

...

ϕn

(4.5)

Equation 4.4 shows that the lower the interval squared per spectral width product is, the

lower the eigenvalues. Also, inside a block, the phase noise will have a limited variance of


2π∆νT [14]. So for small blocks and same spectral width, the estimator will work better.

That is the reason why it is proposed to work with blocks of only 1 symbol.

Figure 4.2: Phase error deviation as a function of time interval squared per spectralwidth product (T 2∆ν).

From one block to another, phase noise is expected to be highly correlated as it is a slow

process compared to data. Thus, the series coefficients also present small changes from

one block to the next one. So, coefficients are going to be calculated by using an adaptive

algorithm. In this case the Least Mean Square (LMS) method will be used.

The estimation algorithm diagram used in the following section is the one depicted in

figure 4.3. There, the M sinusoidal waveforms needed for phase estimation are stored in

the DSP memory. Next, a coefficient (coming from the LMS estimation block) is applied

to each of the waveforms. The sum of all the waveforms multiplied by the coefficients

results to be the estimated phase, and the phase error is used as the LMS input.

4.1.1.3 Algorithm performances and discussion

In order to evaluate the performances of the proposed receiver architecture, firstly a

BPSK data stream was simulated, running at 10 Gb/s with variable phase noise. The

linewidths ranged from 100 kHz to 10 GHz. Phase noise was modeled using the technique

proposed in appendix E. Such a phase noise was used to compare the proposed algorithm

performances with respect to a Wiener filter with a lag of 10 symbols (optimum), as

described in [26] and in chapter 2. In both cases a data stream of 220 = 1048576 symbols

was simulated, and the received signal was resampled at 16 samples per symbol. Then,

the digitized I and Q signals were used to reconstruct the received optical signal and its

phase was packet into blocks of 16 samples (one symbol). The phase error deviation after


Figure 4.3: Block diagram of the phase estimation algorithm.

phase estimation was used as a measure for the quality of the algorithm. Results are

shown in figures 4.2 and 4.4.

Figure 4.4: Phase error deviation as a function of the spectral width per bitrate ratio.

Regarding the term where the KL expansion is truncated, in figure 4.2 is shown that there

is almost no difference on the estimation for M = 5 and M = 15; so the best decision

was to keep it at 5.

From figure 4.4, it is shown that when using the KL series estimation for a 11 maximum

phase error deviation (1 dB penalty for a BER of 10−9) the system is limited, working

at a maximum spectral width of 4% of the bit rate. Also, if Forward Error Correction


(FEC) codes are used and a BER of 10−3 is operable with only 7% overhead [11], and a

maximum phase error deviation of about 19 is allowed for less than 1 dB penalty, leading

to a maximum spectral width of 11% of the bit rate.

4.2 Time switched phase / polarization diversity

This section presents a novel phase/polarization diversity receiver based on a time switch-

ing between phase and (or) polarization orthogonal states.

The general idea is to have the orthogonal states for phase and polarization in the same

bit, not concurrently but sequentially. Thus, for the first half of the bit the signal relative

to one orthogonal component (I or H) will appear, whereas for the second half of the bit

the signal relative to the other orthogonal component (Q or V) will be seen.

First the time switched phase diversity will be explained, with all of its approaches: phase

diversity with differential detection, fuzzy logic data estimation, and simplified diversity

with laser direct drive. Finally, analyze the time switching polarization diversity will be

analyzed.

4.2.1 Phase diversity combined with differential detection

The receiver has two main parts: the first is a homodyne coherent photo-receiver with

an Automatic Wavelength Controller (AWC), instead of an OPLL, with an added phase

modulator (PM) at the local laser output, and the second is the electrical post-processing.

The coherent photo-receiver mixes the incoming optical field with the local laser carrier

in the balanced photo-detector stage. The optical phase modulator at the local laser

output is controlled by the data clock (50% duty cycle) producing a fixed 0 − 90 phase

modulation, to obtain the I and Q signal components, at the first and second half part

of each Tb (bit time) respectively, after the optical homodynation.

By gating the photo-receiver output with the data clock signal and its inverse, the I and

the Q components are obtained separately in the two branches, now with RZ shape. The

electronic signal processing performs differential demodulation of both I and Q compo-

nents, with a delay time equal to Tb; and the synchronous combination of the I and Q

components. Given the post-processing scheme, lets analyze how it can improve the data

detection. Also, in order to synchronize data signals at the two branches, the I com-

ponent is delayed by half of a bit time, and, finally, both demodulated components are

synchronously combined with an adder.

The signal power fluctuates between the I and the Q branches randomly, due to the phase

noise, at a rate of the order of the laser linewidth, and the combination of both outputs


Figure 4.5: Time-switched diversity differential homodyne receiver scheme.

can assure its recovery. This operates like a phase-diversity system. Compared to an

OPLL, the phase noise swing time has been shortened from the loop delay to the bit

time, which, in contrast, reduces with the bit rate.

The local laser does not need to be phase coherent with the incoming optical carrier, al-

though an automatic wavelength controller is convenient to maintain the two wavelengths

close each other. It can be regarded as intradyne or heterodyne receiver with near-zero

intermediate frequency. At the transmitter, the optical carrier is feedforward PSK mod-

ulated. The NRZ data is previously differentially coded; thus, the RX decoded data is

d(t) = d(t)′ ·d(t−Tb)′. By performing the calculation of the optical homodynation process

and the electrical post-procesing, the signal can be obtained at the receiver output, where

the laser phase noise is considered as the limiting impairment,

Vout(t) =C2

2d(t)


)+ cos


)+

+ cos(φe(t− Tb/2)− φe(t− 3Tb/2)

)− cos

(φe(t− Tb/2) + φe(t− 3Tb/2)

))(4.6)

where C = 2<RL

√PSPLO is the peak voltage available at the output of the photo-receiver

and φe(t) is the TX+LO laser total phase noise, which can be in the margin [-π, π],

producing signal amplitude reduction. The result is governed by the noise decorrelation

in the Tb/2 and Tb. This signal Vout(t) is fed back to the AWC of the local laser, with

dithering electronics, to track the wavelength, maximizing the output amplitude. It is


not affected by the loop delay: the I/Q post-processing reduces the error phase down to

its bit time variations.

4.2.1.1 Expected system performances

The scheme proposed is difficult to implement mainly because of the lack of high speed

switches, the high number of four quadrant multipliers used for differential detection,

and the electrical branches synchonization. Thus, a simplified version of the receiver has

been developed (referred as second approach) and will be deeply analyzed in the next

subsections. Its scheme is shown in figure 4.10.

The proposed receiver (first and second approaches) is compared to a lock-in amplified

OPLL homodyne receiver. In these two cases, the output parameter measured was the

statistical eye-opening of the received data, accounted as the mean amplitude minus twice

the standard deviation, which provides a fair measure of the sensitivity penalty.

The eye-opening estimation was made at several linewidths from 225 kHz to 1 GHz. Bit

rate was set at 10 Gb/s; and a 4th-order 7.5 GHz Bessel low-pass filter was placed before

decision. Figure 4.6 shows an example of the time traces of the signals Vouti, Voutq and

Vout, from figure 4.5.

Figure 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.

Figure 4.7 shows the resulting eye-diagrams for a large linewidth (50 MHz), for the I and

Q branches and the combined output. While I and Q branches have their eye totally

closed, the post-processing output has a similar opening as for very low linewidths.

The resulting system tolerance to the laser phase noise is depicted in figure 4.8. It shows

the normalized eye opening measured as a function of the laser linewidth, showing that

the phase noise tolerance can be greatly extended, from 1 MHz to 100 MHz (for about

2dB sensitivity penalty).


Figure 4.7: I, Q, and I+Q outputs Eye-diagrams, at 50 MHz total laser linewidth.

Figure 4.8: Statistical normalized eye opening (20Log) for the I/Q receiver (both firstand second approach) and a lock-in oPLL.

Also, the I/Q processing demonstrates to be insensitive to the loop delay and to the

wavelegth drift (up to 10%Rb), and does not require fast tuning lasers. These results have

been validated through extensive numerical simulations, and are shown in figure 4.9.

4.2.1.2 Simplified scheme and phase noise analysis

A simplified version of the time-switch phase diversity receiver is shown in figure 4.10. In

this case, the proposed diversity receiver has two main parts, too. The first is a coherent

photo-receiver with added clock-synchronous phase switching (0−90). The second part

is an electronic postprocessing of the signal demodulation and synchronous combination


Figure 4.9: Statistical normalized eye-opening (20log) for the I/Q receiver (both firstand second approach) as a function of the laser frequency drift.

of the orthogonal components. At the transmitter, the digital data modulate the optical

phase [0-180], after a differential precoder (differential phase shift keing).

Figure 4.10: Receiver scheme for phase noise analysis.

The electronic signal processing stage performs the parallel differential demodulation.

Next, a delay-and-add block is placed. It properly combines the orthogonal components.

As a result, the same theoretical results as those obtained in [24] were retrieved in the

present case, except for the extra Tb/2 delay. Besides, it must be taken into account that

the reduced duty-cycle and the correspondingly increased electrical bandwidth produces

a 3dB signal-to-noise ratio penalty.

After the photo-detection stage, typical differential phase shift keying data that is cor-

rupted by phase noise describe a circle in the IQ plane when the data are represented as

a phasor. When differential demodulation is performed, a change of phasor bases takes


place; data points affected by the phase noise then fall either at the first or the third

quadrant of the IQ signal plane depending on the data value (1 or 0).

The receiver decoded data are d(t) = d(t)′ · d(t − Tb)′, where d(t)′ is the differentially

precoded version of data. The combination of the detected I and Q components after

differential demodulation can be written as:

Vout = C2

2d(t)

[cos(φe(t)− φe(t− Tb)

)− (4.7)

− cos(φe(t) + φe(t− Tb)

)+

+ cos(φe(t− Tb/2)− φe(t− 3Tb/2)

)+

+ cos(φe(t− Tb/2) + φe(t− 3Tb/2)

)]where C = 2<RL

√PSPLO is the peak voltage available at the output of the photo-

receiver, RL is the receiver impedance, < is the photodiode responsivity, and φe(t) is the

total laser phase noise (transmitter plus local), which is in the margin [−π, π], producing

signal amplitude reduction. Since the data are differentially coded, in this expression the

relevant terms are those relative to the phase-noise difference. After some trigonometric

algebra, this expression can be properly expanded for evaluating the phase noise effects:

Vout =C2

2d(t)

[1− sin2

(∆φ1(t) + ∆φ2(t)

2

)− sin2

(∆φ2(t) + ∆φ3(t)

2

)+ (4.8)

+1

2cos(2φe(t)

)[2 cos

(∆φ1(t) + ∆φ2(t)

)sin2

(∆φ1(t) + ∆φ3(t)

2

)+

+ sin(∆φ1(t) + ∆φ2(t)

)sin(∆φ1(t) + ∆φ3(t)

)]+

+1

2sin(2φe(t)

)[2 sin

(∆φ1(t) + ∆φ2(t)

)sin2

(∆φ1(t) + ∆φ3(t)

2

)−

− cos(∆φ1(t) + ∆φ2(t)

)sin(∆φ1(t) + ∆φ3(t)

)]]

where the phase error on each half bit has been defined as:

∆φ1(t) = φe(t)− φe(t− Tb

2

)

∆φ2(t) = φe

(t− Tb

2

)− φe(t− Tb)

∆φ3(t) = φe(t− Tb)− φe(t− 3Tb

2

)


Figure 4.11: BER-floor of several cases: theoretical (dashed line), theoretical butincluding the penalty due to phase switching (dotted line), numerical simulation (con-

tinuous line) and measurements (square points).

As phase noise is a modeled as a Wiener process, its differences in time are Gaussian

random processes [14]. So, the three arguments, ∆φ1(t), ∆φ2(t) and ∆φ3(t); are indepen-

dent identically distributed Gaussian random processes with zero mean and a variance

proportional to the linewidth per half of bit-time product. Thus the terms containing

φe(t), tend to 0 as they are multiplied by sine terms near 0, and the only remaining terms

will be near 1. ∆φ3(t) is an added delay due to the fact that time-switched architecture

is used instead of the architecture proposed in [24]. So, in the ∆φ3(t) = 0 limiting case,

a BER-floor can be easily calculated in equation 2.29, and this theoretical limit is shown

in figure 4.11.

An early evaluation of the receiver performance was carried out by means of numerical

simulations. This was calculated from the same equation 2.29 used before but including

additive noise effects due to the use of the phase scrambler. As shown in figure 4.11, the

calculated results differ by only 3 dB from the theoretical calculations, as expected.

Since in this type of system the phase scrambling is done on the receiver side, the system

is less affected by fiber impairments, such as chromatic dispersion, than an alternative

approach [48]. It is potentially useful to recover the orthogonal I and Q components of

the complex received signal (phase and magnitude), opening the door to the electronic

compensation of transmission impairments by means of new digital signal processing

techniques.

An experimental prototype of the proposed receiver has been developed and was tested

in a laboratory setup. Sensitivity and frequency drift impacts were evaluated. Although

the proposed receiver architecture was demonstrated to be highly insensitive to phase


noise effects, low linewidth lasers were initially used; the total linewidth was 350 kHz,

much smaller than the bit rate. Two external-cavity tunable lasers were used, one on

each branch (Transmitter, TX, and local oscillator, LO) of the setup (see figure 4.12).

Figure 4.12: Experimental setup

The TX branch was binary phase shift keying modulated with a Mach-Zehnder Modulator

(MZM, a Fujitsu FTM7921ER) at 1 Gb/s. The local oscillator branch was 0− 90 mod-

ulated with a standard LiNbO3 phase modulator (PM, a JDSU IOAPMOD9183), driven

by the clock signal (CLK) of the pseudo-random binary sequence (PRBS) generator used

to provide data at the first branch. These two optical signals are coupled and detected by

a balanced detector followed by an electrical processing stage (a delay-and-multiply mod-

ule plus a delay-and-add stage, as shown in figure 4.10). A microwave double-balanced

mixer (Marki Microwave M20004) was used as a four-quadrant multiplier.

Firstly, sensitivity measurements were carried out, obtaining −38.7 dBm for BER= 10−9

(see figure 4.13). As the Tx laser used was a high power laser (about 9 dBm), a power

budget of 47 dB could be reached. For the 10−3 BER, the sensitivity was found to be at

−44.3 dBm, achieving 53.3 dB of power budget.

Finally, in order to evaluate the impact of the critical phase noise on our system, the

transmitting laser was changed by a standard linewidth distributed feedback laser (Fujitsu

YM004). Varying the laser’s bias, the total laser linewidth ranged from 18 MHz up to

30 MHz, yelding a BER-floor of from 10−3 to 10−2. These linewidth values (1.8%-3% Rb)

are lower than the theoretical limit (3.6%-5.9% Rb) calculated in [13] and the simulation

results, as shown in figure 4.11. The difference between the experimental points and

the theoretical curve is explained by the frequency response distortion of the microwave

mixers and the 3 dB penalty due to phase switching.


Figure 4.13: Sensitivity results and output eye-diagram

4.2.1.3 Frequency drift

For the frequency drift impact evaluation, equation 4.7 can be revisited. Assuming no

phase noise, φe(t) will be only contributed by the frequency drift. For a generic frequency

drift fd, equation 4.7 can be rewritten as:

Vout = C2

2d(t)

[cos(2πfdTb

)− (4.9)

− cos(4πfdt+ 2πfd(t− Tb)

)+

+ cos(4πfdTb

)+

+ cos(2πfd(t− Tb/2) + 2πfd(t− 3Tb/2)

)]After some algebra, the expression can be rearranged as:

Vout = C2

2d(t)

[2 cos

(2πfdTb

)− (4.10)

− cos(2πfdt+ 2πfdTb

)+

+ cos(4πfdt− 4πfdTb

)]Note that the cos(2πfdt + 2πfdTb) and cos(4πfdt − 4πfdTb) terms are running at much

lower speed than the bit rate and, in the worst case condition, its argument can be

approximated by a uniformly distributed random variable ranging from −π to π. In this

case, these processes can be approximated by its mean [12]. Thus, these last cosine terms

cancel each other. Then, the output voltage of the add block is approximated by:

Vout ≈C2

2d(t)2 cos

(2πfdTb

)(4.11)


Using the proposed model and taking into account that data is differentially encoded, the

probability of error can be written as:

Pe =1

2exp

(−SNR · cos2

(2πfdTb

)2

)(4.12)

Numerical evaluation of such expression is shown in figure 4.14. There it is shown that

for Pe = 10−9 and no frequency shift a minimum SNR of 16 dB is required, whereas for

Pe = 10−9 and a frequency shift of 10% (100 MHz at 1 Gb/s) a minimum SNR of 17.9

dB is needed.

Figure 4.14: Modeled BER as a function of the laser frequency drift per bitrate ratio.

To experimentally evaluate the detuning tolerance between transmitter laser and the

receiver local laser, the setup of figure 4.12 was also used. There, a manual frequency

drift was carried out around 1550 nm. As it is shown in figure 4.15, a drift of about 60

MHz (6% of the bit rate) leads to 10−3 BER, that can be considered as the operating

limit (using forward error correction codes, equivalent to 10−9).


Figure 4.15: Measured BER as a function of the laser frequency drift.

4.2.1.4 Channel spacing

Several adjacent channel interference studies have been carried out regarding coherent

system [10, 49], but it has never been done in this homodyne system.

It is shown that for a generic optical receiver, assuming only additive white Gaussian

noise, the optical power penalty due to channel crosstalk can be expressed as:

penalty(dB) = −10 · log(

1− SNR

SIR

)(4.13)

where SNR is the electrical signal to noise ratio for the reference Bit Error Ratio (BER),

and SIR is the electrical signal to interference power ratio. This SIR mostly depends on

the architecture of the receiver, the modulation format used, and the power difference

between main channel and those undesired. In order to accurately calculate this SIR, next

an analysis of the signals detected will be performed. Please note that in this analysis

the phase and additive noises will not be taken into account.

Figure 4.16 shows a block diagram of the time-switched phase-diversity differentially

encoded BPSK receiver under study. In an equally-spaced multiple channel environment,

it satisfies the following set of equations:

eS(t) =N∑

i=−N

√PS exp(j(ωt+ 2πDit+ φSi(t))) (4.14)



Figure 4.16: Time-Switched Phase-Diversity DPSK receiver for channel spacingstudy.

