1. Ph. D. Thesis
Optical Communications Group
Department of Signal Theory and Communications
Universitat Politècnica de Catalunya
Homodyne OLTONU design for
access optical networks
Author
Josep Mª Fàbrega
Advisor
Josep Prat
Thesis presented in fulfillment of the doctorate program of
the signal theory and communications department
March 2010
3. ”The most exciting phrase to hear in science, the one that heralds the most discoveries,
is not Eureka! (I found it!) but ’That’s funny...’”
Isaac Asimov
4. `
UNIVERSITAT POLITECNICA DE CATALUNYA (UPC)
Abstract
Optical Communications Group (GCO)
Signal Theory and Communications Department (TSC)
Doctor of Philosophy
by Josep M. F`brega
a
Nowadays, when talking about access networks, advanced multimedia applications are
changing customer demands, requiring much higher speed connection. Thus, other al
ternatives to deployed Time Division Multiplex Passive Optical Networks (TDMPONs)
are appearing to increase available bandwidth. Wavelength Division Multiplex provides
virtual pointtopoint connections, so multiplies the eﬀective bandwidth that the ﬁber can
oﬀer. A signiﬁcant step forward is UltraDense WDM (UDWDM), 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 channelspacing could be achieved,
a new philosophy of WavelengthToTheUser (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 testbed. For that prototype, transmission experiments demonstrate a sensitivity
of −38.7 dBm sensitivity at 1 Gb/s, while featuring a power budget of 47 dB.
Furthermore, diﬀerent PON architectures are proposed and speciﬁcally designed for the
proposed transceivers. With the experimental prototype previously developed, network
deployment is obtained, capable to serve up to 1280 users at maximum distance of 27 km
and featuring a maintained data rate of 1 Gb/s per user.
5. Acknowledgements
First of all I want to express my gratitude to my advisor Prof. Josep Prat for having given
to me the opportunity to join the optical communications research group and develop
my Ph.D. within it. His guidance and friendship have set the cornerstone of the work
presented in this thesis.
These investigations would not have been possible without the full support of the optical
communications group at UPC. My special thanks to Jos´ L´zaro, Bernhard Schrenk,
e a
Carlos Bock, Joan Gen´ and Jaume Comellas for their advice and fruitful discussions,
e
also demonstrating their sincere friendship. A warm hug to thank all the colleagues for
making an enjoyable atmosphere everyday during these years. In this aspect I would
like to emphasize the support of the remaining members of the Access and Transmission
team: Eduardo T. L´pez, Mireia Omella, Victor Polo and specially Francesc Bonada,
o
for his unvaluable help in the network administration. Also I want to acknowledge the
support of those that not belong to GCO: The entire SITSC 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 cosupervised. The
herewith presented work wouldn’t been possible without their contributions. In chrono
ıs u n `
logical order: Llu´ Vilabr´, Joan Miquel Pi˜ol, Miquel Angel Mestre and Marc Vilalta
(almost ﬁnishing).
On the personal level, I would like to thank all my family for their support, specially the
most important person in my live, Vanessa Ortega, for her encouragement and endurance.
For ﬁnancial assistance I am indebted to several public projects and private contracts:
COTS contract (Nortel Networks), SCALING contract (Tellabs Inc.), EUFP7 BONE
and SARDANA projects; Spanish MICINN projects TEC200801887 (TEYDE), RA4D
and RAFOH; EUFP6/7 EPhoton(+) and EuroFOS networks of excellence, and the
MEC PTA20030200874 grant.
vii
11. List of Figures
1.1 Nielsen’s law prediction of bandwidth and data obtained until 2006 (square
points). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 FTTH access roadmap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Coherent receiver scheme, using balanced photodetection. . . . . . . . . 10
2.2 Optical spectrum of a wavelength to the user environment. λLO is the
nominal wavelength of the local oscillator, for a homodyne case. . . . . . 11
2.3 Comparison between homodyne and heterodyne electrical spectra. . . . . 11
2.4 Generic homodyne receiver. . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Constellation representation of a BPSK signal in the I and Q plane. . . . 14
2.6 Bit error probabilities for BPSK and DPSK, as a function of SNR. . . . . 16
2.7 BPSK error probability for diﬀerent phase error standard deviations. . . 17
2.8 BERﬂoor 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 Isocurves of √ variance of additive noise (left) and phase noise (right),
the
all for ξ = 1/ 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.12 PLL parameters optimization for 1 ns loop delay and 1 MHz linewidth. . 27
2.13 Isocurves of the variance of additive noise and phase noise, all for ξ = 2.
(ab) are for a null loop delay, whereas (cd) 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 phaselocked loop. 36
2.20 Scheme of a phase diversity front end. . . . . . . . . . . . . . . . . . . . . 38
2.21 Schematic of phase and polarization diverse receiver. . . . . . . . . . . . 39
2.22 Scheme of a DPSK detection, in a phase and polarization diversity homo
dyne receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.23 LMS error for a Wiener ﬁlter with a lag of 10 symbols. . . . . . . . . . . 43
2.24 Scheme of a phase estimator for polarization multiplexed QPSK signals
based in regenerative frequency dividers. . . . . . . . . . . . . . . . . . . 44
3.1 Voltage after balanced detector (V3 (t)) as a function of the phase error
(φS (t) − φLO (t)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
xv
12. List of Figures xvi
3.2 LockIn 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 BERﬂoor for optimal conﬁgurations as a function of the laser linewidth
evaluated at several main loop delays. . . . . . . . . . . . . . . . . . . . . 58
3.7 OPLL time response for a phase step of 1 rad. Inset ﬁgure is a zoom
between 500 ns and 550 ns. . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.8 Setting time of the optimal conﬁgurations for several loop main delays. . 59
3.9 Rise time of the optimal conﬁgurations for several loop main delays. . . . 60
3.10 Maximum overshoot of the optimal conﬁgurations for several loop delays. 61
3.11 Phase dithering eﬀect for large loop delays. . . . . . . . . . . . . . . . . . 61
3.12 Phase error deviation evaluated at a loop delay of 10 ns. . . . . . . . . . 62
3.13 Pull in margins of the simulated architectures. . . . . . . . . . . . . . . . 63
3.14 Hold in margins of the simulated architectures. . . . . . . . . . . . . . . . 63
3.15 Experimental Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.16 Electrical power spectrum after photodetection. . . . . . . . . . . . . . . 65
3.17 Electrical power spectrum after photodetection. . . . . . . . . . . . . . . 66
4.1 Scheme for a standard intradyne receiver. . . . . . . . . . . . . . . . . . . 70
4.2 Phase error deviation as a function of time interval squared per spectral