φLO(t) =π

2p(t) (4.16)

where eS(t) is the transmitted optical field; eLO(t) is the local oscillator optical field;

2N + 1 is the total number of channels; PSi and φSi(t) are the transmitter optical power

and the phase coded data [0, π] of the ith channel, respectively; D is the channel spacing;

PLO is the local oscillator optical power; φLO(t) is the phase introduced by local laser;

and p(t) is a pulse train [0, 1] at same frequency than bit-rate used for phase scrambling.

Please note that this notation implies an odd number of channels, where the central

channel is the desired one.

After the balanced detection stage, the photo-detected current can be written as:

Ip(t) =N∑

i=−N

2<√PSiPLO cos

(φSi(t) + 2πiDt− π

2p(t)

)+ n(t) (4.17)

where < is the detector responsivity and n(t) is the overall noise process. Let us as-

sume that all channels have the same bit rate and are BPSK modulated by statistically

independent sources, and further calculate the power spectral density (PSD) of the mod-

ulated signal in the desired channel. Before calculating that PSD, the modulation signal

pulses shape (including p(t)) should be carefully analyzed. Assuming ideal pulses and

data alphabet [0, π], Ip(t) can be also expressed as:

Ip(t) =N∑

i=−N

2<√PSiPLO cos

(g1(t)φSi(t)

)· cos

(2πiDt

)+ n(t) (4.18)


where g1(t) is defined as when t ∈ [0, T ], g1(t) =

1 0 ≤ t ≤ T

212

T2< t ≤ T

g1(t+ T ) = g(t)

being T the bit time (the inverse of the bit rate).

Since cos(π) = −1, cos(0) = 1 and cos(±π/2) = 0, it can be rewritten as:

Ip(t) =N∑

i=−N

2<√PSiPLO · g2(t) · d · cos

(2πiDt

)+ n(t) (4.19)

where d is defined to be 1 when φSi(t) = 0; and -1 when φSi(t) = 0.

Also g2(t) is defined as: when t ∈ [0, T ], g2(t) =

1 0 ≤ t ≤ T

2

0 T2< t ≤ T

g2(t+ T ) = g(t)

g1(t) and g2(t) waveforms are shown in figure 4.17. Please note that g2(t) has a triangular

shaped autocorrelation (R2(t)), but defined in the [−T/2, T/2] interval. This is also

shown in figure 4.17. The ideal autocorrelation of a differentially coherent BPSK signal

is a triangular function defined in the [−T, T ] interval [9]. Since the PSD is defined as the

Fourier transform of the autocorrelation function, Ip(t) has the same PSD as a general

differentially coherent BPSK, but spread with a factor of 2. This is shown in figure 4.18.

Figure 4.17: g1(t) and g2(t) pulse shapes and autocorrelation of g2(t), R2(τ)

Then, from equation 4.19, the double-sided PSD of Ip(t) is found to be:

Gp(f) =N∑

i=−N

4<2PS0PLOT

4

[sinc2

(πT (f − iD)

2

)]+N(f) (4.20)

where N(f) is the PSD of n(t). Note that all channels are assumed to have the same

power. Then, the SIR is defined as the power of the useful channel versus the power of

the interferent channels. Taking into account only the terms 0 and 1, the SIR can be


Figure 4.18: Spectrum after photodetection: Ideal homodyne reception (a) and usingtime-switched phase-diversity (b)

calculated from If (t):

SIR ≈

∫ +∞−∞ |H(f)|2

[sinc2

(πTf

2

)]df∫ +∞

−∞ |H(f)|2[sinc2

(πT (f−D)2

)]df

(4.21)

where H(f) is the transfer function of the channel filter placed after photo-detection stage,

depicted in figure 4.16. Here the total SIR is approximated to the signal-to-strongest-

interference (due to the adjacent channel). If channel spacing penalty is calculated using

equation 4.13 with SIR values provided by equation 4.21, results do not resemble so much

to experimental results (Figure 4.20) because it is a very rough approximation. Thus, a

more precise model must be developed in the time domain.

Let us assume that a signal sample is taken at the output of the channel filter, plus an

interference signal which has a phase θ(t), as shown in figure 4.19. This phase can be

written as:

θ(t) = φS1(t) + 2πDt+π

2p(t) (4.22)

where the signal-to-strongest-interference approximation is applied. θ(t) varies rapidly

during the symbol interval (at speed near D). So its increments between consecutive

symbols represents a residual filtered phase that can be regarded as a random phase

process uniformly distributed from −π to +π along the bits.

In the proposed receiver, decision stage input samples are signal plus interference vector

projections onto In-phase straight line. Thus, the decision variable, X, can be expressed

as:

X ∝ d(

1 +1√SIR

cos(θ))

(4.23)


Figure 4.19: Complex representation of signal samples including interference.

Figure 4.20: Sensitivity penalty due to channel crosstalk. Square points are experi-mental data.

where θ is the residual phase after filtering θ(t) increments between two consecutive

symbols. Thus, for a DPSK signal [10], the error probability conditioned to the value of

θ in the optimum sampling instant is found to be:

Pe(θ) =1

2exp

(− SNR

2

(1 +

1√SIR

cos(θ)

)2)(4.24)


Finally, the overall bit error rate can be written as:

Pe =1

4π

∫ +π

−πexp

(− SNR

2

(1 +

1√SIR

cos(θ)

)2)dθ (4.25)

This BER expression was used to evaluate by means of numerical calculations the pro-

posed receiver performances. It was also compared to the Gaussian approach (based on

equation 4.13), and to an ideal coherent receiver, described in [10].

In these three cases, the output parameter measured was the 10−9 BER sensitivity penalty

due to channel crosstalk. The penalty crosstalk measures were made at several channel

spacing, from 1 GHz to 6 GHz. Bit rate was 1 Gb/s; and a 4th-order 2 GHz Bessel

low-pass filter was placed after photo-detection stage. For the ideal system, that filter

was also 4th-order Bessel, but with 750 MHz bandwidth.

The resulting system tolerance to the channel crosstalk is depicted in figure 4.20. It shows

that for a 1 dB penalty the minimum spacing between channels is around 3 GHz for both,

Gaussian model and the proposed approach. However, if channel spacing decreases, the

Gaussian model becomes useless. For the ideal system the 1 dB penalty channel spacing

is of only 1.25 GHz.

Figure 4.21: Experimental setup.

An experimental prototype of the proposed receiver has been assembled into a laboratory

setup, shown in figure 4.21. Although the proposed receiver architecture has demon-

strated to be highly insensitive to phase noise effects, low linewidth lasers (hundreds of


kHz) were used. Precisely, total laser linewidth was 300 kHz, much smaller than bit rate.

Three external cavity tuneable lasers were used, one on each branch of the setup.

First, transmitter branch (TX) was modulated by a standard LiNbO3 phase modulator

(PM, Avanex IMP10) at 1Gb/s. Next, interference signal (INT) was obtained by a

Mach-Zehnder Modulator (MZM, Fujitsu FTM7921ER) properly biased to work in the

0 − 180 range. This modulator was driven by the complementary Pseudo-Random

Binary Sequence (PRBS).

Afterwards, these two branches were coupled and launched in to a 27 km standard G-652

fiber spool. On the other side, the local oscillator branch (LO) was 0−90 modulated by

another phase modulator, now driven by the clock (CLK) signal of the generator used to

provide data at the TX and INT branches. LO and interfered signals were finally coupled

and detected by a balanced detector followed by a 4th-order 2 GHz Bessel-Thomson filter.

Under these circumstances, the power penalty due to channel crosstalk was measured.

Results are shown on figure 4.20, square points. While 3 GHz spacing was the minimum

for a 1 dB penalty, the 3 dB point was found to be between 1.5 GHz and 2 GHz. Also,

when channel spacing is greater than 6 GHz, adjacent channel interferences can be almost

neglected. Thus, the curve depicted by experimental points is very close to the theoretical

one.

In summary, a channel crosstalk penalty model have been discussed and experimentally

demonstrated, when using a time-switched phase-diversity homodyne receiver. 3 GHz

minimum channel spacing was obtained for a 1 dB sensitivity penalty, and 1 Gb/s bit-

rate. In other words, more than 1500 wavelength can be easily accommodated in the C

band if no other non-linear effects are generated.

4.2.2 Fuzzy data estimation

This section aims to change the combination (delay-and-add) block placed after differen-

tial demodulation, shown in figure 4.10. This combination block is replaced by a digital

signal processing block, containing a data estimation algorithm based on Fuzzy logic.

Fuzzy logic techniques have been applied in several fields because of its performances with

respect to non-linear systems and its easiness of implementation [50, 51], constituting a

reliable approach to hard estimation problems.

Thus, novel receiver concept is proposed, based on combining both techniques: time-

switched phase diversity and fuzzy logic based digital processing. The first part allows

making a homodyne receiver with simple optical and electrical components. This enables

a receiver prototype implementation, as this digital processing can be made using off-the-

shelf electrical components: digital gates and other simple digital components.



As previously shown, in the proposed phase diversity homodyne receiver, the coherent

photo-receiver mixes the incoming optical field with the local laser carrier in the balanced

photo-detector stage. The optical phase modulator at the local laser output is controlled

by the data clock producing a periodic 0 − 90 phase change, to obtain the Inphase (I)

and Quadrature (Q) signal components, at the first and second half part of each bit time

(Tb) respectively.

After the conventional balanced photodetector, a differential decoder is placed. As the

limiting impairment of homodyne systems is phase noise, this detector reduces the com-

plexity of the problem to a possible phase cycle-slipping limited by the bounds of a bit

time, achievable only when using extremely high linewidths.

Figure 4.22: Receiver scheme.

Next, an analog to digital converter (ADC) is placed. In order to digitize the I and Q

components of the signal received, a minimum of two samples per bit must be taken.

Afterwards, digitized signals are processed by the fuzzy-logic-based data estimator. A

receiver scheme is shown in figure 4.22.

4.2.2.2 Data estimation

Since data is DPSK coded and initial phase is random, after differential decoding, data

contaminated with phase noise points fall either at the first or the third quadrant of the

IQ signal plane depending on data value (1 or 0).

After the photodection stage typical BPSK data only corrupted by a certain amount

of phase noise describes a circle in the IQ plane when data is represented as a phasor.

When differential decoding is performed the phasor bases changes. The detected I and Q


component after differential decoding can be written as:

VI(t) ∝ cos(φd(t)− φd(t− Tb) + φN(t)− φN(t− Tb)

)+ (4.26)

+ cos(φd(t) + φd(t− Tb) + φN(t) + φN(t− Tb)

)

VQ(t) ∝ cos

(φd

(t− Tb

2

)− φd

(t− 3Tb

2

)+ φN

(t− Tb

2

)− φN

(t− 3Tb

2

))−

− cos

(φd

(t− Tb

2

)+ φd

(t− 3Tb

2

)+ φN

(t− Tb

2

)+ φN

(t− 3Tb

2

))(4.27)

where φd(t) is the received coded data phase (either 0 or π ), and N is phase noise term

due to the total laser linewidth (∆ν).

Figure 4.23: IQ plane data plotting without differential decoding (left), and afterdifferential decoding (right) for a signal corrupted by a phase noise due to 100 kHz of

total laser linewidth

As the laser phase noise is a Wiener process, after differential demodulation it is trans-

formed to a Gaussian random process. Then a data remapping is achieved, between the

first and the third quadrant, now clearly separated. This is shown in figure 2 for a small

linewidth (100 kHz). For convenience, it is assumed 0 when it falls on the third quadrant

and 1 when it falls on the first quadrant. Also I and Q digitized components are assumed

to take values from -1 to +1.

Thus, a reasonable way to delimit the areas of data value is to classify the universe of

discourse of these two components into five membership functions: negative, moderate-

negative, null, moderate-positive and positive. These functions are plotted in figure 4.24.

In a similar way, the classification for the estimated data must be done in two membership

functions: one and zero. As fuzzy membership functions are heuristically determined,

their sigmoid shape and the values covered by anyone of them where optimized by means


Figure 4.24: I and Q components membership functions

of numerical evaluation of their robustness in front of phase noise, since this is the major

limitation of homodyne systems.

I/Q Negative Moderate Null Moderate PositiveNegative Positive

Negative Zero Zero Zero Zero -Moderate Negative Zero Zero Zero - One

Null Zero Zero - One OneModerate Positive Zero - One One One

Positive - One One One One

Table 4.1: Fuzzy logic estimator rules base.

Since membership functions are complex functions, the membership of the digitized signal

after the ADC will be determined by means of a look-up table. Based on these member-

ship functions, simple rules like ”If [(I is moderate-positive) and (Q is moderate-positive)

then (data is one)]” construct a solid fuzzy rules base to estimate detected data. This is

shown in table 4.1.

It is shown in [51] that for the same membership functions and given a rule base, there

are multiple methods to implement the fuzzy estimator. The key point of such methods

is to work on the undefined zone of table 4.1, to achieve a higher phase noise tolerance.

After extensive numerical simulations, the optimum method is found to be the so called

Method of Maximum (MoM), which gives us a maximum linewidth tolerance.

Just for summarizing and clarifying, a scheme for data estimation after analog to dig-

ital conversion is shown in figure 4.25. First I and Q components are separated (not

shown). Next, in the fuzzyfication module, the membership function of each component


is determined by a look up table (LUT). Finally the decision is performed by the chosen

defuzzyfication method (MoM).

Figure 4.25: Data estimation scheme.

4.2.2.3 System performances

When the optimum fuzzy logic data estimator was obtained, it was used to evaluate the

proposed receiver performances by means of numerical simulations. It was compared to

the time-switched phase diversity receiver with analog signal processing described before,

which provides high phase noise tolerance compared to conventional homodyne systems.

In these two cases, the output parameter measured was statistical counting of received

bits, which provides the best measure of the system BER. The BER-floor measures were

made at several linewidths from 22.5 kHz to 100 kHz. Bit rate was 1 Gb/s. As time-

switching diversity introduces a penalty due to its nature and simulations of this kind

require high computational resources, minimum BER simulated was 10−4.

The resulting system tolerance to the laser phase noise is depicted in figure 4.26. It shows

the BER-floor measured as a function of the laser linewidth, showing that the phase noise

tolerance can be extended, from 2.8% bit rate of the best known technique to 3.5% bit

rate for a 10−3 BER-floor. This is a 26 % improvement of the bit rate per linewidth

product. The use of this type of codes is inevitable mostly due to the penalty inherent

to the nature of the time-switching diversity (3 dB penalty due to the half-bit 0 − 90

modulation).


Figure 4.26: BER-floor as a function of the laser linewidth at 1 Gb/s

4.2.3 Direct drive time switching

This subsection will deal with a third approach to the time diversity switching. Such

approach tries to further simplify the optical parts of the receiver by driving directly the

laser, and avoiding the phase scrambler module needed in the previous subsections.


The proposed diversity receiver has also two main parts: the first is a coherent photo-

receiver with added clock-synchronous sinusoidal phase switching (0 − 90). The sec-

ond part is an electronic post-processing performing the signal demodulation and a syn-

chronous combination of the orthogonal components, too. Furthermore, a polarization

controller is assumed to compensate signal fluctuations due to SOP changes, although a

polarization diversity scheme can be implemented with increased receiver complexity.


in the balanced photo-detector stage. The local laser is controlled by the filtered data

clock producing a sinusoidal phase change, to obtain the In-phase (I) and Quadrature

(Q) signal energy, at the first and second half part of each bit time (Tb) respectively.

The laser is driven by VLO = Acγ cos(2πfct); where Ac is the main amplitude, γ is a gain

factor, and fc is the fundamental harmonic frequency of the recovered clock. Adjusting

the amplitude and the gain factor is critical in order to obtain the desired performances.


Figure 4.27: Generic receiver module

The photocurrent present at the output of the balanced detector can be written as:

Ipd(t) = 2<√PSPLO cos

(φS(t)− φLO(t) + φd(t) +

π

4+AcγKLO

2πfcsin(2πfct)

)(4.28)

where AcKLO2πfc

is assumed to be π4; < is the photodetector responsivity, PS the transmitter

power, PLO the local laser power, KLO is the local laser FM sensitivity, φd(t) is the

phase containing the data information, φS(t) is the generic phase at the transmitter side

(including phase noise) and φLO(t) is the phase but at the local laser side.

This phase modulation can be easily obtained even with a standard DFB laser, with few

mA driving amplitude.

Regarding the gain factor, as a first approach it can be fixed to 1, in order to achieve a

full 0 − 90 peak-to-peak modulation; but a better performance is obtained when gain

factor of about√

2 is used (Figure 4.28). It is assumed to be the best-fit of the sinusoid

energy when comparing to a square wave.

After the conventional balanced photodetector, an electrical filter is placed to properly

reduce the noise and reject the interference from adjacent WDM channels. Due to the

synchronous 0−90 phase scrambling, at this point the bandwidth obtained is two times

the low-pass equivalent data power spectrum. As a consequence, this first filter must be

twice as broad as usual. This produces 3 dB Signal-to-Noise Ratio penalty with respect to

an ideal phase-locked homodyne receiver. However, as seen in the previous subsections,

it has much higher linewidth tolerance, about two orders of magnitude.

After filtering, a post-processing module is placed in order to make data decision. This

is the main core of this receiver and it can be more or less complex depending on the

modulation format used. For example, when differentially coded BPSK is detected, the

post-processing module is implemented by a delay and-multiply block followed by a delay-

and-add block to combine the I and Q infos, as done in the previous subsections. Thus,

it reduces the complexity of the phase noise problem to a possible phase cycle-slipping in


Figure 4.28: BER floor versus the linewidth per bitrate ratio

the bounds of a bit time, possible only when using extremely high linewidths. A possible

scheme is depicted in figure 4.29, similar to the previously evaluated one.

Figure 4.29: Differential BPSK receiver scheme


4.2.3.2 Phase noise analysis

For the phase noise analysis of the DPSK case, lets start the analysis with the current

present at the output of the multiplier (Im(t)):

Im(t) = 4<2PSPLOd(t) cos

(φe(t) +

π

4+AcγKLO

2πfcsin(2πfct)

)· (4.29)

· cos

(φe(t− Tb) +

π

4+AcγKLO

2πfcsin(2πfc(t− Tb)

))= 2<2PSPLOd(t)

[cos(φe(t)− φe(t− Tb)

)+

+ cos(φe(t) + φe(t− Tb) +

π

2+ β sin(2πfct)

)]where the phase error is expressed as φe(t) = φS(t)− φLO(t).

Then, the expression can be rearranged as,

Im(t) = 2<2PSPLOd(t)

[cos(θ1(t)

)−

∞∑n=−∞

Jn(β) sin(θ2(t)

)](4.30)

with β = AcγKLOπfc

; θ1(t) = φe(t) − φe(t − Tb) and θ2(t) = φe(t) + φe(t − Tb) + 2πnfct.

Here, the undesired effects of sin(θ2(t)

)can be minimize by making γ near

√2, meaning

that β takes a value that makes J0(β) very low. As a useful example the positive Bessel

coefficients have been plotted for different orders at the desired β value. It is shown in

figure 4.30. There, the Bessel coefficients that are above −20 dB respect the unity, are

the corresponding to orders 1, 2 and 3; while the other terms can be neglected. Please

note that for the odd order coefficients J−n(β) = −Jn(β), being n positive. Oppositely,

for the even coefficients J−n(β) = Jn(β), being n positive. As a sum from −∞ to +∞is obtained, the only surviving terms will be those corresponding to even orders of the

Bessel function. Thus, for the assumption made, the only surviving terms are those

corresponding to J−2(β) = J2(β).

Taking into account such approximation, the current after the delay-an-add module, can

be written as:

Id(t) = Im(t) + Im

(t− Tb

2

)(4.31)

= 2<2PSPLOd(t)

[cos(θ1(t)

)+ cos

(θ1

(t− Tb

2

))−

−2J2(β) sin(θ2(t)

)− 2J2(β) sin

(θ2

(t− Tb

2

))]


Figure 4.30: Bessel coefficients for γ =√

2

In a similar way as equation 4.8, Id(t) can be rewritten as:

Id(t) = Io(t) + Io(t− Tb/2) (4.32)

= 2<2PSPLOd(t)

[cos(∆φ1 + ∆φ2) + cos(∆φ2 + ∆φ3) +

+2J2(β) sin

(2φe(t)± 2π2fct−

3∆φ1 + 2∆φ2 + ∆φ3

2

)cos

(∆φ1 + ∆φ2

2

)]where

∆φ1(t) = φe(t)− φe(t− Tb

2

)∆φ2(t) = φe

(t− Tb

2

)− φe(t− Tb)

∆φ3(t) = φe(t− Tb)− φe(t− 3Tb

2

)as when talking about the first time-switching case, shown in figure 4.10, and expressed

in the same equation 4.8. Here they are also independent and identically distributed

gaussian random processes, with zero mean and a variance proportional to the linewidth

per half of bit-time product.

In principle, when phase noise can be neglected, performing decision on Im(t), is slightly

better than deciding on Id(t). This is shown in figure 4.31. It is due to the fact that

low linewidth can be cancelled by the differential detection itself and the interference of

the Bessel function terms. On the other hand, when phase noise becomes important,

the cos(∆φ2 + ∆φ3) and cos(∆φ1 + ∆φ2) terms grow, and are the main phase noise


contribution. To see it more clearly, three aspects should be highlighted regarding the

Bessel coefficients terms:

1. The ideal receiver bandwidth of such a diversity receiver is 1.5 times data rate.

2. The phase noise will vary more slowly than data rate (i.e. its bandwidth is much

narrower than data signal bandwidth).

3. Noise terms contributed by the Bessel function are over a carrier running at a

frequency two times the data rate.

Figure 4.31: Comparison between decision on Id(t) (using delay-and-add, DAD) andIm(t) (NDAD).

Thus, it can be assumed that these terms are going to be filtered by the matched filter

placed before decision block, and will not interfere in data detection. Thus, Id(t) can be

approximated by:

Id(t) ≈ <2PSPLOd(t)[

cos(∆φ1 + ∆φ2) + cos(∆φ2 + ∆φ3)]

(4.33)


4.2.3.3 Frequency drift analysis

Now, the goal is to have a look on what happens when a frequency drift 2πfd is applied.

In this case, Im(t) can be rewritten as:

Im(t) = 4<2PSPLOd(t) cos(φe(t) + 2πfdt+

π

4+AcγKLO

2πfcsin(2πfct)

)·

· cos(φe(t− Tb) + 2πfd(t− Tb) +

π

4+AcγKLO

2πfcsin(2πfc(t− Tb))

)= 2<2PSPLOd(t)

[cos(φe(t)− φe(t− Tb) + 2πfdTb

)+

+ cos(φe(t) + φe(t− Tb) + 4πfdt− 2πfdTb +

π

2+ β sin(2πfct)

)]= 2<2PSPLOd(t)

[cos(θ1(t)

)−

∞∑n=−∞

Jn(β) sin(θ2(t)

)](4.34)

being β = AcγKLOπfc

; θ1(t) = φe(t) − φe(t − Tb) + 2πfdTb and θ2(t) = φe(t) + φe(t − Tb) +

2π(2fd + nfc)t− 2πfdTb.

For the correct development of the model, no phase noise is assumed. Then:

Im(t) = 2<2PSPLOd(t)[

cos(2πfdTb) + cos

(4πfdt− 2πfdTb +

π

2+ β sin(2πfct)

)]= 2<2PSPLOd(t)

[cos(2πfdTb

)−

∞∑n=−∞

Jn(β) sin(2π(2fd + nfc)t− 2πfdTb

)](4.35)

Next, the output of the delay-and-add module can be calculated, obtaining:

Id(t) = Im(t) + Im(t− Tb/2) (4.36)

= 2<2PSPLOd(t)

[cos(2πfdTb)−

∞∑n=−∞

Jn(β) sin(2π(2fd + nfc)t− 2πfdTb

)−

−∞∑

n=−∞

Jn(β) sin(2π(2fd + nfc)t− 2π(6fd + nfc)Tb/2

)]= 2<2PSPLOd(t)

[cos(2πfdTb)−

−2∞∑

n=−∞

Jn(β) sin(2π(4fd + 2nfc)t− 2π(10fd + nfc)

Tb2

2) cos(

−2π(2fd + nfc)Tb4

)

]

Revisiting the assumptions made in the last sub-subsection, here the main cotributing

Bessel term is also the corresponding to order 2, and will produce a carrier running at

twice the data rate plus the correspondent tones due to the frequency drift. As such

a frequency drift can be also assumed to be much lower than data rate, Id(t) can be


approximated as:

Id(t) ≈ <2PSPLOd(t) cos(2πfdTb) (4.37)

That is the same expression than the one reported in equation 4.11, and the same effects

on the overall BER are expected, shown in figure 4.14.

4.2.3.4 Simulations

In order to evaluate the performances of the proposed receiver architecture, a BPSK

configuration was used (Figure 4.29). It was compared to a classical time-switching phase

diversity receiver by means of numerical simulation with Monte-Carlo BER estimation.

First of all, the linewidth per bit rate tolerance was evaluated at 1 Gb/s. The output

parameter measured was error counting of received bits. The BER measures were made at

several linewidths from 10 MHz to 100 MHz and assuming an infinite signal to noise ratio

(SNR) in order to properly evaluate the phase noise effects. Due to high computational

resources required by simulations of this kind, minimum BER simulated was 10−4. The

resulting system tolerance to the laser phase noise is depicted in figure 4.28. When a

sinusoidal phase switching is used with a 0−90 peak-to-peak phase swing, the maximum

tolerated linewidth at 10−3 BER is shown to be as low as 2% bit rate, whereas using

square phase switching it is 2.8% bit rate. This is mainly due to the penalty when

moving from square waveform to a sinusoidal wave. Note that FEC codes must be used

to increase this 10−3 BER up to 10−9. When the amplitude of the sinusoidal wave

is increased to its optimum, the spectral broadening is near-optimum, increasing the

maximum tolerated linewidth up to 3.5% bit rate. It is slightly higher than the 3.2%

reported in subsubsection 4.2.1.2, but now using a much simpler scheme.

Next, the effects of changing the gain factor were evaluated. The optimum value was

found to be√

2, as expected. This is shown in figure 4.32.

Afterwards, the sensitivity penalty was obtained when using this new configuration con-

sidering the additive noise. Here the laser linewidth was disabled. Hence, the probability

density function of the output bits was found to be the same as when having a pure

DPSK, but with a certain penalty. Results are shown in figure 4.33. As expected, a

certain penalty is observed when replacing the square signal by the sinusoid: 0.5 dB

when γ =√

2 , and 0.7 dB when 1 for a 10−9 BER. Almost no penalty is observed when

comparing at 10−3 BER (−40 dBm).

4.2.3.5 Experiments

An experimental prototype of the proposed receiver has been developed and was tested in

a laboratory setup. It is shown in figure 4.34. Sensitivity penalty for gamma parameter

(gain factor) and frequency drift impacts were evaluated. Although the proposed receiver


Figure 4.32: Maximum tolerated linewidth per bit rate ratio at BER 10−3 as afunction of the gain factor.

Figure 4.33: Receiver sensitivity for several configurations.

architecture was demonstrated to be highly insensitive to phase noise effects, an external

cavity tunable laser was used featuring low linewidth. The total linewidth was 300 kHz

(2x150 kHz), much smaller than the bit rate (1 Gb/s).

The TX branch was binary phase shift keying modulated with a Mach-Zehnder Modu-

lator (MZM, Fujitsu FTM7921ER) at 1 Gb/s. The local oscillator branch was 0-127

modulated with a standard LiNbO3 phase modulator (PM, Avanex IMP10), driven by

the clock signal (CLK) of the pseudo-random binary sequence (PRBS) generator used to

provide data at the first branch. These two optical signals are coupled and detected by a


balanced detector followed by an electrical processing stage (a delay-and-multiply mod-

ule plus a delay-and-add stage). A microwave double-balanced mixer (Marki Microwave

M20004) was used as a four-quadrant multiplier.

Figure 4.34: Experimental setup for the direct drive time-switching.

Some preliminar experiments were carried out, measuring the SNR penalty at BER 10−3.

First, for the γ factor (from γ = 1 to γ = 2), and afterwards for a laser fluctuation of up

to ±200 MHz.

The gain factor results are shown in figure 4.35. Where it is shown that the optimum is

achieved at γ =√

2. Also the 1 dB penalty points were mesured to be at γ = 1.3 (117)

and γ = 1.8 (162), meaning 0.5 (45) tolerance.

Regarding frequency drift tolerance results are shown in figure 4.36. There it is shown

that 1 dB penalty was achieved for 75 MHz detuning. Meaning that the system is very

sensitive to the laser wavelength fluctuations.

4.2.4 Searching for a polarization diversity

In this case, the diversity receiver has two main parts: the first is a coherent photo-receiver

with added clock-synchronous phase (0− 90) and polarization (H-V) scrambling at the

local laser output. The second part is an electrical post-processing performing the signal

demodulation and the synchronous combination of the orthogonal components. The

local laser does not need to be coherent with the incoming optical carrier, although an

automatic frequency controller is convenient to maintain the two wavelengths close. It

can be regarded as a heterodyne receiver with near-zero intermediate frequency.


Figure 4.35: SNR factor penalty at 10−3 BER vs gain factor γ.

Figure 4.36: SNR factor penalty at 10−3 BER vs frequency drift.


in the balanced photo-detector stage. These components are no coincident with the

Tx-generated ones due to the unlocked transmission phase, but, with post-processing

performing the operations in [24], the phase-modulated information is fully recovered.

The optical phase scrambler at the local laser output is controlled by the data clock

(50% duty cycle) producing a 0 − 90 phase modulation, to obtain the I and Q signal

components, at the first and second half part of each bit time (Tb) respectively, after the

optical mixing. In a similar way, the polarization components V and H, are at even and

odd quarters of the bit time, respectively. This is indicated in figure 4.37.


Figure 4.37: I, Q, H, V time distribution of each bit

Correspondingly, the photo-receiver output is gated with the data clock signal, its in-

verse, and a doubled frequency version of them to obtain the I and the Q separately

for every polarization component in the four branches, now with RZ shape. In order to

re-synchronize the data clock signal with the signals introduced to the post-processing

block and phase modulator, the respective relative delays are introduced in the branches,

and a variable delay is added to compensate for the RX propagation delays.

The electronic signal processing stage performs the differential demodulation of the four

components, separated by electronic switching, with a delay time equal to Tb. All demod-

ulated components are synchronously combined with an adder. Due to the phase noise

and the SOP random variation, the signal power fluctuates between the four branches

randomly, at a rate in the order of the laser linewidth and SOP fluctuation, and the

detailed combination of all the outputs assures its recovery (Figure 4.38). In terms of

phase noise, compared to an oPLL, the phase-swing time has been shortened from the

loop delay to only a bit time, which, in contrast, reduces while bit rate increases.

Figure 4.38: Intradyne differential receiver with polarization and phase diversity.


To achieve the best performances in polarization diversity terms, the scrambler must in-

troduce a clock-synchronous 90 rotation. In is implemented with a highly birefringent

phase modulator, with its input 45 linearly polarized. The results obtained after com-

bining all the branches are the same theoretical results obtained in [24, 52]. However, it

must be taken into account that the reduced duty-cycle and the correspondingly increased

electrical bandwidth produces 6dB SNR penalty.

The analysis of such receiver is complex, and it would be good to take into account the

phase noise and polarization effects separately. First, lets deal with the polarization. In

fact, polarization varies very slowly (in the order of ms) when compared to data rates. So,

the parameters regarding polarization can be assumed to be constant and the equations

governing the receiver can be set as:

eS(t) =√PS(cos(ϕ)x+ sin(ϕ)e−jθy) exp

(jω0t+ φS(t)

)(4.38)

eLO(t) =√PLO(x+ y) exp

(jω0t+ φLO(t)

)(4.39)

φe(t) = φS(t)− φLO(t) (4.40)

As now the point under study is the polarization the phase noise term φe(t) can be

neglected, and the currents after photodetection can be described as:

IHI(t) = Cd′(t) cos(ϕ) (4.41)

IV I(t) = Cd′(t) sin(ϕ) cos(θ)

(4.42)

IHQ(t) = Cd′(t) cos(ϕ) (4.43)

IV Q(t) = Cd′(t) sin(ϕ) sin(θ)

(4.44)

Thus, after data demodulation and delay alignment of the components:

IHIo(t) =C2

2d(t) cos2(ϕ) (4.45)

IV Io(t) =C2

2d(t) sin2(ϕ)

(1 + cos(2θ)

)(4.46)

IHQo(t) =C2

2d(t) cos2(ϕ) (4.47)

IV Qo(t) =C2

2d(t) sin2(ϕ)

(1− cos(2θ)

)(4.48)

And after combination it leads to:

Io(t) = IHIo(t) + IV Io(t) + IHQo(t) + IV Qo(t) =C2

2d(t) (4.49)

having no polarization influence on data decision.

Regarding phase diversity, it should be noted that time distribution of the I and Q

components are the same as the first time-switching diversity receiver analyzed. So it can

be better implemented with the simplified scheme presented in figure 4.39. Please note


Figure 4.39: Alternative implementation for achieving time-switched phase and po-larization diversities.

that in such receiver the signals that are added at each Tb/4 are the ones corresponding

to polarization diversity, while the ones corresponding to phase diversity are combined

each Tb/2. Then, the assumptions made in sub-subsection 4.2.1.2 are still valid for this

receiver, as well as the results of equation 4.8.

4.3 Chapter summary

In this chapter four novel techniques were introduced for achieving high phase noise and

SOP tolerances: a phase estimation algorithm based on Karhunen-Loeve series expan-

sion for standard full phase diversity receivers, a simple time-switching phase diversity

architecture, a Fuzzy logic data estimation algorithm, and a time-switching polarization

diversity architecture.

For the phase estimation algorithm based on Karhunen-Loeve series expansion, the con-

cept was developed theoretically and performed some simulations. Due to its spectral

properties, it remarkably increases the phase noise tolerance of conventional coherent ho-

modyne receivers, up to a linewidth of 4 % bit rate for the 1 dB penalty point at a BER

of 10−9, and it also avoids the need for oPLL.

Next, the time-switching phase diversity architecture has been discussed. Here the objec-

tive was to obtain a phase diverse coherent receiver, using standard off-the-shelf optical

components. This is achieved by introducing a phase dithering that covers the entire

bit time with a [0, 90] switch. Two variations have been presented: using a phase

scrambler/switch, and directly driving the local laser. With them the obtained phase

noise tolerance was of 1.8 % and 5.4 % of the bitrate, respectively (BER-floor 10−3).

Also channel spacing penalty has been analyzed and measured to be of 1 dB for 3 GHz

spacing at 1 Gb/s. Nevertheless, the fact of switching between 0 and 90 in the same bit


broadens the signal bandwidth and introduces a non-negligible penalty of 3 dB respect

to a theoretical coherent receiver.

In between, the concept of combining Fuzzy logic data estimation and time-switching was

proposed and analyzed. It is an interesting approach that also combines low-complexity

field programmable arrays, avoiding the need for a digital signal processor that would

be needed for the first proposed phase estimation algorithm. In this case, the linewidth

tolerance was of 3.5% bit rate for a 10−3 BER-floor, equivalent to a 10−9 when FEC codes

are used.

Finally, a time-switching polarization diversity receiver architecture has been presented.

In this case the concept has been theoretically demonstrated, achieving a total SOP

insensitivity. However, it must be taken into account that the reduced duty-cycle and the

correspondingly increased electrical bandwidth produces a 3dB SNR penalty, like in the

time-switching phase diversity architecture.

Chapter 5

ONU and OLT architectures

5.1 Summary of techniques and issues to take into

account

Homodyne systems today are mainly investigated toward long-haul WDM applications

and not being seriously considered for use in access passive optical networks (PONs). As

these networks have multiple low capacity channels, a major concern is the use of optical

filters in order to delimitate these channels in direct-detection based systems, mainly

because of the commercial filter’s low selectivity. Thus, if demand increases, a coherent

receiver using electrical filtering is an alternative way to solve this problem. Heterodyne

optical receivers can be a first approach, as in [5], but due to its inherent image frequency

problem, a better solution is homodyne reception.