width product (T 2 ∆ν). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 Block diagram of the phase estimation algorithm. . . . . . . . . . . . . . 73
4.4 Phase error deviation as a function of the spectral width per bitrate ratio. 73
4.5 Timeswitched 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 Eyediagrams, at 50 MHz total laser linewidth. . 77
4.8 Statistical normalized eye opening (20Log) for the I/Q receiver (both ﬁrst
and second approach) and a lockin oPLL. . . . . . . . . . . . . . . . . . 77
4.9 Statistical normalized eyeopening (20log) for the I/Q receiver (both ﬁrst
and second approach) as a function of the laser frequency drift. . . . . . 78
4.10 Receiver scheme for phase noise analysis. . . . . . . . . . . . . . . . . . . 78
4.11 BERﬂoor 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 eyediagram . . . . . . . . . . . . . . . . . 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 TimeSwitched PhaseDiversity DPSK receiver for channel spacing study. 85
4.17 g1 (t) and g2 (t) pulse shapes and autocorrelation of g2 (t), R2 (τ ) . . . . . . 86
13. List of Figures xvii
4.18 Spectrum after photodetection: Ideal homodyne reception (a) and using
timeswitched phasediversity (b) . . . . . . . . . . . . . . . . . . . . . . 87
4.19 Complex representation of signal samples including interference. . . . . . 88
4.20 Sensitivity penalty due to channel crosstalk. Square points are experimen
tal data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.21 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.22 Receiver scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.23 IQ plane data plotting without diﬀerential decoding (left), and after dif
ferential decoding (right) for a signal corrupted by a phase noise due to
100 kHz of total laser linewidth . . . . . . . . . . . . . . . . . . . . . . . 92
4.24 I and Q components membership functions . . . . . . . . . . . . . . . . . 93
4.25 Data estimation scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.26 BERﬂoor 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 delayandadd, DAD) and
Im (t) (NDAD). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.32 Maximum tolerated linewidth per bit rate ratio at BER 10−3 as a function
of the gain factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.33 Receiver sensitivity for several conﬁgurations. . . . . . . . . . . . . . . . 103
4.34 Experimental setup for the direct drive timeswitching. . . . . . . . . . . 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 timeswitched phase and polar
ization diversities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1 Transceiver with 90◦ hybrid and digital processing. . . . . . . . . . . . . 114
5.2 Transceiver with 90◦ hybrid and analog processing. . . . . . . . . . . . . 115
5.3 Digital conﬁguration scheme using 90◦ hybrid combined with PBS. . . . . 116
5.4 Analog conﬁguration scheme using 90◦ hybrid combined with PBS. . . . 116
5.5 Digital conﬁguration scheme using phase switch. . . . . . . . . . . . . . . 117
5.6 Analog conﬁguration scheme using phase switch. . . . . . . . . . . . . . . 118
5.7 Digital conﬁguration scheme using standard balanced detector. . . . . . . 118
5.8 Analog conﬁguration scheme using standard balanced detector. . . . . . . 119
5.9 Analogue conﬁguration scheme for the oPLL transceiver prototype. . . . 119
5.10 OLT scheme with double ﬁber and including the birefringent polarization
switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.11 OLT scheme with double ﬁber and including the FRM based polarization
switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.1 Pure coupler splitting network scheme. . . . . . . . . . . . . . . . . . . . 126
14. 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 Upand Downstream 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 Halfduplex experimental setup. . . . . . . . . . . . . . . . . . . . . . . . 143
A.2 Low pass equivalent of the mixer’s response for a 5 GHz carrier. . . . . . 144
A.3 Sensitivity results for setup described on ﬁgure A.1 . . . . . . . . . . . . 144
A.4 Downstream power penalty at BER 10−10 due to extinction ratio. Square
points are experiments, whereas continuous line is derived from Eqs. 1 and
2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
A.5 Experimental setup for single ﬁbre fullduplex measurements. . . . . . . . 146
A.6 Electrical power spectrums after photodetection at the receiver side: (a)
before electrical ﬁltering at the ONU, (b) after electrical ﬁltering at the
ONU; (c) before electrical ﬁltering at the OLT, and (d) after electrical
ﬁltering at the OLT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A.7 Sensitivity results for the proposed OLT and ONU architectures. . . . . . 147
A.8 Scenario 1 schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
A.9 Downstream sensitivity curves for the three diﬀerent network scenarios. . 148
A.10 Upstream sensitivity curves for the three network scenarios. . . . . . . . 149
A.11 Schematic of scenario 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
A.12 Scheme for scenario 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
B.1 Scheme of the proposed analog frequency estimation loop. . . . . . . . . 152
B.2 Optical SSBmodulation VCO. . . . . . . . . . . . . . . . . . . . . . . . . 152
B.3 Frequency discriminator output vs. frequency diﬀerence between LO and
received signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
B.4 Loop delay impact on loop setting time. . . . . . . . . . . . . . . . . . . 154
B.5 Error signal variance vs. laser linewidth. . . . . . . . . . . . . . . . . . . 155
B.6 Schematic to be implemented. . . . . . . . . . . . . . . . . . . . . . . . . 155
B.7 Max hold function for the output spectrum of the optical VCO. . . . . . 156
B.8 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
C.1 Experimental setup for stability regions characterization. . . . . . . . . . 160
C.2 (a) Wavelength map: Plot of the wavelength (colour scale) in function of
reﬂector currents. (b) Logic stable regions map in function of reﬂector
currents. The phase current for a) and b) is Iph = 2.4 mA. . . . . . . . . 161
C.3 (a) Plot of the wavelength in function of the phase current. Reﬂector cur
rents are biased at Iref 1 = 22.8 mA and Iref 2 = 8.6 mA. (b, c) Wavelength
region map as a function of both reﬂector currents for a phase current of
1.8 and 2.2 mA, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 162
15. List of Figures xix
C.4 Plots of the wavelength as a function of the gain current for diﬀerent re
ﬂector currents (Iph = 2.4 mA): (a) Ir ef 1 = 10.8 mA, Iref 2 = 29 mA; (b)
Iref 1 = 12.4 mA, Iref 2 = 8.9 mA; (c) Iref 1 = 10.2 mA, Iref 2 = 11.9 mA. . 162
C.5 Experimental setup for transient response characterization. . . . . . . . . 163
C.6 (a) Stable regions map for Iph = 2.4 mA. The black points denote working
points used to measure the transition between two modes. The white lines
denote such transitions, and the number is used as experiment identiﬁer.