Nevertheless, the implementation of homodyne transceivers has not been commercially

deployed in part because of its stringent requirements in terms of laser spectral width

(laser’s phase noise) and polarization mismatch. Also, other issues more related to generic

transceiver’s bidirectional transmission over a single fibre are relevant: Rayleigh backscat-

tering and modulation formats to be used.

5.1.1 Phase noise

In order to properly synchronize local laser and received signals, early homodyne coher-

ent systems used an optical Phase-Locked Loop (oPLL) module. Several architectures

were proposed and analyzed: Decision driven [19], Costas [18], Balanced [21], Subcarrier

modulated [23], and heterodyne loops [33]. However, they had the same problem: optical

path between local laser and optical mixer (e.g. optical hybrid + photo-detection stages)

introduces a non-negligible loop delay [17], resulting in a significant penalty. In order to

avoid it, extremely low linewidth external cavity lasers had to be used.

111

Chapter 5. ONU and OLT architectures 112

In chapter 2, it has been shown that another approach towards homodyne reception

came later, with the concept of zero-IF/intradyne diversity receivers. The main goal of

these receivers is to replace the feedback loop (oPLL) by a feed-forward post-processing.

For full phase diversity schemes (using a 90 Hybrid), the architecture is based on an

intradyne system, using a free-running local oscillator which is nominally at the same fre-

quency as the incoming signal. Several relevant post-processing approaches, depending on

the estimation/decoding performed are: differential detection in the analog domain [24],

digital Wiener filtering [26], regenerative frequency dividers [28], Viterbi-Viterbi algo-

rithm [30, 31], and Fuzzy logic data estimation [45]. The core component is the 90

hybrid, which can be integrated as a polymer waveguide device [53], offering a fairly sim-

ple and low cost fabrication involving low-temperature processes and low cost packaging

based on passive alignment [54].

A third approach is time-switching phase diversity, where the receiver has two main parts:

the first is an intradyne coherent receiver, with an added phase modulator at the local

laser output; the second is the electrical post-processing. The optical phase modulator at

the local laser output is controlled by the data clock (50% duty cycle) producing a fixed

0 − 90 phase modulation, to obtain the I and Q signal components, at the first and

second half part of each bit time respectively, after the optical homodynation [41, 45]. As

seen in section 4.2, a further simplification consists in driving directly the local laser with

a sinusoidal wave at the bit frequency [46]. So, if the laser is working in saturation mode,

one can take advantage of its adiabatic chirp and perform a sinusoidal frequency modula-

tion resulting in a phase modulation 0-127.3, obtaining a further tolerance enhancement

of the time-switching diversity performances.

Technique Linewidth Penalty Required key Complexitytolerance component

Decision-drive loop 5 MHz 0 dB 90 hybrid HighCostas loop 4.9 MHz 0 dB 90 hybrid Medium/High

Subcarrier loop 5.1 MHz 0 dB 90 hybrid HighBalanced loop 2.4 MHz 2 dB Optical coupler Low

Heterodyne loop 6.4 MHz 1 dB Optical coupler LowFull phase diversity 5% bitrate 0 dB 90 hybrid Medium

Time-switch (Scrambler) 1.8% bitrate 4 dB Phase modulator MediumTime-switch (Direct drive) 5.4% bitrate 4 dB High-chirp laser Low

Table 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.

5.1.2 Polarization mismatch

Polarization is one of the major problems for the coherent systems, as the optical mixing

of the LO and received signals needs to be aligned in polarization. There are four different


approaches to deal with a possible polarization mismatch: full polarization diversity, time-

switching polarization diversity, polarization scrambling and local polarization control.

A full polarization diversity scheme, using a polarization beam splitter (PBS) and double

receiver, has been already investigated [24, 26, 55]. However, it means doubling the

number of optical components and precise match. A decisive enhancement would be to

integrate it with the 90 hybrid in polymer technology, as for reduced fabrication costs

would be possible.

In time-switching polarization diversity, each bit time would be split into two, one con-

taining H polarization information and the other one containing V polarization infor-

mation [47, 56]. This diversity is achieved by driving the clock signal to a polarization

switch/scrambler. Afterwards, at the electronic post-processing block, H and V compo-

nents can be properly combined. A drawback can be the loss of 3 dB of sensitivity, but it

can be afforded due to the inherent high sensitivity of the receiver. For the polarization

scrambler, it can be implemented by a highly birrefringent phase modulator, with its

input light beam polarization properly aligned. It can be done either at the customer

premises, or better at the central office to share the cost of the device, that would not

have to be integrated. Additional options can be investigated [57, 58].

Local polarization control requires a polarization actuator (Liquid crystal, Fibre squeezer,

Faraday rotator, to mention a few) at the customer’s equipment, with a related high cost.

It also means an additional electronic control (at low frequency) should be placed at the

electric part of the receiver.

Local control Polarization diversity Polarization switchingPenalty 0 dB 0 dB 3 dB

Key component Polarization actuator Pol. beam splitter Pol. scrambler/switchResponse time 1 ms – 1 s < 10 µs < 10 µs

Complexity High Med./high Low (if placed at CO)

Table 5.2: Polarization handling methods summary table [56].

5.1.3 Modulation techniques and Rayleigh backscattering

Even though it is not an objective of the present thesis, one of the key issues in PONs

is the full bidirectionality of a transmission system over a single fiber. If down-stream

and up-stream spectra overlap, the Rayleigh backscattering may become a substantial

interference to the received signal, for fiber lengths of more than 10 km [59]. A double

fiber scenario will be asumed for the architectures under discussion, while keeping in

mind a couple of approaches to solve this in future lines: dual laser configuration (one

used as a reference for detection, and the other for upstream transmission), and inclusion

of a wavelength shifter at the ONU, using a wavelength shifting device [60]. For the


targeted low cost in access, to achieve phase modulation with laser direct modulation,

the technique in [61] can be adopted.

5.2 ONU and transceiver architectures

In this section, some coherent ONU schemes are presented. Concerning the modulation

data rate, will be 1 Gb/s to directly transmit the common EPON protocol over fiber.

In general terms, the downstream modulation format to be used is PSK, because of its

good trade-off between performances and simplicity. For upstream modulation, PSK is

also preferred, but the simpler IM option can be also used with an asymmetrical up/down

data rate, in order not to penalize optical power budget. In principle it is assumed that

a modulator can be placed at each transceiver and leave other implementations as open

issues for future lines. Precisely, recently it has been demonstrated a coherent receiver

integration with an optical phase modulator [62].

Regarding electronics, digital and analog signal processing will be the adopted solutions

against the impairments. A key element is the broadband 4-quadrant multiplier required

for the differential demodulation of I and Q components.

5.2.1 Transceivers based in a full phase diversity scheme

5.2.1.1 Transceiver with 90 degree hybrid and digital processing

The basic implementation uses 90 hybrid with 2 pairs of balanced photo-detectors. The

electronic post-processing combines both I and Q detected components optimally. Scheme

is shown in figure 5.1. The targeted modulation format is BPSK, although other multilevel

Figure 5.1: Transceiver with 90 hybrid and digital processing.

modulations can be used and investigated, e.g. QPSK.


Channel selection is performed by tuning the local laser to the right wavelength and fil-

tered by the electrical low pass filters. In the digital implementation, data is sampled

and converted into digital domain by high-speed analog-to-digital converters (ADCs).

Inside digital I and Q post-processing several basic operations are performed: Phase es-

timation, frequency estimation and control, data estimation, and polarization switching

combination. Phase and data estimations can be performed taking as a basis well-known

techniques, like Wiener filter [26] or Viterbi-Viterbi [31], which have proved their fea-

sible implementation. Also other new algorithms can be used, as the one proposed in

section 4.1.1. Regarding frequency estimation, standard digital controls can be used, like

the ones used in RF communications [6] or the most advanced recently demonstrated for

optical communications [63, 64]. Polarization is managed at the OLT side, performing a

switching that covers the two H and V orthogonal states in the same bit time period.

5.2.1.2 Transceiver with 90 degree hybrid and analog processing

This is the analog version of the previous transceiver, with lower consumption require-

ments, data is differentially encoded and demodulated (DPSK), for higher tolerance

against phase noise. Its scheme is shown in figure 5.2. The post-processing is now

composed by two parallel delay-and-multiply blocks, for differential detection. The com-

bination of the I and Q component output by a standard electrical combiner may require

optimal weightening (not shown in the figure) for optimal performance. Next, a delay

and add module may perform the proper polarization switching combination, also not

shown in the figure. Finally, before data decision, a 4th order Bessel low pass filter is

placed.

Figure 5.2: Transceiver with 90 hybrid and analog processing.

5.2.1.3 Transceiver including 90 degree hybrid and PBS, with digital pro-

cessing

This is the natural extension of architecture 5.2.1.1, using polarization beam splitters for

achieving polarization diversity. The transceiver architecture is shown in figure 5.3. With


them, a full polarization diversity is achieved and the sensitivity penalty can be neglected.

However, the number of optical and electronic components is doubled, increasing the

complexity and cost of the transceiver.

Figure 5.3: Digital configuration scheme using 90 hybrid combined with PBS.

5.2.1.4 Transceiver including 90 degree hybrid and PBS, with analog pro-

cessing

Similarly to the previous one, this is the natural extension of architecture 5.2.1.2, using

polarization beam splitters for achieving polarization diversity. Also, the only differences

are the duplicity of optical and electrical components. Now the post-processing is com-

posed by four parallel delay-and-multiply blocks, for differential detection, as proposed

in [24].

Figure 5.4: Analog configuration scheme using 90 hybrid combined with PBS.


5.2.2 Transceivers based in time-switching phase diversity

5.2.2.1 Transceiver including phase switch with digital processing and stan-

dard balanced detector

As an alternative to 5.2.1.1, 5.2.1.2, 5.2.1.3 and 5.2.1.4 it is proposed to implement a

time-switching scheme for data detection, described in section 4.2 and reported in [41].

Here, by means of fast phase scrambling, the 90 hybrid can be avoided and a simple

3dB coupler can be used. For the digital version, the targeted modulation format is

also PSK. Polarization is managed at CO, performing an H and V alternate switching,

too. A remarkable difference is the data rate clock recovery unit, placed before the

A/D conversion block; its output drives a phase modulator/scrambler, performing the

0 − 90 phase switching needed. Also, a similar structure has been integrated in an InP

substrate [62].

Figure 5.5: Digital configuration scheme using phase switch.

5.2.2.2 Transceiver including phase switch with analog processing and stan-

dard balanced detector

For the analog version of 5.2.2.1, the targeted modulation format is DPSK. Then, after

channel selection filter, a couple of switches perform the I and Q components distribution,

and a delay and multiply block is placed at each branch, for differential detection.

5.2.2.3 Transceiver including direct laser switching with digital processing

and standard balanced detector

Here, by means of fast phase scrambling of the local laser, the phase scrambler can be

avoided simplifying even more the transceiver architecture. For the digital version, the

targeted modulation format is PSK, too. Polarization is also managed at CO. A slight

difference with architecture 5.2.2.1 is that the data rate clock recovery output is filtered


Figure 5.6: Analog configuration scheme using phase switch.

for obtaining a sinusoidal signal, which drives directly the laser, performing the 0-127

phase modulation needed [46].

Figure 5.7: Digital configuration scheme using standard balanced detector.

5.2.2.4 Transceiver including direct laser switching with analog processing

and standard balanced detector

For the analog version of 5.2.2.3, the targeted modulation format is DPSK. So, a delay and

multiply block is placed at each branch, for differential detection. Next, a delay-and-add

block (T/2 delay) can be placed (not shown), for combining the orthogonal polarization

components of the received signal. Finally, before data decision, a 4th order Bessel low

pass filter is placed.


Figure 5.8: Analog configuration scheme using standard balanced detector.

5.2.3 Transceiver based in Optical Phase-Locked Loop

5.2.3.1 Transceiver with OPLL and analog processing

This architecture has a more advanced electronics implementing homodyne detection with

optical coupler. In this case, the targeted modulation format is DPSK, and polarization

is managed by switching at OLT side. It is a homodyne balanced receiver with fast lock-

in dithering and proportional-integral optical tuning loop. This leads to an amplitude

modulated error phase ranging signal after balanced receiver. Next, a squaring module

(or an electrical double rectifier) removes data modulation, and its output is filtered and

down-converted in a proper way [33]. At data detection branch, a delay-and-multiply

block performs differential demodulation, and next a delay-and-add block can be placed

(not shown), for combining the orthogonal polarization components of the received signal.

Figure 5.9: Analogue configuration scheme for the oPLL transceiver prototype.


5.2.4 Transceiver comparison

Table 5.3 summarizes the requirements of the different architectures presented, in terms

of optical phase handling, polarization handling, electronic processing type, sensitivity

penalty with respect an ideal homodyne system and the laser linewidth tolerance at

1 Gb/s (these values are approximated, since depend on the precise implementation).

Arch. Phase Polarization Electronic Sens. Linewidth Costhandling handling processing penalty tolerance

5.2.1.1 90 hybrid Switch at CO Digital 3 dB 5 MHz Med./High5.2.1.2 90 hybrid Switch at CO Analog 4 dB 5 MHz Med./High5.2.1.3 90 hybrid PBS Digital 0 dB 5 MHz Very high5.2.1.4 90 hybrid PBS Analog 1 dB 5 MHz Very high5.2.2.1 Switch (Scr.) Switch at CO Digital 6 dB 1.8 MHz Medium5.2.2.2 Switch (Scr.) Switch at CO Analog 7 dB 1.8 MHz Medium5.2.2.3 Switch (Dir.) Switch at CO Digital 6 dB 5.4 MHz Low5.2.2.4 Switch (Dir.) Switch at CO Analog 7 dB 5.4 MHz Low5.2.3.1 OPLL Switch at CO Analog 4 dB 525 kHz Low

Table 5.3: Transceiver architectures summary table. The linewidth tolerance is for 1dB penalty at 10−10 BER, whereas the penalty is respect to an ideal system.

Among them, it should be remarked that the architecture presenting higher performances

is the one combining 90 hybrids, a PBS and digital signal processing ( 5.2.1.3). It presents

no additional penalty with respect to an ideal system, while achieving high linewidth

tolerance. But it is costly because it implies the duplication of many components needed.

Another architecture that should be highlighted is the one that uses a direct-drive time-

switching in combination with time-switching and digital signal processing (5.2.2.3). Even

though it presents a high penalty (6 dB), it has a high linewidth tolerance and a reduced

complexity and, thus, cost. Nevertheless, it requires a fully engineered laser, capable to

be phase modulated. In principle a standard DFB laser can be used, but it would have

an undesired residual intensity change.

Finally, OPLL approach (5.2.3.1) should not be forgotten, as it is an architecture featuring

low complexity, but with lower linewidth tolerance (525 kHz). An additional handicap,

is the delay associated to the optical path length. As this delay dramatically limits the

OPLL performances, the local laser should be ideally embedded with the optical reception

front-end (couplers and photodetector).

5.3 OLT architecture

Regarding the OLT implementation it will be strongly linked with the network archi-

tecture to be deployed. For example, the case of having only a power splitting stage at


the external plant is different than when a wavelength routing device is present at the

distribution network. Nevertheless, there are several parts that will be common to all the

networks, and they are going to be discussed in this section. Here our purpose is to give

an overview of the problems that can arise when designing the OLT, not giving a detailed

analysis.

First of all the transceivers used at the OLT should be commented. For the proposed

double fiber network approach the same architectures suggested for the customer premises

equipment could be used.

Figure 5.10: OLT scheme with double fiber and including the birefringent polarizationswitch.

Apart from the transceivers, an additional polarization actuator should be placed in

order to perform the high speed polarization switch needed for architectures 5.2.1.1,

5.2.1.2, 5.2.2.1, 5.2.2.2, 5.2.2.3, 5.2.2.4, and 5.2.3.1. A first approach can be the

use of a birefringent component to perform this switch [56]. The problem with these

devices is that for performing an aproppiate switching they need at their input a SOP

corresponding to equal powers in the two principal modes of the birefringent component.

Usually, 45 linearly polarized light is used. Thus, in order to deliver the needed SOP, the

transceivers should be carefully designed, combining optical waveguides and polarization

mantaining fibers. So, it should be not feasible to place a single polarization switch

stage after combining all the OLT transceivers. The most viable but less affordable

approach would be to place the birefringent modulator at the output of each transceiver.

Also, as the SOP of the ONU’s signals is completely random, a polarization controller

should be used for each one. A scheme of the OLT with a polarization switch based

in birefringent modules is shown in figure 5.10, where an external plant having only a

power splitting stage is assumed. There it is shown that the transceiver optical output

is connected to the birefringent high-speed modulator, which is driven with a high-speed

signal (e.g. the data clock). There the retardation is performed and the two orthogonal

polarizations are obtained in the same bit slot. For example if a 45 linearly polarized

beam of light is present at the input, a ±45 linear polarization alternate will be present at

the output. For upstream signals, only a polarization control is needed, with a polarization


actuator (Liquid crystal, Fiber squeezer, Faraday rotator,. . . ) driven by an electrical

signal provided by the reception part of the transceiver. Of course, this signal type will

depend on the modulation format used and the transceiver architecture.

Figure 5.11: OLT scheme with double fiber and including the FRM based polarizationswitch.

A more cost effective alternative to the birrefringent based polarization switch can be

the use of a single switch for all the transceivers of the OLT, shown in figure 5.11. Here

it is also assumed to have an optical network having only a power splitting distribution

stage. In that scheme, first an intensity modulator shapes the input signals, giving at

its output pulses with half of the bit time length. Next, an optical isolator is placed for

ensuring unidirectionality. After the isolator, these pulses enter a planar lightwave circuit

(PLC) composed of 3 optical couplers, a controlled length delay, and a Faraday Rotator

Mirror (FRM). At the output of this structure a secondary pulse is obtained, with 90

polarization rotation respect to first, plus the pass-through result of the introduced pulse.

As the output power for the first half of a bit would be higher than for the second half, a

gain controlled EDFA [65] should be placed after the PLC, for maintaining a fixed output

power during all the bit time.

These two alternatives are so complex and have to be further investigated. The first one

is based in an architecture that has been demonstrated a long time ago [56], whereas the

second one is more background breaking and has to be carefully examined before practical

implementation. In fact, one should pay special attention to the the delay difference

between the two possible paths of the optical couplers network present in figure 5.11.