(b) Voltage versus time plot of the signals driving reﬂector sections for
experiment 4 (see table C.1). . . . . . . . . . . . . . . . . . . . . . . . . . 164
C.7 (Id.a) WPT plot: Plot of the wavelength versus time, and power (gray
scale) versus both wavelength and time for experiment ’Id’ (see table C.1
and/or ﬁgure C.6 (a)). (Id.b) SMSR versus time plot for experiment ’Id’
(see table C.1 and/or ﬁgure C.6 (a)). . . . . . . . . . . . . . . . . . . . . 165
C.8 (a) WPT plot: Plot of the wavelength versus time, and power (logarithmic
colour scale) versus both wavelength and time for experiment 4. (b) Main
mode and secondary mode power versus time (in logarithmic scale). . . . 166
C.9 (a) WPT plot zoom of experiment 5: Plot of the wavelength versus time,
and power (logarithmic colour scale) versus both wavelength and time. (b)
Wavelength versus time of the main and secondary modes of depicted in
(a). (c) Zoom of (b) during the transition between intermode (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 LockIN OPLL prototype. . . . . . . 173
16. List of Tables
2.1 Common modulation formats and their SNR diﬀerences. . . . . . . . . . 9
2.2 Comparison between BER values, the standard deviation of the phase error
process for 1 dB penalty at such BER, and the BERﬂoor for that standard
deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Comparison of phase estimation methods. . . . . . . . . . . . . . . . . . 44
3.1 Phase error standard deviation for the optimal conﬁgurations as a function
of linewidth and delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Convergence values for setting and rise times, at several loop delays. . . . 60
3.3 Table summarizing results at 10 ns delay. . . . . . . . . . . . . . . . . . . 64
3.4 Measured values of the local oscillator linewidth. . . . . . . . . . . . . . . 64
4.1 Fuzzy logic estimator rules base. . . . . . . . . . . . . . . . . . . . . . . . 93
5.1 Phase noise cancellation techniques summary table. The linewidth toler
ance is for a 10−3 BERﬂoor, whereas the penalty is respect to an ideal
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2 Polarization handling methods summary table. . . . . . . . . . . . . . . . 113
5.3 Transceiver architectures summary table. The linewidth tolerance is for 1
dB penalty at 10−10 BER, whereas the penalty is respect to an ideal system.120
6.1 Power budget summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B.1 Comparison between possible optical VCO approaches. . . . . . . . . . . 156
C.1 The acronyms read in ”kind of transition” column, have a brief explana
tion of the working points location: InM (Inside the same Mode); CM
(Consecutive Modes in the same supermode); NCM (NonConsecutive
modes in the same supermode); CS (Consecutive Supermodes); NCS
(NonConsecutive Supermodes); Iph (change in phase current). . . . . . 167
xxi
17. Abbreviations
ADC Analog to digital converter
AFC Automatic frequency control
ASK Amplitude shift keying
AWC Automatic wavelength control
AWG Arrayed waveguide grating
BER Bit error ratio
BPF Band pass ﬁlter
BPSK Binary phase shift keying
CO Central oﬃce
CPE Customer premises equipment
DAC Digital to analog converter
DD Direct detection
DFB Distributed feedback
DPSK Diﬀerential phase shift keying
ECL External cavity laser
ER Extinction ratio
FEC Forward error correction
FRM Faraday rotator mirror
FTTH Fiber to the home
FWHM Full width half maximum
GCSR Gratingcoupled sampled reﬂector
GPON Gigabitcapable passive optical network
I Inphase
IM Intensity modulation
LD Laser diode
LMS Least Mean Square
LPF Low pass ﬁlter
MAP Maximum a posteriori
MGY modulatedgrating Ybranch (laser)
MZI MachZehnder interferometer
xxiii
18. Abbreviations xxiv
MZM MachZehnder modulator
NRZ Non return to zero
OLT Optical line termination
ONU Optical network unit
OPLL Optical phaselocked 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 Phaselocked loop
PM Phase modulator
PON Passive optical network
PPG Pulse pattern generator
PRBS Pseudorandom 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 Subcarrier modulation
SIR Signal to interference ratio
SNR Signal to noise ratio
SOP State of polarization
SSB Single side band
TDM Time division multiplexing
UD UltraDense
VCO Voltage controled oscillator
VOA Variable optical attenuator
WDM Wavelength division multiplexing
19. Symbols
∆ν Laser linewidth
∆f Signal bandwidth
F Electronic receiver equivalent noise factor
Fa Excess noise factor
Id Photodiode dark current
k Boltzmann constant
m Modulation index
M Multiplication factor of the APD
PS Optical received power from transmitter
PLO Optical power from local
q Electron charge
Photodiode responsivity
Rb Bit rate
RL Load resistor
Rx Receiver part
T Room temperature
Tb Bit time
Tx Transmitter part
xxv
20. To my family. . .
xxvii
21. Chapter 1
Introduction
More than 40 years have passed since Charles K. Kao publicly demonstrated the pos
sibility of transmitting information through optical ﬁbers [1]. During this time, optical
networks have evolved from being an entelechy to a reality that sustains and makes possi
ble the information society in which we live. In recognition, Kao received the 2009 Nobel
prize in physics for the groundbreaking achievements concerning the transmission of light
in ﬁbers for optical communication.
Actually, the concept of optical access networks is very wide and includes many ap
proaches. One of the most popular is the socalled 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 tripleplay
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 10GEPON P802.3av and the FSAN has the NGPON1 rec
ommendation for 10 Gb/s (also named as XGPON) well advanced. In these systems, the
1
22. 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 150300 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 optoelectronics transceivers just to use a small fraction of it.
If that is considered in fast electronics (e.g. in CMOS ASICs) the power consumption is
almost proportional to the clock speed, one can infer that there is a huge power ineﬃciency
corresponding to the user bandwidth ineﬃciency; leading to a substantial global power
waste.
To reverse this tendency, it is obvious that some new philosophy has to be investigated
with the corresponding technology challenges. The answer proposed is to try to exploit
the pure WDM dimension while minimizing the electronics speed, and maintaining the
global numbers unchanged:
• Number of served users per PON (in the order of magnitude of 1000).
• Guarantied bandwidth per user. If today’s goal is to serve 100 Mb/s, a next step
in longer term it can be up to 1 Gb/s; for example current personal computers are
nowadays including a 10/100/1000 MEthernet interface, thus 1GEthernet can be
considered a very practical goal.
23. Chapter 1. Introduction 3
• Total ﬁber bandwidth (40 nm ≈ 5 THz in Cband); 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 longhaul WDM applications, but not seriously
considered to be used in access PONs. As these networks have multiple low capacity
channels, a major concern in directdetection (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 photodetected. Afterwards, signal processing (analog or digital) is applied to the
electrical signal in order to recover transmitted data. The improvements are clear, with
respect to other options:
24. Chapter 1. Introduction 4
• Allows the use of advanced modulation formats (like Phase Shift Keying  PSK, or
OFDM), while extending the reach of the networks.
• Uses electrical ﬁltering for channel selection, achieving narrow channel spacing while
maintaining high speed connection.
• Concurrent detection of light signal’s amplitude, phase and polarization recovering
more detailed information to be conveyed and extracted, thereby increasing toler
ance to network impairments (such as chromatic dispersion) and improving system
performance.
• Linear transformation of a received optical signal to an electrical signal that can
then be analyzed using modern DSP technology.
• Local laser can be tuneable, allowing colourless operation, and it can be reused as
an optical source for data transmission.
• An increase of receiver sensitivity by 15 to 20 dB compared to incoherent systems.
So, homodyne systems match perfectly the proposed network requirements, though some
issues like transceivers’ cost have to be addressed.
Summarizing, with a coherent transceiver at both sides of the access link, the capabilities
can be extended to:
• High density, enabling the connection to a high number of users (more than 1000
users per output ﬁber), meaning narrow channel spacing.
• High transmission speed, guaranteeing a minimum bandwidth of 1 Gb/s per user.
• External network totally passive, with no insertion of any type of equipment that
could include an electrical supply at the external plant (optical distribution net
work).
• High power budget, for maintaining a standard central oﬃce output power, a low
sensitivity receiver has to be implemented, reaching less than −30 dBm.
• Highest ONU bandwidth eﬃciency, with lowest electronics requirements (1 GHz
BW), serving every user with the 1G Ethernet LAN standard.
• High optical spectral eﬃciency, by minimizing the wavelength channel spacing below
5 GHz only.
• Low power consumption ONUs, reducing it in about one order of magnitude.
• Transparency and Independence among channels, in terms of coding, protocol and
bit rate, thus avoiding the complex synchronization and ranging of current PONs.
25. Chapter 1. Introduction 5
1.1 Objectives
The objective of this thesis is to evaluate and propose advanced OLT and ONU archi
tectures based on coherent systems for access network deployments. The idea is not to
restrict to the receiver architecture itself, but also evaluate the uplink and downlink per
formances of the network in order to ﬁnd the most eﬀective solution. Speciﬁcally the
objectives of the thesis are the following:
• Identify current coherent systems architectures. Perform an study of the state of the
art analyzing the main coherent technologies that are currently being investigated.
• Propose advanced architectures that overcome the limitations of the existing ones
and ﬁt with the speciﬁcations of passive optical networks.