Nevertheless it was proposed here for future lines of research, as it can be an interesting

way to follow.

5.4 Chapter summary

As the thesis is focused on access networks, in this chapter a discussion has been performed

for the possible transceiver architectures for OLT and ONU.

After discussing the main problems and summarizing the results obtained after the pre-

vious work of the thesis, 9 new transceivers were presented for being used at both sides,

OLT and ONU. They are all based in a double fiber network approach, as a first step for

avoiding Rayleigh backscattering, leaving it for further investigations. Furthermore, since

recently a coherent receiver integration with an optical phase modulator has been demon-

strated [62], a phase modulator has been assumed to be integrated at each transceiver

leaving other implementations as open issues for future research, too.

As a first conclusion, the ONU transceiver architecture that has demonstrated to be the

most appropriate for the first network tests which are going be performed in this thesis,

is the one that uses a direct-drive time-switching in combination with time-switching and

analog signal processing. Even though it presents a high penalty (6 dB), it has a high

linewidth tolerance and a reduced optical complexity. Thus, potential cost is very low.

Also, the sensitivity demonstrated (−38.7 dBm) is enough for achieving the high power

budget required for PONs.

Regarding the particular designs of the OLT, the implementation of the polarization

switching has been discussed. A first approach including birefringent phase modulators

has been analyzed and found to be not optimum due to the amount of components needed.

Thus, another architecture, based on Faraday rotating mirrors has, been proposed. As it

uses few optical components and its cost can be shared among all network users, it is a

more affordable way to achieve the desired polarization switch.

Chapter 6

Network topologies

Usually, the architecture of a PON has some flexibility depending on the balance between

distance reach, number of users served and its geographical distribution. In our ultra

dense (UD) WDM approach, the passive losses can be balanced by combining coupler

splitting and wavelength multiplexing with different density or granularity levels.

6.1 Pure coupler splitting

A first topology to work with can be one of the most simple: a network with one splitting

stage (only a power splitter), typically used in GPON [2]. In this topology, the Central

Office (CO) is provided with an OLT that serves all the users. Then, a feeder fiber

connects the power splitter with the OLT. Each user has a customer premises equipment

(CPE), and is connected to the splitting stage by a distribution fiber. The typical fiber

length between CO and CPE is of about 10-20 km.

This is compatible with currently deployed PONs, but with high extension and splitting

capability with the proposed transceivers.

6.2 Subband WDM tree

To reduce the overall external plant loss, and maybe get a better adaptation to the

laser tuneability range, WDM demultiplexers can be introduced in the PON, subdividing

the optical spectrum in several sub-bands, that fit several ultra-densely spaced channels

allocated in the sub-PON with coherent ONUs or narrow filtering ONUs.

In this case, the network outside plant is composed by a classical dense WDM routing

stage, which routes a set of ultra-dense wavelengths to a power splitter. Such a power

splitter distributes the signal to each of the ONUs connected to the branch.

125

Chapter 6. Network topologies 126

Figure 6.1: Pure coupler splitting network scheme.

Figure 6.2: Network scheme and routing profile.

Ultra-dense WDM wavelengths are generated at the central office by a set of tunable

lasers which are modulated with downstream data. At the ONU side, the tuneable local

oscillator at the customer premises equipment (CPE) selects the assigned channel and

decodes downstream data.

In terms of available bandwidth, the proposed network offers huge transmission capabil-

ities. For example, in the experimental testbed that will be shown in section 6.4, using

2-GHz channel spacing and 1 Gb/s data rate, 32 channels can be easily accommodated in

an ITU-T G.694.1 100-GHz DWDM channel. So the network can potentially serve 1280

users, offering a total capacity of slightly more than 1 Tb/s.


6.3 Advanced: WDM ring-tree SARDANA network

This network is based in a WDM double-fibre-ring with single-fibre wavelength-dedicated

trees connected to the main ring at the Remote Nodes (RN) (Figure 6.3); switchless

add&drop is simply performed by broadband optical couplers at the ring, to maximize

cascadability in terms of optical transfer function at the RNs. To hold increased power

budged, remote amplification is introduced at the RN by means of Erbium Doped Fibres

(EDFs), remotely pumped by 1480 nm lasers located at the CO [66].

Figure 6.3: SARDANA network architecture.

Downstream and upstream signals are coupled into the corresponding ring fibers by means

of the Resilient Network Interface, that allows for adjustment of the transmission direc-

tion, providing always a path to reach all the RNs even in case of fiber failure. Two pump

lasers are WDM coupled for bidirectional, balancing pumping and resilience against fiber

failure.

At the RNs, simple Optical Add-Drop Multiplex (OADM) is accomplished by two 90/10

couplers (for the OADM function) and a 50/50 coupler (for protection function).

Fixed filters determine the dedicated wavelength of each Network Tree. Pump is pre-

viously demultiplexed and led to the EDFs for amplification of up/downstream of each

tree (in-line EDFs are also possible). Two single-fiber PON trees are connected to each

RN; a 1:32 TDM PON is considered at each tree-PON network section. Using standard

2.5 Gb/s transmitters and receivers, an average bandwidth close to 100 Mb/s can be

offered to each ONU. A SARDANA network with 16 RNs and 32 wavelengths serves up

to 1024 ONUs.

A goal on this architecture would be to upgrade it using some of the already proposed

transceiver, serving the same number of ONUs but increasing the guaranteed bandwidth

up to 1 Gb/s. As the users would have an assigned wavelength, a full transparent re-

mote node could be foreseen, using only couplers. Also, by using homodyne technology,


remote amplification could be shut down, because of the relaxed sensitivity requirements

associated to coherent systems.

6.4 Case studies

After taking a look at the transmission/reception techniques developed, a full working

prototype has been patented and build for the most promising one: the coherent system

with time-switching phase diversity reception.

With such a prototype two cases of future deployment were tested in the laboratory:

• Subband WDM tree PON, featuring wavelength grooming [67].

• Ring-tree ultra-dense WDM-PON, with transparent remote nodes [68].

Both networks are based on the ultra-dense WDM concept introduced before, aiming to

give service to a high number of users (around 1000), at very high speed (1 Gb/s).

6.4.1 Subband WDM tree PON

In this case, the network outside plant is based on two splitting stages (see figure 6.2).

Firstly, a classical dense WDM routing stage routes a set of UD wavelengths to the

secondary splitting stage where a power splitter distributes the signal to each of the

Optical Network Units (ONUs) connected to the branch.

A stack of thermally controlled lasers located at the CO generate all the UD wavelengths

which are modulated with downstream data and transmitted to the ONUs. Each ONU re-

ceives the set of wavelengths that have been passed through the first WDM demultiplexer

(typically a 1xN AWG). Then, the tuneable local oscillator at the CPE selects the ONU’s

assigned channel and decodes downstream data by means of optical homodyning. This

same optical oscillator carrier is then used for upstream transmission. It is modulated

using again BPSK modulation format. At the CO a symmetric receiver is implemented

(see figure 6.4).

In terms of available bandwidth, the proposed network offers huge transmission capa-

bilities. Using 2 GHz channel spacing and 1 Gb/s data rate, 32 channels can be easily

accommodated in an ITU-T G.694.1 100-GHz D-WDM channel. On the C-band, 40-

channel AWGs are commercially available so the network can potentially serve 40 x 32 =

1280 users, offering a total capacity of more than 1 Tb/s.

In terms of transmission robustness, the use of a local oscillator and homodyne detection

increases the system sensitivity thus enhancing the tolerance of the network to power


Figure 6.4: OLT and CPE transmission modules.

losses and relaxing power budget restrictions. This permits to use the time switching

phase diversity homodyne receiver in both OLT and ONU instead of a typical homodyne

receiver (with an optical phase-locked loop).

A network testbed was implemented to demonstrate the feasibility of the proposed net-

work design. Two consecutive channels were transmitted while measuring upstream and

downstream sensitivity with 2 GHz channel spacing. The impact of the interference signal

was also evaluated obtaining the sensitivity penalty as a function of the channel spacing.

Although the proposed receiver architecture has demonstrated to be highly insensitive to

phase noise effects, sub-MegaHertz (hundreds of kHz) linewidth lasers were used in order

not to have linewidth limitations and explore the full potential of the network. A DFB

tuneable laser was modulated using DPSK modulation at 1 Gb/s and coupled by means

of a 3 dB coupler. A 25 km fiber spool simulated the access trunk fiber and a 1 x 40

AWG acted as the first remote node (RN) and routed both signals to the output port

corresponding to the D-WDM band input wavelength. Losses at the RN were measured

to be 6.47 dB. Finally, the power splitter stage was implemented with a 1:32 power splitter

and added 16 dB losses.

Firstly, sensitivity measurements of downlink and uplink were carried out with no adjacent

interfering channel. −38.7 dBm of sensitivity (BER=10−9) were measured (see figure 6.5).

To analyse penalties due to adjacent channels, two consecutive downstream channels were

transmitted adjusting the channel spacing between them. The reference wavelength was

1549.70nm. With the proposed 2-GHz spacing sensitivity worsened by about 2 dB, as

shown in figure 6.6. When the interference was separated just 1 GHz, sensitivity was

degraded more than 3 dB. On the other hand, when channel spacing was greater than

6 GHz, sensitivity was barely affected so penalty due to adjacent transmission could be

neglected. So, almost no change was appreciated when comparing to the study performed

in section 4.2.1.4.


Figure 6.5: Up-and Down-stream transmission results.

Figure 6.6: Sensitivity penalty as a function of channel spacing.

6.4.2 Ring-tree ultra-dense WDM PON

As shown in figure 6.7, the network topology fiber, is based on a two-stage outside plant,

with a primary coupler-based feeder ring and a secondary power-splitter-based distribu-

tion stage. The central ring multicasts all the wavelengths transmitted on the trunk fiber

to the different networks sub-segments. Subsequently, the secondary power-splitters mul-

ticast the signals to the end users. At the customer premises equipment (CPE) side, the

receiver selects the wavelength that has been assigned to establish a virtual point-to-point

link. Even though it is not explicitly shown in figure 6.7, this is a double fiber topology,

with separate fibers for upstream and downstream.

This topology has some interesting features: total transparency and scalability. The

addition of a new user simply requires the installation of an optical 1:2 coupler and the


Figure 6.7: Network topology and wavelength plan.

interface at Central Office (CO). Also, resilience is achieved naturally with the central

ring, the bidirectional design of the RN and by means of an optical switch that connects

the interfaces at the head-end with the branch of the ring that offers the best connectivity.

This is shown in figure 6.8. In case of a fiber break, there is always a light path to reach

all the remote nodes.

Figure 6.8: Central office scheme.

Transmission losses are increased due to the use of power couplers instead of wavelength

multiplexers. This is the price to pay for total transparency and scalability. Homodyne

detection can be used to overcome this problem, as it is known to offer much better

sensitivity than direct detection systems.


A stack of thermally controlled lasers located at the CO generate all the wavelengths,

which are Differential Phase Shift Keying (DPSK) modulated with downstream data and

transmitted to the ONUs. Then, at the CPE, the tunable local oscillator selects the

ONU’s assigned channel and decodes downstream data by means of optical homodyning,

IQ phase switching, differential demodulation and post-processing, following the steps

described in chapter 5. This same optical oscillator carrier is then used for upstream

transmission. It is modulated using again DPSK modulation format. At the CO a

symmetric transceiver is implemented similarly to the previous section (see figure 6.4).

The main feature of the transceiver design used is its potential low cost. According to [62],

the optical circuit used for reception (and transmission) can be integrated into an InP

substrate. This may enable a potential low cost implementation of such solution.

The network implemented is designed to offer connectivity to 1024 users (U) per fiber

in a 4-node (N) configuration with 8 secondary trees with 1:128 (K) splitting factor.

Other topologies are also possible taking into account that the total number of users is

U = 2 ·N ·K and that total link losses are:

L = Lfiber + (N − 1) · 10 · log(x) +N · Lex + 3 + 3 log2(K) (6.1)

where x and y are the remote node coupling factors (typically x = 0.9; y = 0.1), Lfiber is

the attenuation along the fiber, and Lex are excess losses due to alignment and manufac-

turing imperfections of the components per remote node. A priori, the number of users

is mainly limited by the available power budget.

Regarding available bandwidth in the proposed network, a 4 GHz channel spacing can be

used, at 1 Gb/s data rate, as demonstrated in section 4.2.1.4. Thus, 1024 channels can be

easily accommodated in the overall C-band. So the network can potentially serve those

1024 users at the same time, offering a huge total capacity, of slightly more than 1Tb/s.

Please note that, unlike in section 6.4.1, in this special case the channels doesn’t have to

fit in the 100 GHz WDM space, having more freedom to design the network spectrum.

A possible limit of the network is the total optical power that can be launched into the

ring fiber. According IEC safety rules [69], that power should not exceed 1270 mW

(approx. 31 dBm) at 1550 nm. In the network plan described in figure 6.7, all the

operative wavelengths are launched into the ring fiber at the same time. In the worst

case, working in resilient mode, all 1024 wavelengths would be launched on the same side

of the ring. Thus, the maximum power of each wavelength should not exceed 0.9 dBm.

To demonstrate the feasibility of the network, proof-of-concept network experiments were

carried out using the network setup detailed in figure 6.9.

At the CO, a 1550 nm Distributed Feed-Back (DFB) commercial laser was externally

DPSK modulated at 1 Gb/s, with a LiNbO3 phase modulator. The output power was

of 0 dBm. To simulate the case in a UD-WDM scenario, a 4-GHz-spaced signal was


Figure 6.9: Experimental network testbed

also inserted, using another continuous wave laser. A 30 km fiber spool was used as the

access trunk fiber to reach the first remote node (L=5.2 dB). This remote node (RN)

was based on two 90/10 couplers and a 3-dB coupler to connect to two access trees.

Insertion losses of this device were measured to be 1.6 dB for pass-through signals and

13.2 dB for dropped signals. Finally, the second distribution stage, emulated by means

of a variable optical attenuator (VOA), added 21 dB losses to the link, corresponding to

1:128 splitting.

The network tested had four remote nodes (RN) thus total outside measured plant losses

ranged from 39.4 dB on RN1 to 44.2 dB on RN4. In standard operation, the optical

switch at the head-end would be configured to connect the users to the light path with

less lossess. The case of passing through three remote nodes to reach RN4 simulates

the network working in resilient mode after a fiber break in the worst case (between the

head-end and RN 4).

Three different cases were investigated: RN1, RN2 and RN4. RN2 represents the worst

case in standard operation and RN4 the worst case in resilient mode. Results are shown

in figure 6.10.

Regarding sensitivities, for a BER of 10−9 in RN1 sensitivity was measured to be−43 dBm

and in RN2 a sensitivity of −41.3 dBm was obtained. Thus, the system performed

correctly in standard operation mode.

In resilient mode, a BER of 10−9 at RN4 could not be reached due to a BER-floor.

That floor is explained as deriving from the linewidth of the system (1MHz), and the

frequency response distortion of the microwave mixers used at the reception side of the

transceiver. Nevertheless, a BER of 10−6 was measured at −44.3 dBm. To compare with

the other cases, in RN 1 BER of 10−6 was measured at −48.1 dBm, whereas in RN2 it was

measured at −46.3 dBm. A Forward Error Correction (FEC) coding scheme, with only

7% overhead, is able to recover (quasi) error-free data for a raw BER below 10−3 [11]. So,


Figure 6.10: Sensitivity results

Normal operation Resilient modeRN1 RN2 RN4 RN1 RN2 RN4

Sensitivity −43 dBm −41.3 dBm - −49.1 dBm −49.3 dBm −49.1 dBmLink Losses 39.4 dB 41 dB 44.2 dB 39.4 dB 41 dB 44.2 dB

Power Budget 42.9 dB 41.2 dB - 49 dB 49.2 dB 49 dB

Table 6.1: Power budget summary

FEC strategies should be applied to increase BER over 10−9 in resilient mode. In that

case one can work with an increased sensitivity of −49.1 dBm.

Penalty to adjacent channels at 4-GHz channel spacing was measured to be 0.1 dB, as

expected.

Table 6.1 I shows a summary of the experiments carried out. There one can see that

the power budget for the best case (RN1) is of 42.9 dB, including the channel spacing

penalty. For the worst case in normal operation, power budget is of 41.2 dB. At a first

glance, one could think on doubling the number of users supported in RN1 and RN4 in

order to balance such power budget, while increasing the total number of users up to

1536. In that case, to maintain the total output power at the CO, each wavelength power

should be reduced to −0.8 dBm.

Consequently each power budged would be reduced by 0.8 dB, and in RN2 link losses

would become higher than the power budget. So, even the power budget is not balanced

at all for the different cases, the maximum number of users to serve is 1024, due to safety

power limits.


6.5 Chapter summary

In this chapter, several advanced UD-WDM access solutions have been presented. Among

them, two case studies have been experimentally demonstrated: A subband WDM tree,

and a Ring-tree ultra-dense WDM network architectures.

In both cases, the networks potentially offers terabit transmission capabilities, and are

based on the transmission of narrowed-spaced dedicated wavelengths to each end user

and optical homodyning to tune and decode each transmission channel.

For the first case, transmission experiments showed a network sensitivity of −38.7 dBm

after 25 km, and a sensitivity penalty of about 2 dB in the case of 2 GHz channel spacing,

meaning that it can potentially serve up to 1280 users at 1 Gb/s.

The Ring-Tree ultra-dense WDM network is capable to provide a flexible and scalable

architecture with large capabilities in terms of number of users (up to 1024) or in capacity

(more than 1 Tb/s). Also, it features a completely passive outside plant, wavelength-

transparent remote nodes and high transmission capabilities and resilience. Transmission

experiments at 1 Gb/s show a sensitivity of −43 dBm in the first RN, after 30 km and

a power budget of 42.9 dB. For the worst case (RN4), when the network is operating in

resilient mode, BER better than 10−9 could be reached by applying FEC strategies. In

that case a sensitivity of −49.1 dBm was achieved, showing a power budget of 49 dB.

Thus, 1 Gb/s per user could be guaranteed, achieving a total network capacity of 1024

Gb/s.