• Evaluate some of the advanced techniques by means of simulations and experiments:
– Optical PhaseLocked Loops: Costas, Decisiondriven, Balanced subcarrier
and LockIn 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: IMDD 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 bidirectional fullduplex
2.5 Gb/s / 1.25 Gb/s in a SCM single ﬁber PON. The downstream signal is DPSK coded
and upconverted by using a 5 GHz subcarrier, while the upstream data is transmitted in
26. Chapter 1. Introduction 6
burstmode 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 proofofconcept experiments were
performed in an 8PSKRZ 30 Gb/s transmission system.
Last but not the least, through the highresolution wavelengthpowertime measurement,
the dynamic behaviour of a tunable laser (a modulatedgrating Ybranch, MGY) while
switching between modes has been also characterized. A complete report on these mea
surements can be found in appendix C. The optical spectrum at every instant and its
evolution along the tuning transient was obtained. With this, it was easy to identify, not
only the wavelength temporal drift, but also the transitory mode hopping or interferences
over other wavelength channels.
1.3 Thesis overview
All the presented objectives and concepts will be explored and analyzed in the present
document, which has been organized in 7 chapters.
In chapter 2, the most important coherent technologies, that shape the actual scene,
will be introduced. After a brief analysis of the coherent detection of BPSK and DPSK
modulation formats, optical phase locked loops will be introduced and their inﬂuence on
phase modulated signals detection will be evaluated. Next, the phase and polarization
diversity concepts will be explained as well as the main techniques used in these receivers.
Chapter 3 will put forward a new optical phase locked loop (OPLL), based in the lock
in ampliﬁcation concept. There, the inﬂuence of noise will be analyzed, jointly with
its associated penalties for a coherent receiver using phase modulated signals. Also,
comparison will be performed between this new OPLL and the schemes presented in the
state of the art.
Chapter 4 will deal with some advances proposed towards an improved and lower cost
phase/polarization diversity receiver. There new digital phase/data estimation methods
27. Chapter 1. Introduction 7
will be described, and a step forward will be taken by proposing a novel coherent receiver
type searching timeswitched phase and polarization diversities.
Chapter 5 describes a set of possible OLT and ONU designs. Special emphasis is put on
the possible transceiver architectures, aiming to use the same design at both sides, OLT
and ONU.
Chapter 6 will give an overview of standard and advanced topologies for FTTx, driven
by the concepts presented in this ﬁrst chapter and taking into account the transceivers
discussed in chapter 5. Afterwards, two case studies are presented demonstrating exper
imentally the two more promising network architectures.
Finally, the conclusions chapter will summarize the work and present future research lines
to continue developing this topic.
28. Chapter 2
State of the art
2.1 Modulation formats
The modulation format to be used in a network is strongly linked with the fact of how it
will be generated at the transmitter side, and the type of reception. As an example, a table
can be found, where SNR increments are depicted when switching from one modulation
format to another [7]. This is shown in table 2.1. In that table, the modulation format
that has better SNR performances is homodyne phase shift keying (PSK).
Heterodyne Homodyne
IMDD ASK FSK PSK ASK PSK
IMDD  10/25 dB 13/28 dB 16/31 dB 13/28 dB 19/34 dB
ASK Het. −10/−25 dB  3 dB 6 dB 3 dB 9 dB
FSK Het. −13/−28 dB −3 dB  3 dB 0 dB 6 dB
PSK Het. −16/−31 dB −6 dB −3 dB  3 dB 3 dB
ASK Hom. −13/−28 dB −3 dB 0 dB −3 dB  6 dB
PSK Hom. −19/−34 dB −9 dB −6 dB −3 dB −6 dB 
Table 2.1: Common modulation formats and their SNR diﬀerences.
In the access networks that are being deployed today, the modulation format used is
IM/DD due to its simplicity. However, its low SNR performances are a major inconvenient
when regarding an extended reach access network. That is the reason why it would be
preferable to use a more robust format, like PSK, and a coherent detection scheme.
According to table 2.1, a minimum SNR increment of 19 dB is expected when migrating
from IM/DD to a PSK with homodyne detection. Of course, it is not a ﬁxed increment,
as it also depends on the photodetector type. E.g. if a PIN diode is used, the receiver
performances in IMDD are going to be worse than when using an avalanche photodiode.
9
29. Chapter 2. State of the art 10
2.2 Homodyne systems
Nowadays, optical ﬁbre communications are, in a certain sense, as primitive as radio
communications when crystal (galena) radio receivers were used. The reason is that there
is no need to recover phase information of the optical carrier. Among all, coherent optical
transmission systems were investigated at the late 80s, but abandoned due to electronics
limitations and the irruption of the EDFA at the beginning of the 90s. Almost 20 years
after, technology is more advanced, allowing a full development of coherent systems.
Coherent systems present many advantages with respect to the conventional direct de
tection systems because of its excellent wavelength selectivity and low sensitivity. First,
in a WDM environment, when using a coherent receiver, channel selection is done after
photodetection, 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 IntensityModulation DirectDetection (IMDD) system [7].
Figure 2.1: Coherent receiver scheme, using balanced photodetection.
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
photodetected. This is shown in ﬁgure 2.1. Current after photodetection Ip (t) has all
information carried by the received optical ﬁeld.
In this chapter, a review of the synchronous detection technology is presented. Depending
on the use of an intermediate frequency stage, coherent systems can be homodyne or
heterodyne.
In a heterodyne system, incoming signal is downconverted into an intermediate frequency
(usually higher than bit rate). Afterwards, in a second stage, signal is mixed with an
electrical oscillator, now downconverting into a baseband signal. As signals are electrically
synchronized inside intermediate frequency module, it is an interesting implementation
of a synchronous receiver. Namely, it avoids the need of very narrow lasers. However,
the problems are:
• This Intermediate Frequency (IF) is very high, limiting the electronics functionality.
30. Chapter 2. State of the art 11
• The electrical spectrum is doubled, thus introducing a 3 dB penalty. This is shown
in ﬁgure 2.3.
• An additional ﬁlter should be placed in order to avoid image frequency in a multi
channel environment.
Figure 2.2: Optical spectrum of a wavelength to the user environment. λLO is the
nominal wavelength of the local oscillator, for a homodyne case.
Figure 2.3: Comparison between homodyne and heterodyne electrical spectra.
A further simpliﬁcation, at least at a ﬁrst glance, is the use of homodyne systems. In
such systems intermediate frequency is zero. This avoids image frequency problems and
the 3 dB penalty. But it needs to directly synchronize local laser and received signals,
entailing some handicaps:
• Laser phase noise impact on overall receiver performances.
• Penalty due to synchronization loop delay.
Optical homodyne systems were presented at the 80s, when one of the main investigation
ﬁelds was coherent systems. In order to properly synchronize local laser and received
signals, early systems used an optical PhaseLocked Loop (OPLL) module. But the
optical path between local laser and optical mixer (i.e. optical hybrid + photodetection
stages) introduces a nonnegligible loop delay, resulting in a signiﬁcant penalty. Thus, in
order to avoid it, extremely low linewidth lasers had to be used.
31. Chapter 2. State of the art 12
Another approach towards homodyne reception came later, with the concept of zero
IF/intradyne diversity receivers. The main goal of these type of receivers is to replace
the feedback loop (OPLL) by a feedforward processing. So, phase locking is done inside
this feedforward processing.
2.3 PSK receivers
As shown in the introduction, the main core of a coherent system is the receiver. This
subsystem, properly combined with a robust modulation format, improves the optical
link as commented.
This section is organized as follows: First, homodyne receivers are introduced and ba
sic results are summarized. Next OPLLs are introduced and the existing approaches
developed are explained. Finally, optical diversity techniques are discussed.