Chapter 7

Conclusions and future work

7.1 General conclusions

The use of coherent systems in access networks appear as a promising mid to long-term

solution to the high-speed and ultra dense PONs. By replacing the transceivers at both

the central office and customer premises, a dedicated wavelength per user is allowed. On

this basis, the present thesis identifes and addresses the inherent problems of coherent

transceivers, while mantaining low cost. The overall goals of this study were homodyne

OLT and ONU designs for upgrading the current standard passive optical networks.

In order to provide some background, a survey of the evolution of optical homodyne

systems was performed, dealing with their fundamental problem: the phase noise. Special

attention was paid to BPSK and DPSK modulation formats, due to their simplicity and

robustness. Furthermore, the main OPLL and phase diversity techniques have been

analyzed. Therein, the phase noise impact has been the main impairment to report on.

Next, several coherent detection techniques have been proposed, improving the perfor-

mances of the receivers that shape the current state of the art. A novel OPLL has

been analyzed and prototyped, reaching an improved phase noise tolerance of 3.1 MHz

with low cost optical components. Also, several new phase diversity systems and phase

estimation algorithms have been analyzed: Karhunen-Loeve series expansion phase es-

timation, Fuzzy logic data estimation, time-switched phase diversity, and time-switched

polarization diversity.

Among them, the Karhunen-Loeve series expansion phase estimation should be high-

lighted, which can tolerate linewidth up to 11% of the bitrate, for the 1 dB penalty point

at a BER of 10−3.

A very simple and robust architecture has been prototyped, featuring time-switching

phase diversity and tolerating linewidths up to 1.8% of the bitrate. i. e. at 1 Gb/s it

137

Chapter 7. Conclusions and future work 138

can tolerate linewidths up to 18 MHz (BER-floor 10−3). For such architecture, channel

spacing has been evaluated in both senses, theoretically and experimentally, achieving a

3 GHz spacing for 1 dB penalty at 10−9 BER.

Another architecture that should be taken into account, is the direct drive time switching.

With it, the linewidth tolerance is enhanced, permitting linewidths up to 5.4% of the

bitrate (BER-floor 10−3). A first experimental tuning has been made, confirming the

expected optimum value of√

2 for the gain factor.

Fuzzy logic data estimation and time-switched polarization local diversity have been

analyzed, demonstrating the concept theoretically.

Furthermore, several transceiver architectures have been proposed and discussed, some

of them including well-known techniques (as the full phase diversity receivers) whereas

others have been designed using the novel approaches previously reported in this thesis.

The trade-off between performances and cost has been difficult to overcome, but finally

the decision of implementing the time-switched diversity transceiver has been made. Ad-

ditionally, OLT designs searching for a time-switched polarization diversity have been

discussed, proposing a couple of alternative implementations, one based in birefringent

modulators and the other one based in Faraday rotating mirrors.

Finally, the upgrading of PON architectures has been discussed for implementing full

ultra-dense WDM networks. Laboratory testbeds have been developed for two of the

presented schemes (subband WDM tree and ring tree transparent ultra-dense WDM

networks), which demonstrate that the proposed topologies and transceivers are feasible,

achieving transmission of up to 1 Gb/s in links higher than 25 km.

7.2 Future lines

During this Ph.D. thesis, research has been developed in access networks towards an

optimal coherent transmission and reception technique for reaching high density, power

budget, and bandwidth efficiency; points that were mentioned in the introductory chap-

ter. Moreover, proof of concept experiments were performed. However, there are some

improvements to be achieved, that will result in a significant step forward:

1. Compact coherent transceiver.

2. Full bidirectionality over a single fiber.

3. Spectrum management.

All of them are going to be briefly commented in the next subsections, as well as the

approaches that can be followed.


7.2.1 Compact coherent transceiver

A compact and simple version of the transceiver can be developed, in the sense that less

number of devices should be used. This can be achieved by using a digital signal processor

in order to perform all the operations to cancel the noises, and recover data. In principle

it should contain the key modules: Phase recovery and/or estimation, and automatic

frequency control of the local laser (in order to keep it in the same wavelength as the

received signal). However this presents some problems to solve before implementation:

1. State of polarization mismatch between local oscillator and received signal. In order

to have an optimal reception, they have to be coincident. This is critical issue. A

consequence may be that more optical components are needed at the user premises

(higher cost).

2. Careful design of the modulation formats to be used. In principle the optimum mod-

ulation format is PSK for both, upstream and downstream, as stated before. But,

reusing the local laser may entail an additional external device. So other modulation

formats that can be generated using only a laser (no external modulator), can be

investigated. Along this line, also coherent optical Orthogonal Frequency Division

Multiplexing (OFDM) techniques can be studied, as they have been demonstrated

to be more robust against fiber dispersion and other impairments.

7.2.2 Full bidirectionality over a single fiber

This is a key issue for simplifying the access network architecture and save costs. In prin-

ciple, using only one fiber per user in the last mile, the cost can be reduced significantly;

since it is the part of the external plant of the network that is not shared among all users.

Thus, a big effort should be done when dealing with bidirectionality over a single fiber.

Nevertheless, there are a couple of main undesired fiber effects to mitigate:

1. Rayleigh backscattering. This refers to the amount of backscattered light when

propagating a light beam over a fiber. It basically depends on the amount of fiber

on which the light beam is launched. This backscattered light becomes a substantial

interference to the received signal, for fiber lengths of more than 10 km [59].

2. Light reflections. They are mainly due to optical connectors, which may reflect a

part of the incoming optical power. It also represents a non-negligible interference

at the receiver side. However, it can be mitigated by fusion splicing as many network

components as possible, and using angled connectors.

Please note that these impairments are strongly related to the modulation format used

for upstream and downstream, so they have to be taken into account when designing the

modulation format to be used.


7.2.3 Spectrum management

In the case of 1000 different wavelengths propagating over a single fiber, before the dis-

tribution stage of the access network, they can be interfering one to each other. Also,

depending on the modulation format used, upstream and downstream spectra can be

interfering at the same wavelength. Thus, not only a careful design of the modulation

format is a must, and there is a need to work in additional topics:

1. Spectral efficiency maximization. This includes the proper dimensioning of the

spacing between channels, as well as the maximum number of users to serve simul-

taneously.

2. Wavelength monitoring, control and stabilization, in order to limit the maximum

wavelength drifts of the lasers used, that can produce an added penalty in the

transmission system. Commercially available lasers emit at 1550 nm ( 193 THz,

when propagating over fiber), thus a high spectral purity of 1 ppm means that the

laser should be stable in a 200 MHz range. This is a substantial drift for the

intended low channel spacing ( 3 GHz). This monitoring and control should be

centralized at the CO premises. An important problem can be the characterization

of the lasers that are going to be used at each side (central office, and user premises).

At least, at central office side, lasers are expected to switch from one wavelength

to another, distributing the traffic among the users, and each type of laser has its

switching transient characteristics.

Appendix A

Passive optical network solution

using a subcarrier multiplex

A.1 Introduction

Access Passive Optical Networks (PONs) have emerged as an effective platform to pro-

vide advanced bandwidth demanding services to the final users. Thus, next generation

PONs have to match several issues, including high bandwidth delivering and Wavelength

Division Multiplexing (WDM). An interesting specification is the use of one single fiber

for both, upstream and downstream transmission, to reduce the size of the network’s

external plant and the complexity of the Optical Network Unit (ONU).

In the past, some advanced designs which avoid the generation of light at the ONU

by using different modulation schemes for downlink and uplink transmission have been

demonstrated [70–74]. However, these methods may not be cost-effective due to the

components needed for the modulation and detection of the upstream and/or downstream

signals. A more cost-effective solution is the use of SubCarrier Multiplexing (SCM)

techniques with direct modulation [75, 76]. But they have been limited to 1.25 Gb/s

downstream, with the electrical schemes not optimized.

In this appendix, a 20 km full duplex PON will be analyzed operating at a rate of 2.5

Gb/s downstream and 1.25 Gb/s upstream, using the SCM technique and giving service

to a maximum of 1280 users. Aiming to reach the user with single fiber-scheme, the

tolerance against Rayleigh backscattering ratios is evaluated.

141

Appendix A. Passive optical network solution using a subcarrier multiplex 142

A.2 Receiver scheme

The subcarrier transmission system has two main parts: The first is an electrical 2.5

Gb/s DPSK upconverting module, inside the transmitter of the OLT, prior to optical

modulation. The second part is an electrical delay-and-multiply DPSK detector placed

after photodetection, at the ONU. This scheme avoids the need of an electrical oscillator

at the receiver, increasing its simplicity.

For a downstream rate of 2.5 Gb/s, the subcarrier frequency is fixed at 5 GHz, allowing a

good band margin between downstream and upstream. As the 3dB bandwidth of the data

stream is approximately 4 GHz (double-sided), the photo-detection bandwidth needed is

of almost 7 GHz. Thus, for maintaining the BPON/GPON link compatibility in terms

of sensitivity at the specified bandwidth, an Avalanche Photo-Detector (APD) should be

used instead of standard PIN diodes. It is shown in [77] that the electrical SNR after an

APD can be written as:

SNR =12(mM<PS)2

4kTF∆fRL

+ 2qFa(<PS + Id)∆f(A.1)

where m is the modulation index, M is the multiplication factor of the APD, < is the

photodiode responsivity, PS is the received optical power, k is the Boltzmann constant,

T is the room temperature (in K), F is the electronic receiver amplifier noise factor, RL

is the photodiode load resistor with a 50 Ω nominal value, ∆f is the signal bandwidth

(one-sided), q is the electron charge (in C), Fa is the excess noise factor, and Id is the

photodiode dark current.

The modulation index can also be expressed as [78]:

m =1− ER1 + ER

(A.2)

where ER is the Extinction Ratio, in linear units, defined as the off-state power over the

on-state power.

On the other hand, according to the SNR definition of equation A.1, the probability of

error can be easily found for an electrical DPSK signal as [9]:

Pe =1

2exp(−SNR) (A.3)

The next section shows the experimental implementation of the SCM-system by means

of a simplified electrical scheme, showing a good agreement with equations A.1 and A.3.

Also, some deployment scenarios are proposed and discussed.


A.3 Experiments and discussion

Two kinds of measurements were performed for the system modelled. First of all, only

SCM downstream measurements were carried out, for validating the theoretical model.

Afterwards, full-duplex transmission over a single fiber was characterized.

A.3.1 Downstream characterization

Figure A.1 shows the experimental setup. For the 2.5 Gb/s downstream signal, a Mach-

Zehnder Modulator (MZM) is used for modulating a CW laser signal, as a first approach

that allows a better control of the modulation. However, a more cost-effective solution

can be the use of direct modulated lasers. In our case, an ER of 8.4 dB can be easily

achieved, enough for our purposes as it will be shown.

Figure A.1: Half-duplex experimental setup.

The downstream signal, a PRBS with a length of 231−1, is precoded inside the first Pulse

Pattern Generator (PPG1) and mixed with a 5 GHz electrical oscillator by using a stan-

dard double balanced mixer. The electrical oscillator is not synchronized with the PPG1

clock, constituting a more realistic platform and allowing the analysis of frequency drift

tolerances. Along a different line, the band-pass filter typically used at the transmitter

side is not required, thanks to the mixer’s frequency response, which ensures a band-pass

filtering as shown in figure A.2. The mixer’s bandwidth has been measured by using the

three-mixer method [79], showing: a bandwidth of ± 1.9 GHz, centred at 5 GHz, enough

for 2.5 Gb/s; and a rejection better than 20 dB for frequencies beyond ± 2.9 GHz.

At the electrical side of the ONU receiver a delay-and-multiply scheme [9] was imple-

mented using a double balanced mixer. Since it does not require any electrical oscillator

placed in the ONU, data detection becomes simpler and phase-locking between detected

carrier and electrical oscillator is avoided. The sensitivity and extinction ratio penalty

measurements, at a reference wavelength 1550 nm, are shown in figures A.2 and A.3.


Figure A.2: Low pass equivalent of the mixer’s response for a 5 GHz carrier.

Figure A.3: Sensitivity results for setup described on figure A.1

Applying the specific characteristics of the APD employed and applying the model de-

scribed in section A.2, a theoretical sensitivity of −28.3 dBm for a BER of 10−10 has been

obtained. It did not fully match with the measurements at a PRBS length of 231 − 1.

In this case the sensitivity was −26.6 dBm for a BER of 10−10. Using a shorter length

of 27 − 1, a sensitivity of −28.2 dBm is obtained, only 0.1 dB away from theoretical val-

ues. The sensitivity differences between different PRBS lengths are explained as deriving

from the ripple of the mixers response and the low frequency response of the base-band

amplifiers used (cutting off at 30 kHz).

Regarding extinction ratio penalty for BER at 10−10, shown in figure A.4, the baseline

ER of 8.4dB provided by the OLT-TX generates a penalty of 1.5 dB, both experimentally

or theoretically. Also, experimental points follow quite well theoretical calculations, just

with a deviation of less than 1 dB.


Figure A.4: Downstream power penalty at BER 10−10 due to extinction ratio. Squarepoints are experiments, whereas continuous line is derived from Eqs. 1 and 2.

A.3.2 Full-duplex measurements

For this case, the experimental setup is shown in figure A.5. Downstream parameters

for this configuration were exactly the same used before, when testing only downstream

transceivers’ interfaces. The splitting ratio at the input of the ONU was 50:50 and the

reference wavelength was 1550 nm.

For the 1.25 Gb/s upstream signal, another pulse pattern generator (PPG2) was used,

independent from PPG1 and driving an RSOA in the ONU. Data injected was operating

with a PRBS length of 231−1. The RSOA small signal gain was of 17 dB. The downstream

signal is modulated by the RSOA with the upstream data, and sent back to the OLT. Note

that the downstream signal is not constant power, but sinusoidal. At the OLT side, after

photo-detection, a low pass filter was placed in order to properly reject re-modulation

noise from downstream signal. Figure A.6 shows the detected power spectrums at the

ONU and OLT sides before and after filtering. The residual downstream signal detected

could be rejected by more than 20 dB.

The sensitivity has been also evaluated and shown in figure A.7. Both directions were

measured (upstream and downstream) at the reference wavelength of 1550 nm. For the

downstream −23.4 dBm wer achieved for a BER of 10−10, whereas for the upstream,

−22.6 dBm were measured. Please note that downstream sensitivity is 3.3 dB away from

the value obtained in figure A.3. This is explained by the 3 dB coupler present between

the ONU input and the APD of the SCM receiver (shown in figure A.5). Please note that

upstream curve is much steeper than downstream. This is due to the fact that the VOA

is placed in between OLT and ONU, attenuating not only the signal transmitted by the


Figure A.5: Experimental setup for single fibre full-duplex measurements.

ONU, but also the RSOA input power. Therefore, the OSNR is degraded at the ONU

output.

A.4 Network measurements

Based on the proposed ONU/OLT designs shown in figure A.5; three different PON

scenarios were tested, trying to keep a minimum system margin of 3 dB: first a pure

TDM network with low coverage (8 users) used as a reference; secondly an standard

medium hybrid TDM/WDM PON covering 160 users; and finally an optimized network

capable to serve 1280 users. It must be pointed that the 3 dB splitter present at ONU

stage in figure A.5, was replaced by a 70:30 coupler, with 30 % output connected to the

RSOA.

In this first case, total network losses were measured to be 16 dB. The ONU input power

was of −16 dBm, and its output power was measured to be of +1 dBm, meaning that

the ONU net gain was of 17 dB and the RSOA gain was of 20.5 dB. 0 dBm were injected

from the OLT to the feeder fibber, generating a measured Rayleigh Backscattering (RB)

of −33.5 dBm (having a 17.5 dB of upstream optical Signal to Rayleigh-backscattering

Ratio, OSRR). Under these conditions, upstream and downstream transmission curves

were measured. Results are shown in figures A.9 and A.10. For the downstream a

sensitivity of −20.1 dBm was found, while for the upstream the sensitivity found was of


Figure 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.

Figure A.7: Sensitivity results for the proposed OLT and ONU architectures.

−18.4 dBm, both for a BER of 10−10. This means that the achieved downstream power

budget was of 20.1 dB (system margin of 4.1 dB), whereas the upstream power budget

was of 19.4 dB (system margin of 3.4 dB).

The second test-bed was composed of a 16 km feeder spool, followed by a 1:40 AWG

demultiplexer. Next to it, a 2.4 km distribution spool was preceding a 1:4 power splitter

and a 2.2 km drop spool. This is shown in figure A.11. This scenario was for an area

with medium density of users, capable to serve up to 160 users.


Figure A.8: Scenario 1 schematic.

Figure A.9: Downstream sensitivity curves for the three different network scenarios.

Total network losses were measured to be 16.4 dB. The ONU input power was −16.4 dBm,

and its output power was measured to be of +0.8 dBm, meaning that the RSOA gain

was of 20.7 dB. Also, 0 dBm were injected from the OLT to the feeder fibber, generating

a RB of −33.5 dBm; and having a 17.5 dB of upstream OSRR, too. Again, upstream

and downstream transmission curves were measured. Results are shown in figures A.9

and A.10. For the downstream the sensitivity found was of −20.6 dBm, while for the

upstream the sensitivity found was of −19 dBm, both for a BER of 10−10. This means

that the achieved downstream power budget was of 20.6 dB (system margin of 4.2 dB),

whereas the upstream power budget was of 19.8 dB (system margin of 3.4 dB).

Finally, an upgraded third test-bed was assembled. In this case, a double fibre feeder is

proposed, so the RB amount generated was very low; only due to de distribution and

drop stages. Now a couple of 16 km feeder spools were implementing a double fibber

path from the OLT to the AWG. Next to it, a 2.4 km distribution spool was preceding

the 1:32 power splitter and a 2.2 km drop spool. This is shown in figure A.12. Also, an

optical preamp was used for upstream detection, since there was no RB limitation, and

OLT costs are shared among all users. This scenario was intended as an improved access

network, covering as many users as possible (up to 1280).

Now, total network losses were measured to be 26.6 dB. The ONU input power was of


Figure A.10: Upstream sensitivity curves for the three network scenarios.

Figure A.11: Schematic of scenario 2.

−16.6 dBm, and its output power was measured to be of +0.8 dBm, as in the second

scenario. Please note that the Rayleigh backscattered signal was negligible, and the

OLT output power could be increased to +10 dBm. Under these optimized conditions,

upstream and downstream transmission curves were measured. Results are shown in

figures A.9 and A.10. For the downstream the sensitivity found was of −19.6 dBm, while

for the upstream the sensitivity found was of −28.8 dBm, both for a BER of 10−10. This

means that a symmetrical power budget of 29.6 dB (system margin of 4 dB) was achieved.

A.5 Conclusions

The bi-directional full-duplex 2.5 Gb/s / 1.25 Gb/s was demonstrated in a SCM sin-

gle fibre PON. The downstream signal is DPSK coded and up-converted by using a 5

GHz subcarrier, while the upstream data is transmitted in burst-mode NRZ. A simplified


Figure A.12: Scheme for scenario 3.

scheme for the electrical parts of the ONU and OLT has been proposed and demon-

strated. Also a theoretical model for SCM downstream is proposed and experimentally

validated. Furthermore, three different deployment scenarios are evaluated: Large cov-

erage area and low density of users; area with medium density of users; and improved

access network, covering as much users as possible. In the first and second test-beds,

transmission experiments have shown a network power budget of 20 dB, for a single fibre

configuration, combined with the capacity to serve up to 160 users. For the third one,

the power budget could be increased up to 29 dB, matching clearly the typical values of

GPON deployments, and serving up to 1280 users. In all the cases a minimum system

margin of 3 dB was achieved.

Appendix B

Automatic wavelength control design

B.1 Introduction

Homodyne coherent optical reception received great attention at the beginning of the

90s. It presents many advantages with respect to the conventional direct detection be-

cause of its excellent wavelength selectivity, high sensitivity and tuneability performances.

However, there have been never found practical application, mostly due to the complex

receiver structure and the stringent linewidth and loop delay requirements [3]. Recently,

some approaches to solve this have been proposed using ultra-fast digital signal pro-

cessing to estimate and track the carrier phase [27, 28]. However, all these techniques

tolerate only a rather small frequency difference between LO and transmit laser. Thus, a

very important point regarding receiver implementation is the frequency estimation and

locking.

Until now, for the analog domain several designs have been proposed, coming from RF

techniques [6], and being tested in optical communications [80]. Also, two main lines have

been followed for the digital domain: the off-line processing and the real-time approach.

For the off-line approach, the same receiver architecture is used, almost all times [63, 64].

There the challenge is the development of feed-forward processing algorithms that can

compensate the frequency offset between local laser and received signal.

This study presents a reliable, fast and real-time wavelength control for intradyne co-

herent reception, based on a single side-band optical VCO; intended for, at least, 8-PSK

modulation format.

151

Appendix B. Automatic wavelength control design 152

B.2 Loop design and performances

The overall loop proposed is shown in figure B.1. It has a 90 optical hybrid coherent

reception front-end, driven by a local optical Voltage Controlled Oscillator (VCO); a

delay-and-multiply frequency discriminator, and a loop control filter. The VCO device

used is an optical VCO that can be controlled in a stable and fast way, like an electrical

one. Its conceptual scheme is detailed on figure B.2. The objective is to control a Single

Side Band (SSB) tone modulation of the local laser. For that reason an IQ modulator is

used. Details of its performance and characterization for using it in optical phase-locking

can be found in [81].

Figure B.1: Scheme of the proposed analog frequency estimation loop.

Figure B.2: Optical SSB-modulation VCO.

Regarding the frequency discriminator, it was found that a good and reliable implemen-

tation can be just a delay-and-multiply architecture that has been deeply studied and

reported in [6, 35].

In order to evaluate the performances of the proposed receiver architecture, several sets of

simulations were run for different parameters: frequency discriminator performances, loop

delay impact and phase noise impact. Regarding frequency discriminator performances, a


first set of simulations was configured for an RZ-8-PSK scheme, with a coherent receiver

followed by a digitization stage. Since it is digitized, the proposed frequency discriminator

could be compared with a theoretical solution that can be used in off-line processing: a

linear fit of the phase curve. Results are shown in figure B.3. There it can be observed

that, while the proposed scheme gets almost unaffected, the other has a discontinuity

around +-1250 MHz. This is because in the last case, a power-of-eight block is required

to remove the 8-PSK modulation, and this puts a cycle-slipping indetermination on that

frequency, that has to be taken into account when estimating the frequency.

Figure B.3: Frequency discriminator output vs. frequency difference between LO andreceived signal.

After characterizing the frequency discriminator with the proposed modulation, a nu-

merical analysis was made, departing from the theoretical equations that arise from loop

linearization [6, 35]. Regarding this numerical analysis, the transfer function was found

to be expressed as:

HS(S) =K ·Kp · S +K ·Ki

(1 +K ·Kp)S +K ·Ki

(B.1)

K = 8πKLO<2R2LPSPLO (B.2)

T =1 +K ·Kp

K ·Ki

(B.3)

where S is the complex angular frequency, KLO is the sensitivity of the optical VCO

module (Hz/V), < is the photo-detector’s responsivity, RL is the load impedance, PS is

the received optical power, PLO is the local oscillator optical power, Kp is the proportional


gain of the loop filter, Ki is the integral gain of the loop filter, and T is the time constant

of the system.

From this model, the loop delay impact was evaluated. The output parameter evaluated

was the setting time at 10% error from the final value, for a low frequency step (100

MHz). Results are shown in figure B.4. There it is shown that when loop delay is about

one fifth the time constant, the system performances decrease dramatically.

Figure B.4: Loop delay impact on loop setting time.

Afterwards module for the full loop (no data) was implemented using the software VPI-

transmissionMaker. With this model, the phase noise impact to the frequency control

could be evaluated. Results are shown in figure B.5. As expected, it introduces a residual

error, with gaussian statistics, that cannot be tracked nor compensated at all. The vari-

ance of such error is proportional to the laser linewidth, as expected. Thus, this error can

not be compensated at all, and a separate phase compensation method has to be used.

B.3 Practical implementation

In figure B.6 a schematic of the overall loop to be implemented is shown. Of that loop

the optical VCO was characterized and afterwards, with the SSB VCO, some preliminary

measurements (based on off-line processing) were carried out for the frequency estimator.

Regarding VCO characterization, a result of the maximum hold function for the output

spectrum of the optical VCO is shown in figure B.7. There, it is shown that such an optical


Figure B.5: Error signal variance vs. laser linewidth.

Figure B.6: Schematic to be implemented.

VCO has a residual amplitude tilt, with a slope of 2.8 dB. Also, when approaching to

the limit of 4 GHz, a high peak appears at the opposite side of the spectrum. This peak

corresponds to a worst case condition, and is 12.7 dB below the principal component.

Precisely, this is shown in figure B.7 for the -4 GHz case. That range of 4 GHz is set by

the RF components used (hybrid, amps and filters) and is enough for our purposes. Of

course, by carefully setting these RF components, the performances of the VCO can be

substantially improved.

Afterwards, it was compared to other two optical VCO approaches. Results are shown

in table B.1. One approach is based on tuning the current of the phase section of a

GCSR laser. It presents some difficulties for setting the appropriate working point, and

could present some hysteresis, depending on the operation wavelength range [82]. Data


Figure B.7: Max hold function for the output spectrum of the optical VCO.

presented here has been obtained from [82], where a GCSR laser model NYW 30-009

from ALTITUN, was characterized. A second alternative VCO is a DFB laser, working

in a saturation point and modulating its adiabatic chirp for changing the wavelength.

However it could give a high residual amplitude change. For this approach, data was

retrieved from basic measurements carried out of a Panasonic LNFE03YBE1UP.

Laser Tuning Tuning Frequency Residuallinewidth speed range slope amplitude

SSB-IQ mod. 100 kHz 10 MHz 2 GHz 260 MHz/V 2.8 dBGCSR 60 MHz 100 MHz 18 GHz 320 MHz/V 0.1 dBDFB 1 MHz 1 GHz - 1.4 GHz/V 7.4 dB

Table B.1: Comparison between possible optical VCO approaches.

In order to see the potential when using the proposed frequency discriminator, some

off-line experiments were carried out. The setup used is depicted in figure B.8. It is a

back-to-back version of the 10 Gbaud RZ-8PSK (30 Gb/s) transmission system reported

in [83], with the proposed optical VCO. There, the transmitter consists of a laser that

for RZ pulse carving a Mach-Zehnder Modulator (MZM) is used. Regarding the 8-PSK

signal, it was generated by an IQ-modulator, which generated an optical QPSK signal, and

a consecutive phase modulator, which was used for the additional π/4 phase modulation.

The transmitted data signal was a 211− 1 pseudo-random bit sequence, given by a Pulse-

Pattern Generator (PPG). These signals were given to the modulator inputs with different

delays to ensure their independence.


At the receiver side, the RZ-8PSK signal was interfered with the optical VCO in a LiNbO3

2x4 90 hybrid. The output signals of the hybrid were detected by two balanced detectors,

and the I and Q outputs were sampled using a 50 GSa/s digital storage oscilloscope.

Figure B.3 shows the estimation results, for two different discriminators: Linear curve

fitting, and delay and multiply method. 3 different cases were compared: No frequency

difference, 3 GHz of frequency difference, and 3.5 GHz of frequency difference. There

it is shown that for all cases of frequency difference, both methods, linear fitting and

delay-and-multiply, work as expected, but with a non-negligible error. Those differences

are attributable to the laser instability.

Figure B.8: Experimental setup.

B.4 Conclusions

An automatic frequency control design has been proposed and demonstrated. It is based

on a high-speed optical VCO. First proof-of-concept experiments have been performed,

showing the feasibility of the main components of the loop and a good agreement with

simulation results.

Appendix C

Static and dynamic wavelength

characterization of tunable lasers

Tunable laser is a relevant critical device that nowadays is being pursued by several

vendors worldwide. The purpose of this study is to analyze the static and dynamic

behaviors of new generation tunable lasers for advanced applications like dynamic WDM-

PON networks and Optical Burst Switching networks.

In this case, the tuning process of tunable lasers is a critical issue in the performance

of these lasers, usually not straightforward to obtain and to optimize. The main results

of the present test were two: first a working points map for all possible reflectors and

phase currents of the tunable laser (a modulated-grating Y-branch (MG-Y) laser, Syntune

3500) was obtained; and next a high-resolution 3-dimensional wavelength-time-power

measurement of the tuning process of the laser was measured, obtaining the optical

spectrum at every instant and its evolution along the tuning transient. With this, it

is easy to identify, not only the wavelength temporal drift, but also the transitory mode

hopping or interferences over other wavelength channels. Subsequently, this tool can be

used to optimize the driving currents waveforms to improve the tuning process of the

laser module.

C.1 Experiments and discussion

The laser characterized was a tunable modulated-grating Y-branch laser (Syntune 3500).

First, a complete map of wavelengths versus reflectors and phase currents was measured.

Next, switching between different wavelengths using the reflectors electrodes has been

characterized.

159

Appendix C. Static and dynamic wavelength characterization of tunable lasers 160

C.1.1 Static characterization: wavelength map

The aim of this experiment was to obtain a wavelength map as a function of the tuning

currents (phase and reflectors). Such a map was used afterwards, to locate the different

wavelength modes and visualize the regions at which they remain stable.

C.1.1.1 Static characterization setup

The test setup used for characterizing the wavelength modes location and to find the

stable regions of the laser is depicted in figure C.1. As one can notice in the diagram, a

multi current source was used to drive the laser currents: active layer (IACT ), phase (Iph),

reflector 1 (Iref1), reflector 2 (Iref2) and SOA (ISOA). Moreover, a wavelength meter was

employed to measure the output beam wavelength. Both instruments were controlled by

a PC through GPIB port.

During the experiment, the active layer and SOA currents were kept constant, while

phase and reflectors currents did a complete sweep within their range. Precisely, Iph was

working in the 0-5mA range, while Iref1 and Iref2 were between 0 mA and 30 mA.

Figure C.1: Experimental setup for stability regions characterization.

C.1.1.2 Static characterization results

An example of the so called wavelength map can be observed in figure C.2 (a). In this

figure the wavelength (colour scale) is plotted as a function of both reflectors currents

for a fixed phase current (2.4 mA). In the image one can clearly identify large conical

regions (super-modes). Such super-modes start at coordinates (2;2) mA and show abrupt

wavelength changes among them.

In order to obtain a most accurate knowledge of the mode regions, the wavelength maps

were processed using morphological image techniques. The regions shown in figure C.2

(b) were obtained after processing the wavelength map for Iph = 2.4 mA. In this figure


the super-modes can be easily identified. Furthermore, one can also depict that each

super-mode contains various scale shaped regions. Each of these regions correspond to a

different mode.

Figure C.2: (a) Wavelength map: Plot of the wavelength (colour scale) in function ofreflector currents. (b) Logic stable regions map in function of reflector currents. The

phase current for a) and b) is Iph = 2.4 mA.

The wavelength spacing between consecutive modes is much bigger between two consecu-

tive modes placed in different super-modes (∆λ in the order of 5 nm), than between two

consecutive modes placed in the same super-mode (∆λ in the order of 0.5 nm). It can

be also observed that the wavelength decreases within a mode region by increasing both

reflectors currents (approximately at a ratio of 0.08nm/mA).

The fact of changing the phase current has much smaller consequences than changing

the reflector currents. However, two effects can be observed while increasing Iph. One of

the effects is depicted in figure C.3 (a). In this figure, the wavelength of a fixed point

(Iref1= 22.8 mA, Iref2= 8.6 mA) is plotted as a function of the phase current. As can

be noticed in the plot, the wavelength of a fixed point decreases as the phase current

increases (approx. 0.1nm/mA). The other effect arises when comparing figure C.3 (b)

and (c). These figures represent the wavelength maps for Iph = 1.8 mA and Iph = 2.2

mA. Into each wavelength map, several fixed points (in terms of reflector currents) are

plotted in order to see more easily the effect produced. If the points of figure C.3 (b-c)

are observed carefully, one can realize that in figure C.3 (b) they are located just above

the limit of a certain region, while in figure C.3 (c) they are placed under that limit.

Therefore, when phase current increases the complete map shifts towards higher reflector

currents.

Consequently, if Iph is increased enough (2-3 mA) a fixed reflector’s bias point jumps

from one mode to another, producing an abrupt change of wavelength (see figure C.3 (a)

around Iph = 2 mA).

Finally, the wavelength drift was measured for a change of the gain current. Three plots of

the wavelength versus the gain current for different modes can be observed in figure C.4.

In all the graphs, one can depict a quasi-linear wavelength increment while increasing the


Figure C.3: (a) Plot of the wavelength in function of the phase current. Reflectorcurrents are biased at Iref1 = 22.8 mA and Iref2 = 8.6 mA. (b, c) Wavelength regionmap as a function of both reflector currents for a phase current of 1.8 and 2.2 mA,

respectively.

gain current. Please note that the laser is highly stable, so the drift of wavelength per

unit of current is quite low ( 0.001 nm/mA).

Figure C.4: Plots of the wavelength as a function of the gain current for differentreflector currents (Iph = 2.4 mA): (a) Iref1 = 10.8 mA, Iref2 = 29 mA; (b) Iref1 = 12.4

mA, Iref2 = 8.9 mA; (c) Iref1 = 10.2 mA, Iref2 = 11.9 mA.

C.1.2 Dynamic characterization

The aim of this experiment was to perform a high resolution measurement of the laser

response while it was switching between two working points. So, for each case the power

was measured in function of time and wavelength. The result of this experiment was a

3-D wavelength-power-time graph. From such graph, various aspects of the laser response

were calculated: time evolution of the optical spectrum, Side Mode Suppression Ratio

(SMSR) and switching time.


C.1.2.1 Dynamic characterization setup

The test setup for characterizing the laser transient wavelength response is shown in

figure C.5. A function generator excited each laser reflector with a switching square

signal. After the tuneable laser, a Variable Optical Attenuator (VOA) was placed, in

order to not saturate the photo-detector, while being inside the range of the filter. After

the VOA, the optical filter filtered the laser output, centred at the wavelength specified

by the PC and with a bandwidth of 0.08 nm (10 GHz), from 1532 nm until 1562 nm.

The photo-detector output was connected to the oscilloscope and its data was acquired

by the laptop PC by means of a GPIB interface.

Figure C.5: Experimental setup for transient response characterization.

C.1.2.2 Dynamic characterization results

The experiment was performed for different kind of transitions. Figure C.6 (a) depicts

the wavelength map for Iph = 2.4 mA; from which the working points were chosen to

carry out the switching measurements. Most of the measured transitions are denoted in

figure C.6 (a) with a white line and an identification number.

An example of the currents applied to the reflectors in function of time is shown in

figure C.6 (b). Each reflector was excited with a square signal running at 20 MHz, with

a rise/fall times of less than 100 ps.

Along the following lines the response of the MG-Y laser will be discussed for different

kinds of wavelength switching. In the first experiment (depicted in figure C.6 (a-1)), the

laser behaviour was measured when having a change between two working points located

in the same mode (from 1560.24 nm to 1560.46 nm). Figure C.7 (1.a) illustrates a 3-D

Wavelength-Power-Time plot (WPT plot). Such plot represents the wavelength versus

time and power (gray scale). One can observe in this figure that the transition from one

wavelength to the other within the same mode is totally continuous, and mainly due to

thermal effect. The switching time of the laser during this kind of transient is quite long

(3 ns).


Figure C.6: (a) Stable regions map for Iph = 2.4 mA. The black points denote workingpoints used to measure the transition between two modes. The white lines denote suchtransitions, 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).

The lines shown in figure C.6 (a-2) and figure C.6 (a-3) denote the next two experi-

ments. The first transition was measured between two consecutive modes (from 1550.12

to 1550.92 nm), whereas the second was measured between two non-consecutive modes

(from 1559.49 to 1561.93 nm). Please note that the laser modes corresponding to each

test are located in the same super-mode. The WPT plots obtained from these experi-

ments are depicted in figure C.7 (2.a) and (3.a), respectively. In both figures, the same

effect shown in figure C.7 (1.a) can be observed: the wavelength shifts continuously

when the working point changes inside the same mode. Afterwards, when the transient

reaches the limit of the mode, an abrupt (non-continuous) switch of wavelength occurs.

This behaviour is also related to the thermal effect [84]: the gain of the material shifts

continuously towards higher wavelengths when increasing current (what produces the

continuous shifting); however, when the gain curve approaches the following longitudinal

mode, a longitudinal mode-hopping occurs and such mode becomes the main mode (what

produces the non-continuous jump to higher wavelengths). As expected, the switching

time increased with the distance between working points (see table C.1).