2.3.1 Homodyne receiver performances
In this subsection the basic results of an ideal homodyne receiver will be surveyed. First
using Binary PSK modulation and afterwards using diﬀerential encoded PSK. Also the
phase errors inﬂuence (mainly due to laser phase noise) will be theoretically evaluated
for both cases. These modulation formats have been chosen because of their simplicity,
robustness and high performances, as seen in table 2.1.
A generic homodyne receiver can be shown in ﬁgure 2.4, for a balanced structure.
Figure 2.4: Generic homodyne receiver.
From that scheme, the following set of equations can be written [8]:
eS (t) = PS exp j ω0 t + φS (t) (2.1)
eLO (t) = PLO exp j ω0 t + φLO (t) (2.2)
32. Chapter 2. State of the art 13
where eS (t) and eLO (t) are the optical ﬁeld expressions for the received and local oscil
lator signals respectively; φS (t) and φLO (t) are the received and local oscillator phases
respectively; and ω0 t is the nominal wavelength (assuming no mismatch).
Also the complex amplitudes of both signals can be deﬁned as:
ES (t) = PS ejφS (t) (2.3)
jφLO (t)
ELO (t) = PLO e (2.4)
By agreement the optical coupler is assumed to have the following transfer matrix:
1 1 1
S=√ (2.5)
2 1 −1
As the optical combining device is a standard coupler and ideally there is no wavelength
mismatch, the resulting currents I1 (t), I2 (t) at the output of each photodetector can be
expressed as:
2
1
I1 (t) = ES (t) + ELO (t) (2.6)
2
= (PS + PLO ) + PS PLO cos φS (t) − φLO (t) (2.7)
2
2
1
I2 (t) = − ES (t) + ELO (t) (2.8)
2
= (PS + PLO ) − PS PLO cos φS (t) − φLO (t) (2.9)
2
being the responsivity of the photodiode.
Then, the resulting current after the balanced receiver Ip (t) can be written as:
Ip (t) = I1 (t) − I2 (t) (2.10)
= 2 PS PLO cos φS (t) − φLO (t) (2.11)
The signal amplitude at regeneration is highly dependant on the phase mismatch φS (t) −
φLO (t) that must be minimized. The most used module to do so is the OPLL. The
ﬂuctuation phase error mainly comes from the lasers phase noise.
33. Chapter 2. State of the art 14
2.3.1.1 SNR and BER for BPSK signals
One of the most important advantages of homodyne PSK systems is the increase in
receiver sensitivity. For BPSK, the bits are coded into two symbols: 0 and 180. Thus,
Inphase 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
(Inphase) 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 lowpass ﬁltered by a matched ﬁlter [9] and, next, it enters at the decision
and sampling stage. Thus, the bit decision is made upon Ip (t) once ﬁltered. By now,
it can be only assumed that the receiver current ﬂuctuates because of photodetector’s
shot noise (in case a PIN diode is used) and thermal noise. The variance of those current
ﬂuctuations is obtained by adding the two contributions [10]:
σ 2 = σS + σT
2 2
(2.12)
2
σS = 2q (PS + PLO ) + ID BE (2.13)
2 4kB T
σT = FN BE (2.14)
RL
where ID is the dark current of the photodiode (almost negligible), q is the electron
charge, BE is the most limiting electrical bandwidth, kB is the Boltzmann’s constant,
T is the temperature in K, FN is the noise ﬁgure of the electrical stage, and RL is the
impedance of the electrical part.
34. Chapter 2. State of the art 15
From this model, the SNR can be calculated when φS (t)−φLO (t) = 0 dividing the average
signal power by the average noise power:
I 2
SNR = (2.15)
σ2
2
4 PS PLO
= (2.16)
4kB T
2q (PS + PLO ) + ID BE + RL
FN BE
Assuming the symbols are equiprobable, the bit error probability Pe can be calculated
as:
1
Pe = [P (0◦ 180◦ ) + P (180◦ 0◦ )] (2.17)
2
where P (0◦ 180◦ ) is the probability of deciding 0◦ when 180◦ is received, and P (180◦ 0◦ )
is the probability of deciding 180◦ when 0◦ is received.
As shown in ﬁgure 2.5, the only change between 0◦ and 180◦ is the sign along the real
axis, whereas the modulus remains constant. Thus, the optimum decision threshold is
going to be 0 [10]. Simplifying the development and assuming Gaussian statistics, the
conditioned probabilities can be written as [9]:
0
1 SNR
P (0◦ 180◦ ) = √ exp − dI (2.18)
σ 2π −∞ 2
∞
◦ ◦ 1 SNR
P (180 0 ) = √ exp dI (2.19)
σ 2π 0 2
and they can be expressed in terms of the complementary error function (erfc):
1 SN R
P (0◦ 180◦ ) = P (180◦ 0◦ ) = erfc (2.20)
2 2
So, the bit error probability Pe can be calculated as [10]:
1 SNR
Pe = erfc (2.21)
2 2
Figure 2.6 shows how the error probability varies with the SNR. Usually, the receiver
sensitivity corresponds to the average optical power for which SNR = 15.6 dB, being
Pe = 10−9 . Another SNR useful value is 9.8, that corresponds to a Pe = 10−3 because
if Forward Error Correction (FEC) codes are used, errors can be corrected after data
decision, and this 10−3 can be turned on to 10−9 or lower [11].
35. Chapter 2. State of the art 16
Figure 2.6: Bit error probabilities for BPSK and DPSK, as a function of SNR.
2.3.1.2 Phase errors in homodyne detection of BPSK signals
In this subsubsection the phase noise inﬂuences on the BPSK ideal receiver are going to
be evaluated. It is assumed that there is a phase tracking and/or estimation/cancellation
in order to keep the phase errors suﬃciently small. To start such analysis, the received
photocurrent has to be redeﬁned as:
Ip (t) = 2 PS PLO cos φd (t) + φe (t) (2.22)
φS (t) = φd (t) + φN S (t) (2.23)
φLO (t) = φN LO (t) (2.24)
φe (t) = φN S (t) − φN LO (t) (2.25)
where φN S (t) and φN LO (t) are the noise contributions to the phases of the received and
local oscillator signals respectively, and φd (t) is a signal containing data ideal pulses
(0◦ 180◦ ).
Obviously, the phase error term (φe (t)) is modeled as a random variable. For the BPSK
case, its statistical properties depend on the phase tracking method. Previously, the error
probability has been found in terms of SNR. The expression used assumes a perfect phase
match, but usually there is a certain amount of phase error. As there is a phase tracking,
it can be assumed that φe (t) varies at a speed much lower than data. i.e. it remains
constant during the symbol interval [12]. In this case, the conditional error probability
in terms of the sampled phase error φe is:
1 SNR
Pe (φe ) = erfc cos(φe ) (2.26)
2 2
36. Chapter 2. State of the art 17
whereas the average error probability is written as:
π
1 SNR
Pe = p(φe )erfc cos(φe ) dφe (2.27)
2 −π 2
being p(φe ) the probability density function of the phase error. The statistic of the phase
is usually approximated by a Gaussian distribution with zero mean. In this case the
average error probability becomes:
π φ2e
1 −
2σ 2 SNR
Pe = e φe erfc cos(φe ) dφe (2.28)
2
2 2πσφe −π 2
In ﬁgure 2.7 the error probability is plotted versus the SNR for several phase error stan
dard deviation values. As can be seen, the fact of having a phase error deviation diﬀerent
from zero gives an error ﬂoor, i.e., the error probability limit is a ﬁnite value. A useful
example can be that the standard deviation of phase error must be less than 10◦ in order
to maintain less than 0.5 dB power penalty at 10−9 BER.
Figure 2.7: BPSK error probability for diﬀerent phase error standard deviations.
In the limit case of inﬁnite SNR, equation 2.28 gives the ﬂoor value of the probability of
error. It only depends on the variance of the phase error, and gives the limit value. After
37. Chapter 2. State of the art 18
some algebra, such ﬂoor is found to be [13]:
φ2e +∞ − φ2e
1 −
2σ 2 2 2σ 2
Pe = e φe dφe = e φe dφe (2.29)
2 2 π
2πσφe cosφe <0 2πσφe 2
Evaluating this integral, the BERﬂoor 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: BERﬂoor as a function of φe standard deviation.
BER Standard deviation for 1 dB penalty BERﬂoor equivalent
10−9 11◦ 2.31 · 10−16
10−3 19◦ 2.04 · 10−6
4.86 · 10−6 14.9◦ 10−9
2.54 · 10−1 28◦ 10−3
Table 2.2: Comparison between BER values, the standard deviation of the phase error
process for 1 dB penalty at such BER, and the BERﬂoor for that standard deviation.
This BERﬂoor 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 BERﬂoor of 2.31 · 10−16 .
38. Chapter 2. State of the art 19
2.3.1.3 SNR and BER for DPSK signals
In the case of diﬀerentially encoded PSK signals, the coherent detector becomes slightly
diﬀerent, as shown in ﬁgure 2.9. In some books it is referred as diﬀerentially coherent
detector [12]. Special emphasis must be put on the multiplier used, as it should be a four
quadrant multiplier. Also, the local oscillator does not have to be tracking the received
signal phase, since this kind of detection is more robust against phase mismatch.
Figure 2.9: Generic homodyne receiver including a diﬀerential decoder.
As now the receiver frontend is the same as used in the previous subsection, the SNR
expression is the same of equation 2.16. Nevertheless in this case the inputs to the
multiplier during the kth bit interval are:
Ip (t) + n(t) = [I + Ini (t)] cos(φd (t) − φe (t)) − Inq (t) sin(φe (t)) (2.30)
Ip (t−Tb )+n(t−Tb ) = [I +Ini (t)] cos(φd (t−Tb )−φe (t−Tb ))−Inq (t) sin(φe (t−Tb )) (2.31)
The lowpass ﬁlter then removes the highfrequency terms from the product, leaving at
the input of the decision circuit the decision variable amplitude Y . In case the phase
error diﬀerence between consecutive symbols is negligible (φe (t) ≈ φe (t − Tb )), Y can be
written as:
1 1
Y = (I + Ini )(I + Ini ) + Inq Inq = (α2 − β 2 ) (2.32)
2 2
where all four noise components are independent identically distributed Gaussian random
variables with zero mean and variance 2σ 2 . α2 and β 2 variables can be expressed as:
α2 = (I + αi )2 + αq
2
(2.33)
2
β = βi2 + 2
βq (2.34)
39. Chapter 2. State of the art 20
with
1
αi = (Ini + Ini ) (2.35)
2
1
αq = (Inq + Inq ) (2.36)
2
1
βi = (Ini − Ini ) (2.37)
2
1
βq = (Inq − Inq ) (2.38)
2
Note that αi , αq , βi , βq are zeromean Gaussian random variables with variance σ 2 . There
fore, α has a Rician probability density function, whereas β has a Rayleigh probability
density function [14].
The average probability of error is found to be when Y < 0, in the case that the consec
utive symbols (ak , ak−1 ) are equal:
Pe = P (Y < 0ak = ak−1 ) = P (α2 < β 2 ) = P (β > α) (2.39)
So, it can be calculated in a more direct form as:
∞ ∞
Pe = pα (α)pβ (β)dαdβ (2.40)
0 α
where pα (α) and pβ (β) are the probability density functions of α and β respectively.
Calculating the inner integral (β), the probability of error becomes:
∞
α 2α2 + I 2 2Iα
Pe = exp I0 dα (2.41)
0 σ2 σ2 σ2
√ √
So, making a change of variables by letting λ = 2α and ν = I/ 2:
∞
1 −I 2 λ λ2 + ν 2 λν
Pe = exp exp I0 dλ (2.42)
2 2σ 2 0 σ2 2σ 2 σ2
Now, the integrand is exactly the same function as the Rician probability function, with
a total area equal to unity. Hence, the ﬁnal result becomes:
1 −I 2 1 −SNR
Pe = exp = exp (2.43)
2 2σ 2 2 2
Just for comparing both signaling cases, ﬁgure 2.6 shows the two error probabilities
(BPSK and DPSK) as a function of SNR. Even for a Gaussian noise assumption, they
40. Chapter 2. State of the art 21
exhibit diﬀerent statistics when calculating Pe . Nevertheless, note that at 10−9 the dif
ference between them is of only 0.5 dB.
2.3.1.4 Phase errors in homodyne detection of DPSK signals
Just following what has been shown for the BPSK case, the expression reported in equa
tion 2.22 can also be used. For the DPSK case, φe statistical properties depend on the
phase noise source. If it is only coming from the lasers’ phase noise, it can be assumed
that φe (t) varies at a speed much lower than data. i.e. it remains constant during the
symbol interval. Please, remember that phase noise is always of the order of MHz, while
data is supposed to be of the order of Gb/s (3 orders of magnitude diﬀerence). In this
case, the conditional error probability in terms of phase error is:
1 −SNR
Pe (θ) = exp cos2 (θ) (2.44)
2 2
where θ = φe (t0 ) − φe (t0 − Tb ), being t0 the optimum sampling time. So, now the average
error probability can be written as:
π
1 −SNR
Pe = p(θ) exp cos2 (θ) dθ (2.45)
2 −π 2
Regarding θ statistics, the laser phase noise is modeled as a Wiener process [10]:
t
φe (t) = φP N (τ )dτ (2.46)
0
where φP N (t) is a white Gaussian process with variance 2π∆ν, where ∆ν is the total laser
spectral width (also known as Full Width Half Maximum  FWHM). Thus, assuming
Tb t0 :
θ = φe (t0 ) − φe (t0 − Tb ) (2.47)
t0 t0 −Tb
= φP N (τ )dτ − φP N (τ )dτ (2.48)
0 0
Tb
= φP N (τ )dτ (2.49)
0
2
This means that θ is also a Gaussian process [14] with zero mean and variance σθ =
2π∆νTb .
41. Chapter 2. State of the art 22
Continuing the mathematical development, the average error probability becomes:
π θ2
1 −
2σ 2
−SNR
Pe = e θ exp cos2 (θ) dθ (2.50)
2
2 2πσθ −π 2
Please note that this expression is almost the same that has been found in the previous
subsection (equation 2.28). Thus, ﬁgure 2.7 is also valid for the DPSK case, except that
now the phase error standard deviation is known. The 0.5 dB penalty point found before
(10◦ phase error standard deviation), now means that Rb = 1/Tb should be higher than
π∆ν/50.
Similarly to what was shown before, in the limit case of inﬁnite SNR, equation 2.50 gives
the ﬂoor value of the probability of error. Thus, equation 2.29 also gives the BERﬂoor
values for DPSK case.
2.3.2 oPLL based systems
A phase locked loop is a feedback system in which the feedback signal is used to lock the
output frequency and phase of the input signal.
Phase locked loops in electrical domain have been one of the most frequently used com
munications circuits. Several applications like ﬁltering, frequency synthesis, motor speed
control, signal detection, etc. are common users of such device.