In the next set of experiments, which working points can be seen in figure C.6 (a-4, 5,

6 and 7), the measured transitions were between different super-modes: experiment 4

consists in a transition between consecutive super-modes; in experiment 5 the transition

measured was between two super-modes separated by one super-mode; the working points

in experiment 6 are separated by 4 super-modes; and in experiment 7 the two working

points measured gave neighboring wavelengths (see table C.1), but located several super-

modes apart. WPT plots of experiments 4, 5, 6 and 7 are depicted in figure C.7 (4.a,

5.a, 6.a, 7.a), respectively. A common characteristic can be observed in all WPT plots:

there is no continuous wavelength shift as in the previous set of experiments. This is due

to an additive Vernier effect, typical from the MG-Y laser [85]. Thus, when the reflector

currents are not increased/decreased along the same direction, the wavelength remain

constant until it arrives to a mode limit. Then, the wavelength changes suddenly.


Figure C.7: (Id.a) WPT plot: Plot of the wavelength versus time, and power (grayscale) versus both wavelength and time for experiment ’Id’ (see table C.1 and/or fig-ure C.6 (a)). (Id.b) SMSR versus time plot for experiment ’Id’ (see table C.1 and/or

figure C.6 (a)).

Please note that the device lases for a certain period of time with the wavelength that

belongs to each super-mode that crosses during the transient. Such effect slows down

the time response of lasers. Therefore, in a similar way than in the previous set of

experiments, the switching time increases with the number of super-modes between both

working points (see table C.1). Consequently, the fact of not having the continuous

wavelength shift makes the transitions between consecutive super-modes much faster

than the transition between consecutive modes (inside the same super-mode).

Transitions between working points placed at different phase currents were also measured.

The WPT plot of a transition between two working points located in the same mode

and the WPT of a transition between points placed in different modes are depicted in


figure C.7 (8.a, 9.a), respectively. As it has been said previously, the change in wavelength

is much smaller when changing the phase current than when varying the reflector currents.

Nevertheless, a new important fact was observed during these experiments: the switching

time was substantially much slower when the phase current was changed (see table C.1).

Thus, the frequency of the signal driving the laser had to be low, from 20 to 2.5 MHz, in

order to better appreciate the transition.

Each of the plots placed below the WPTs -see figure C.7 (Id.b)- represent the Side Mode

Suppression Ratio (SMSR) calculated for each of the experiments as a function of time

(please note that the SMSR was calculated within the complete C-band range). One

can observe in the plots that the SMSR undergoes the 20 dB only during the transition

between different modes. The mean SMSR for each case can be seen in table C.1. In

order to calculate the SMSR, the power of the main and secondary modes had to be

measured along the transitions. In figure C.8 (a) it is shown the WPT of experiment 4 in

logarithmic scale to be able to visualize the secondary mode. One can observe that such

mode is located at the ”non-lasing” working point of the transition. However, as shown

with the SMSR plots, the power of the secondary mode is 20 dB lower than the main

mode power (see also figure C.8 (b), which depicts the power of the main and secondary

modes versus time).

Figure C.8: (a) WPT plot: Plot of the wavelength versus time, and power (logarithmiccolour scale) versus both wavelength and time for experiment 4. (b) Main mode and

secondary mode power versus time (in logarithmic scale).

As said before, during the experiment shown in figure C.8, the secondary mode was

located always in the non-lasing working point of the transition. However, in much

complex transients, the laser does not have such behaviour. In figure C.9 (a) shows

a zoom of the experiment 5 WPT. Such experiment was a transition between working

points located in two different super-modes (mode 1 at 1534.16 nm and mode 2 at 1545.2

nm) separated by one super-mode (inter-mode at 1539.8 nm). In order to appreciate

more easily the behaviour of the device during the transition, the wavelength versus time

of the main and secondary modes was plotted in figure C.9 (b) (black and green lines,

respectively). In this figure, one can see that the secondary exhibits two kinds of mode-

hopping: a mode-hopping between mode 1 and mode 2 when the device (main mode) is


lasing in the inter-mode; and a mode-hopping between the inter-mode and mode 1/mode

2, when the main mode is located in mode 2/mode 1. In addition, a mode-hopping of the

main mode is also observed in figure C.9 (c), which is a zoom of the transition between

the inter-mode and mode 2 of figure C.9 (b). Please note that this mode-hopping has a

short duration ( 100 ps).

Figure 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) Wavelengthversus 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).

Experiment Kind of transition Wavelengths (nm) Switching SMSRIdentifier time (ns) (dB)

1 InM 1560.08 - 1560.32 3.0 20.142 CM 1550.00 - 1550.80 4.0 23.633 NCM 1559.68 - 1562.08 7.0 22.284 CS 1550.00 - 1555.60 0.40 20.835 NCS (1 super-mode in between) 1534.16 - 1545.20 5.0 22.276 NCS (4 super-modes between) 1534.16 - 1559.68 12.0 23.857 NCS (close wavelengths) 1534.16 - 1535.80 13.0 22.148 Iph: InM 1554.78 - 1554.86 12.0 23.159 Iph: CM 1554.80 - 1554.84 40.0 23.9

Table C.1: The acronyms read in ”kind of transition” column, have a brief explanationof the working points location: InM (Inside the same Mode); CM (Consecutive Modesin 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).

C.2 Conclusions

The topology of the wavelength modes has been fully characterized. The 3-dimensional

(Iref1, Iref2, Iph) wavelength map built, is essential to locate the wavelength modes needed

for certain applications (e.g. the channels for WDM). Moreover, a good knowledge of the

wavelength map topology let us find easily the most stable operation points.


In addition, through the high-resolution wavelength-power-time measurement, the dy-

namic behaviour of the laser while switching between modes has been also characterized.

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.

Appendix D

Phase noise digital modeling

As seen in chapters 3 and 4, the main phase noise simulations were done in Mat-

lab/Simulink. Here the objective is to obtain an expression in order to generate the

phase of phase noise at several linewidths, because the Matlab/Simulink software has no

modules to generate it. Also the phase of phase noise must be generated in a discrete

domain (Matlab), while the simulation with Simulink has to be in the analog domain.

By definition, the phase introduced by an oscillator’s phase noise can be modeled as:

φN(t) =

∫ t

0

ϕN(τ)dτ (D.1)

where ϕN(t) is a Gaussian process, with zero mean and variance 2π∆ν; and φN(t) is the

phase noise (rad.).

Furthermore, it is known that in the frequency domain, this phase will have a power

spectral density defined by the following equation:

S(f) =∆ν

2πf 2(D.2)

where ∆ν is the laser linewidth.

From equation D.1, the integral can be made in a discrete time domain, using the rect-

angles method:

φN [j] =

j∑i=1

∆t · ϕN [i] (D.3)

For every j from 1 until M .

where ϕN is a vector containing random numbers with a Gaussian distribution and zero

mean, ∆t is the time step, M is the number of noise samples generated, and φN is a

vector containing the phase noise.

169

Appendix D. Phase noise digital modeling 170

In order to see the transfer function, this expression can be rewritten and transformed,

first into the z domain and secondly into the DFT domain:

φN [i] = φN [i− 1] + γN [i] (D.4)

so

H(z) =ΦN(z)

ΓN(z)(D.5)

and

H(z) =ΦN(Ω)

ΓN(Ω)=

1

1− e−jΩ(D.6)

where ΦN(z) is the z transform of φN .

ΦN(Ω) is the discrete Fourier transform of φN .

γN [i] is ∆t · ϕN [i].

ΓN(z) is the z transform of γN .

ΓN(Ω) is the discrete Fourier transform of γN .

Ω is the normalized frequency expressed in rad/s.

Thus, as γN is also white noise, it is an order 1 Auto-Regressive (AR) process. Now, one

can work without normalized frequencies and manipulate the expressions, resulting in:

Sφ(f) =Gγ(f)

|1− e−j2πf∆t|2=

Gγ(f)

2(1− cos(2πf∆t)

) (D.7)

Where Gγ(f) is the power spectrum density of γN .

So, when f decreases and takes values near 0, Sφ(f) grows towards +∞, and becomes

similar to equation D.2. Assuming that the integration step is very small (sampling

frequency very high) and that the PSD expression of the AR process is evaluated near

0 (base band), the cosine term can be approximated by its Taylor expansion truncated

after its second term. Then, equation D.7 can be written as:

Sφ(f) =Gγ(f)

4π2f 2∆t2(D.8)

And this has the exact shape of the theoretical expression.

Taking into account the sampling reviewed theorem [86], the last expression from DFT

domain can be moved to analog Fourier domain and terms between D.2 and D.8 can

be identified. In this way the phase noise can be approximated by an AR process if it

accomplishes:

Gγ(f) = 2π∆ν∆t (D.9)


But Gγ(f) is the PSD of γN ; while γN has an autocorrelation of:

γN [i] = ∆tϕN [i] (D.10)

rγ(l) = ∆t2rϕ(l) = ∆t2σ2ϕδ(l) (D.11)

being rgamma the autocorrelation of γN and rϕ the autocorrelation of ϕN .

Thus, as Gγ(f) is the DFT of rγ:

Gγ(f) = DFTrγ = ∆t2 · σ2ϕ (D.12)

And such expression can be made the same as equation D.9:

∆t2 · σ2ϕ = 2π∆ν∆t (D.13)

σ2ϕ =

2π ·∆ν∆t

(D.14)

And this is it. So, to make a phase approximation of phase noise in order to simulate

the proposed systems (oPLLs and diversity schemes) with Matlab/Simulink software it

is needed to:

1. Generate a white Gaussian noise with variance 2π∆f/∆t.

2. Check it is itself uncorrelated.

3. Integrate it using the rectangles method.

4. Estimate its PSD.

5. Check that this PSD fits the theoretical curve.

Figure D.1 show the AR modified covariance method spectrum estimation of a noise gen-

erated by our method (thin black line), scaled discrete theoretical spectrum for the same

noise (square points with dotted line), and analog theoretical spectrum to be approxi-

mated (dashed line). From this figure, it should be noted that below 10 GHz the AR

curve is very close to the analog theoretical curve. So the phase of phase noise generated

is valid at the working frequencies.


Figure D.1: Phase of phase noise spectrum.

Appendix E

Lock-In OPLL prototype scheme

and printed circuit board

Figure E.1: Printed circuit board outline of the Lock-IN OPLL prototype.

173

Appendix E. Lock-In OPLL prototype scheme and printed circuit board 174

Appendix E. Lock-In OPLL prototype scheme and printed circuit board 175

Appendix F

Research publications

F.1 Patents

1. J. Prat, J. M. Fabrega, ”Homodyne receiver for optical communications with post

processing,” app. number US-12521619, date 10/20/2009.

2. J. Prat, J. M. Fabrega, ”Receptor homodino para comunicaciones opticas con

procesado a posteriori,” app. number ES-P200700041 (PCT/ES2007/000778), date

12/29/2006.

3. J. Prat, J. M. Fabrega, J. M. Gene, ”Receptor coherente homodino para comuni-

caciones opticas con demodulacion diferencial,” app. number ES-P200500998, date

04/21/2005.

F.2 Book contributions

1. Contribution to the book ”Next Generation FTTH Passive Optical Networks,”

Springer-Verlag 2008 (Josep Prat Ed.), in the transmission techniques chapter.

F.3 Journal publications

1. J. M. Fabrega, J. Prat, ”Experimental Investigation of Channel Crosstalk in a

Time-Switched Phase Diversity Optical Homodyne Receiver,” OSA Optics Letters,

vol. 34, No. 4, February 2009.

2. J. M. Fabrega, J. Prat, ”Homodyne receiver prototype with time-switching phase

diversity and feedforward analog processing,” OSA Optics Letters, vol. 32, No. 5,

March 2007.

177

Appendix F. Research publications 178

3. J. M. Fabrega, J. Prat, ”Fuzzy Logic Data Estimation Based PSK Receiver with

Time-switched Phase Diversity,” IEE Electronics Letters, vol. 42, no. 16, August

2006.

F.4 Conference publications

1. J. M. Fabrega, J. Prat ”Digital Phase Estimation Method based on Karhunen-Loeve

series expansion for Coherent Phase Diversity Detection,” Optical Fiber Commu-

nication OFC/NFOEC 2010, paper JThA3, San Diego (CA), USA, March 2010.

2. J. M. Fabrega, A. El Mardini, V. Polo, J. A. Lazaro, E. T. Lopez, R. Soila, Josep

Prat ”Deployment Analysis of TDM/WDM Single Fiber PON with Colourless ONU

Operating at 2.5 Gbps Subcarrier Multiplexed Downstream and 1.25 Gbps Up-

stream,” National Fiber Optic Engineers Conference OFC/NFOEC 2010, paper

NWB5, San Diego (CA), USA, March 2010.

3. J. M. Fabrega, V. Polo, E. T. Lopez, J. A. Lazaro, J. Prat ”Optical Network

Based on Reflective Semiconductor Optical Amplifier Using Electrical Subcarrier

Multiplex for Enhancing Bidirectional Transmission,” 6a Reunion espanola de Op-

toelectronica OPTOEL’09, Malaga, July 2009.

4. J. M. Fabrega, J. Prat, ”Ultra-Dense, Transparent and Resilient Ring-Tree Access

Network using Coupler-based Remote Nodes and Homodyne Transceivers,” Inter-

national Conference on Transparent Optical Networks ICTON’09, Paper Th.B3.3,

Azores, Portugal, June 2009.

5. J. M. Fabrega, J. Prat, L. Molle, R. Freund, ”Design of a wavelength control for

coherent detection of high order modulation formats,” International Conference on

Transparent Optical Networks ICTON’09, Paper We.P.21, Azores, Portugal, June

2009.

6. J. M. Fabrega, J. Prat, ”Low Cost Homodyne Transceiver for UDWDM Access Net-

works,” European Conference on Networks and Optical Communications NOC’09,

Invited Paper, Valladolid, Spain, June 2009.

7. J. M. Fabrega, E. T. Lopez, J. A. Lazaro, M. Zuhdi, J. Prat, ”Demonstration of a

full duplex PON featuring 2.5 Gbps Sub Carrier Multiplexing downstream and 1.25

Gbps upstream with colourless ONU and simple optics,” European Conference on

Optical Communications ECOC’08, Paper We.1.F.6, Brussels, Belgium, September

2008.

8. J. M. Fabrega, L. Vilabru, J. Prat, ”Experimental Demonstration of Heterodyne

Phase-locked loop for Optical Homodyne PSK Receivers in PONs,” International

Conference on Transparent Optical Networks ICTON’08, Paper We.C1.5, Athens,

Greece, July 2008.


9. J. M. Fabrega, J. Prat, ”Simple Low-Cost Homodyne Receiver,” European Confer-

ence on Optical Communications ECOC’07, Paper 7.2.5, Berlin, Germany, Septem-

ber 2007.

10. J. Prat, J. A. Lazaro, J. M. Fabrega, V. Polo, C. Bock, C. Arellano, M. Omella,

”Next Generation Architectures for Optical Access and Enabling Technologies,” 5a

Reunion espanola de Optoelectronica OPTOEL’07, Bilbao, July 2007.

11. J. M. Fabrega, J. Prat, ”Channel Crosstalk in ultra-dense WDM PON using Time-

Switched Phase Diversity Optical Homodyne Reception,” International Conference

on Transparent Optical Networks ICTON’07, Paper Tu.A1.3, Rome, Italy, July

2007.

12. J. M. Fabrega, J. Prat, ”Homodyne PSK Receiver with Electronic-Driven Phase

Diversity and Fuzzy Logic Data Estimation”, European Conference on Optical Com-

munications ECOC’06, Paper We3.P.100, Cannes, France, September 2006.

13. C. Bock, J. M. Fabrega, J. Prat, ”Ultra-Dense WDM PON based on Homodyne

Detection and Local Oscillator Reuse for Upstream Transmission”, European Con-

ference on Optical Communications ECOC’06, Paper We3.P.168, Cannes, France,

September 2006.

14. J. M. Fabrega, J. Prat, ”Homodyne Receiver Implementation with Diversity Switch-

ing and Analogue Processing”, European Conference on Optical Communications

ECOC’06, Paper We3.P.100, Cannes, France, September 2006.

15. J. M. Fabrega, J. Prat, ”Optimization of Heterodyne Optical Phase-Locked Loops:

Loop Delay Impact and Transient Response Performances”, International Confer-

ence on Telecommunications ICT’06, Paper Thu.O2, Funchal (Madeira), Portugal,

May 2006.

16. J. M. Fabrega, J. Prat, ”New Intradyne Receiver with Electronic-Driven Phase

and Polarization Diversity”, Optical Fiber Communication OFC/NFOEC’06, paper

JThB45, Anaheim (CA), USA, March 2006.

17. J. Prat, J. M. Fabrega, ”New Homodyne Receiver with Electronic I&Q Differential

Demodulation”,European Conference on Optical Communications ECOC’05, paper

We4.P.104, Glasgow, UK, September 2005.


F.5 Submitted publications

F.5.1 Book contributions

• J. A. Lazaro, J. M. Fabrega, A. L. J. Teixeira and J. Prat, ”Laboratory Set-ups

and Methods for Teaching and Characterizing Optical Polarization Modulators,” in

EuroFOS project Handbook of Experimental Fiber Optics.

F.5.2 Journal publications

• J. M. Fabrega, A. ElMardini, V. Polo, E. T. Lopez, J. A. Lazaro, M. Zuhdi, and J.

Prat, ”Demonstration of a single fibre PON featuring 2.5 Gbps Sub-Carrier Mul-

tiplexing Downstream and 1.25 Gbps Upstream with Colourless ONU,” submitted

to IET proceedings in optoelectronics.

F.5.3 Conference publications

• M. Mestre, J. M. Fabrega, J. A. Lazaro, V. Polo, A. Djupsjobacka, M. Forzati, P.-J.

Rigole and J. Prat, ”Tuning Characteristics and Switching Speed of a Modulated

Grating Y Structure Laser for Wavelength Routed PONs,” submitted to OSA-ANIC

2010.

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homodyne olt-onu design for access optical networks

Technology

access networks

homodyne reception

valuable support

work wouldnt

special thanks

transmission team

narrow channel

net work testbed