While electrical PLL (used in heterodyne systems) is a well known device, optical version
(used in homodyne systems) oﬀers several technological problems which have delayed its
development to the general market. Next ﬁgure 2.10 shows the basic components for
a simpliﬁed OPLL when no noise inﬂuence is considered. The three basic elements are
the phase comparator, the electrical ﬁlter and the VCO module. In our case, the phase
comparator is comprised by the optical coupler and the photodetection front end, while
the VCO module is a tunable laser.
After ﬁltering DC terms and high frequency terms at the output of phase comparator,
the signal remaining is:
V (t) = GP C PS sin(φe (t)) (2.51)
√
where phase error is deﬁned as φe (t) = φS (t) − φLO (t), and GP C = RL PLO
This leads to the wellknown PLL characteristic equation:
+∞
dφe (t) dφS (t) dφLO (t) dφS (t)
= − = − AG sin φe (τ ) f (t − τ )dτ (2.52)
dt dt dt dt −∞
42. Chapter 2. State of the art 23
Figure 2.10: Optical Phase Locked Loop simpliﬁed scheme
√
where A = PS ; G = GV CO GP C , f (t) is the loop ﬁlter transfer function, and GV CO is
the VCO gain in [rad/sV].
Although the PLL is not linear because the phase detector is nonlinear, it can be accu
rately modelled as a linear device when the phase diﬀerence between the phasedetector
input signals is small. For the linear analysis, it is assumed that the phase detector output
is a voltage which is a linear function of the diﬀerence in phase between its inputs. This
oﬀers an easy way to study its behaviour by means of Laplace transformation, being the
OPLL transfer function:
ΦLO (S) AGF (S)
H(S) = = (2.53)
ΦS (S) S + AGF (S)
A ProportionalIntegral (PI) ﬁlter is usually used to act as a PLL regulator. Then F (S)
is:
1 + τ2 S
F (S) = (2.54)
τ1 S
and the OPLL transfer function becomes:
2
2ξωn S + ωn
H(S) = (2.55)
S 2 + 2ξS + ωn2
Being ωn = AG/τ1 the natural frequency of the PLL and ξ = ωn τ2 /2 the loop damping
coeﬃcient.
2.3.2.1 Additive noise impact in a generic OPLL
Phase Locked Loop’s target is to match input signal phase. However this objective can
be limited by several parameters which aﬀect the receiver performance. Additive noise
43. Chapter 2. State of the art 24
can interfere in the phase locked loop behaviour. In fact this noise produces an additional
phase error that reduces the system’s functionality.
In order to show a simpliﬁed model, a unique additive noise source (VN (t)) has been
considered, added after the phase comparator module, and coming from the input shot
noise plus electronic noise. Thus, the resulting characteristic equation for this case, in
the Laplace domain, is found to be [15]:
SΦS (S) GV CO VN (S)F (S)
Φe (S) = − (2.56)
S + AGF (S) S + AGF (S)
The noise transfer function can be deﬁned as follows:
ΦLO (S) Φe (S) GV CO F (S) H(S)
AS (S) = =− =− =− (2.57)
VN (S) ΦS (S)=0 VN (S) ΦS (S)=0 S + AGF (S) AGP C
The phase error is given by the contribution of the signal and the contribution of shot
noise. In steady state the characteristic equation is linear and the superposition principle
can be applied. Then, Φe (S) can be decomposed into two contributions (signal and noise):
Φe (S) = ΦeS (S) + ΦeN (S) (2.58)
where
H(S) GV CO F (S)
ΦeN (S) = VN (S)AS (S) = −VN (S) = −VN (S) (2.59)
AGP C S + AGF (S)
The interesting parameter is the phase error variance. Assuming φeN (t) is a white Gaus
sian process, and that VN (t) has as a power spectrum density SAN (ω):
2
σAN = φ2 (t)
eN (2.60)
+∞
dω
= SAN (ω)AS (ω)2 (2.61)
−∞ 2π
+∞
1 dω
= 2 G2
SAN (ω)H(ω)2 (2.62)
A PC −∞ 2π
1 BN
= (2.63)
SNR Be
+∞
where the noise equivalent bandwidth of the PLL has been deﬁned as BN = −∞
H(ω)2 dω ,
2π
and Be is the electrical input bandwidth (typically 0.7 · Rb ).
44. Chapter 2. State of the art 25
For the case of a ﬁrst order loop ﬁlter BN can be calculated as [15]
ωn 1
BN = ξ+ 2 (2.64)
2 4ξ
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:
Φe (S) = ΦeD (S) + ΦeN (S) (2.65)
ΦeN (S) = ΦN (S)AΦ (S) (2.66)
ΦN (S)
= (2.67)
S + AGF (S)
= ΦN (S) 1 − H(S) (2.68)
+∞
2 dω
σP N = SP N (ω)AΦ 2 (2.69)
−∞ 2π
+∞
dω
= SP N (ω)1 − H(ω)2 (2.70)
−∞ 2π
= 2π∆νBP N (2.71)
where SP N = 2π∆ν/ω 2 is the phase noise baseband equivalent power spectrum density
2
+∞ 1−H(ω) dω
(PSD) with lorentzian shape, and BP N = −∞ ω 2π
For the case of a ﬁrst order loop ﬁlter, shown in equation 2.55, BP N can be easily inte
grated leading to:
1
BP N = (2.72)
2ξωn
45. Chapter 2. State of the art 26
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 lowpass, the PLL bandwidth for phase noise is highpass; 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: Isocurves 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:
AGF (S)e−τ S
H(S) = (2.73)
S + AGF (S)e−τ S
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
46. Chapter 2. State of the art 27
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 ωm
have 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−τ S . 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,
12 + 6τ S + (τ S)2
e−τ S = (2.74)
12 − 6τ S + (τ S)2
thus, phase and additive noises can be calculated as
2 1
σAN τ = ·
x+1
144 + 36xy 2 + 72xy + 144x − x2 y 4 − 48x2 y 2 + 72x2 y − x3 y 4 + 6x3 y 3 − 12x3 y 2 2
· σAN
144 − 144y − 12xy 3 + 36xy 2 − 72xy − x2 y 4 + 6x2 y 3 − 12x2 y 2
(2.75)
47. Chapter 2. State of the art 28
2 144 − 36x2 + 72xy − x2 y 4 + 6x2 y 3 − 12x2 y 2
σP N τ = σ2 (2.76)
144 − 144y − 12xy 3 + 36xy 2 − 72xy − x2 y 4 + 6x2 y 3 − 12x2 y 2 P N
√ √
where ξ = x/2 and ωn τ = 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
2
1 ns loop delay (equivalent to 20 cm of optical ﬁber). For the σAN the bitrate assumed
was 1 Gb/s. Results are shown in ﬁgure 2.13. From these results, without a loop delay,
2 2
σP N and σAN 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: Isocurves of the variance of additive noise and phase noise, all for ξ = 2.
(ab) are for a null loop delay, whereas (cd) 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.
48. Chapter 2. State of the art 29
The ﬁrst speciﬁc implementation is based on CostasLoop design. The receiver extracts
both Inphase 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 Inphase
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:
√ √
E1 1−k √k
√
E2 ¯ ¯
1 1−k
√ − k
ES
Eo = = S · EI = √ √ ·
(2.77)
E3 2 √k j 1−k ELO
√
E4 k −j 1 − k
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) = RL E1 (t)E1 (t)
1
= RL (1 − k)PS + kPL O + 2d k(1 − k)PS PLO cos φe (t) (2.78)
2
∗
V2 (t) = RL E2 (t)E2 (t)
1
= RL (1 − k)PS + kPL O − 2d k(1 − k)PS PLO cos φe (t) (2.79)
2
49. Chapter 2. State of the art 30
∗
V3 (t) = RL E3 (t)E3 (t)
1
= RL (1 − k)PS + kPL O − 2d k(1 − k)PS PLO sin φe (t) (2.80)
2
∗
V4 (t) = RL E4 (t)E4 (t)
1
= RL (1 − k)PS + kPL O − 2d k(1 − k)PS PLO sin φe (t) (2.81)
2
VI (t) = V1 (t) − V2 (t)
= 2 RL d k(1 − k)PS PLO cos φe (t) (2.82)
VQ (t) = V3 (t) − V4 (t)
= 2 RL d k(1 − k)PS PLO sin φe (t) (2.83)
Vm (t) = VI (t) · VQ (t)
2 2
= 2 RL k(1 − k)PS PLO 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)
2 2
Vm (t) = RL PS PLO φe (t) (2.85)
So, the loop can be linearized, leading to equation 2.53, but with some changes: A should
2
be substituted by PS , and GP C by RL PS PLO .
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 IQ 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 DecisionDriven OPLL (DDOPLL)
In this case, the ﬁrst phase comparator is the wellknown DecisionDriven OPLL (DD
OPLL). This is better than CostasLoop 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
50. Chapter 2. State of the art 31
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) + φN S (t) (2.88)
0 d=1
φD (t) = (2.89)
π d = −1
Here φN S (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) + φN LO (t) (2.92)
51. Chapter 2. State of the art 32
being φC (t) the phase introduced by the local loop, and φN LO (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) = GP C PS d sin φN (t) − φC (t) + n1 (t) (2.93)
V2 (t) = GP C PS d cos φN (t) − φC (t) + n2 (t) (2.94)
where the overall phase noise process is φN (t) = φN S (t) + φN LO (t), the shot noise (pho
√
todetection and receiver parts) is characterized by n1,2 (t), and GP C = RL PLO .
As said before, it can be seen in ﬁgure 2.15 that the DecisionDriven 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 ) = dGP C PS d sin φN (t) − φC (t) + dn1 (t) (2.95)
m(t) = GP C 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) = GP C PS φN (t) − φC (t) + n1 (t) (2.98)
Thus the same phasedetection 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
Inphase (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.
52. Chapter 2. State of the art 33
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:
eS (t) = PS exp(j(ωt + φS (t))) (2.99)
ES (t) = PS exp(jφS (t)) (2.100)
φS (t) = φD (t) + φN S (t) (2.101)
eLO (t) = PLO exp(j(ωt + φLO (t))) (2.102)
ELO (t) = PLO exp(jφLO (t)) (2.103)
φLO (t) = φC (t) + φN LO (t) (2.104)
π
φD (t) = + ϕd(t) (2.105)
2
φe (t) = φN S (t) − φN LO (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.
53. Chapter 2. State of the art 34
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:
1 1 1 ES
Eo = √ · (2.107)
2 1 −1 ELO
So, the equations for the photodetected signals are:
1
V1 (t) = RL PS + PLO + 2 PS PLO cos φS (t) − φLO (t) (2.108)
2
1
V2 (t) = RL PS + PLO − 2 PS PLO cos φS (t) − φLO (t) (2.109)
2
Next, V3 (t) can be calculated, and properly rewritten as:
V3 (t) = 2 RL PS PLO cos φS (t) − φLO (t)
π
= 2 RL PS PLO cos + ϕd(t) + φN S (t) − φC (t) + φN LO (t)
2
= 2 RL PS PLO sin ϕd(t) + φN S (t) − φC (t) − φN LO (t) (2.110)
54. Chapter 2. State of the art 35
If V3 (t) is expanded by using trigonometric identities:
V3 (t) = 2 RL PS PLO sin(ϕ)d(t) cos φN S (t) − φC (t) − φN LO (t) +
+ 2 RL PS PLO cos(ϕ)d(t) sin φN S (t) − φC (t) − φN LO (t)
(2.111)
where the phase error term can be easily identiﬁed as φe (t) = φN S (t) − φN LO (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 PS PLO sin(ϕ)d(t) + RL PS PLO 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]:
2 2π∆ν ωn (4ξ 2 + 1) q ωn (4ξ 2 + 1)
σN = + 2Tb tan2 (ϕ) + (2.113)
2ξωn 8ξ 2 PS cos2 (ϕ) 8ξ
2
As an example, the noise variance σN 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.
55. Chapter 2. State of the art 36
Figure 2.18: Noise variance for the balanced PLL scheme.
2.3.2.7 Subcarrier modulated OPLL (SCMOPLL)
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 MachZehnder
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 DecisionDriven 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 phaselocked
loop.
56. Chapter 2. State of the art 37
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(ωS t + φS (t))) (2.114)
φS (t) = φD (t) + φN S (t) (2.115)
eLO (t) = PLO exp(j(ωLO t + φLO (t))) (2.116)
π π
φLO (t) = φC (t) + φN LO (t) + + cos(ωc t) (2.117)
2 2
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 ·
π π
· sin ωS t + φD (t) + φN S (t) − ωLO t − φC (t) − φN LO (t) − − cos(ωc t)
2 2
= RL PLO PS ·
· sin ωS t + φN S (t) − ωLO t − φC (t) − φN LO (t) cos(ωc t)
1
= RL PLO PS ·
2
· sin φN S (t) − φC (t) − φN LO (t) + sin 2ωc tφN S (t) − φC (t) − φN LO (t)
(2.119)
Assuming ωc big enough, this signal can be lowpass ﬁltered. Also, the phase error can
be identiﬁed as φe (t) = φN S (t) − φN LO (t) − φC (t), and rewrite the expression as:
1
e(t) = RL PLO PS sin φe (t) (2.120)
2
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:
1
GP C = RL PLO (2.121)
2
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 higspeed 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
57. Chapter 2. State of the art 38
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 freerunning laser is placed at the LO side.
Figure 2.20: Scheme of a phase diversity front end.
In the postprocessing 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, InPhase 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 frontend 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 frontend becomes much complex. It is shown in ﬁgure 2.21.
Once seen the frontend 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 frontend. It was ﬁrst analyzed and
58. Chapter 2. State of the art 39
Figure 2.21: Schematic of phase and polarization diverse receiver.
Figure 2.22: Scheme of a DPSK detection, in a phase and polarization diversity
homodyne 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 frontend, a diﬀerential detector (delay and multiply) is placed.
Next, all signals coming from this detectors are added.
59. Chapter 2. State of the art 40
Given eS (t) the received signal optical ﬁeld, and eLO (t) the local oscillator optical ﬁeld,
for this receiver:
eS (t) = PS (cos(ϕ)ˆ + sin(ϕ)e−jθ y ) exp jω0 t + φS (t)
x ˆ (2.122)
eLO (t) = PLO (ˆ + y ) exp jω0 t + φLO (t)
x ˆ (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
ˆ ˆ
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 PS PLO 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:
C2
VHIo (t) = d(t) cos2 (ϕ) cos φe (t) cos φe (t − Tb ) (2.129)
2
C2
= d(t) cos2 (ϕ) cos φe (t) − φe (t − Tb ) + cos φe (t) + φe (t − Tb )
2
C2
VV Io (t) = d(t) sin2 (ϕ) cos φe (t) + θ cos φe (t − Tb ) + θ (2.130)
2
C2
= d(t) sin2 (ϕ) cos φe (t) − φe (t − Tb )) + cos φe (t) + φe (t − Tb ) + 2θ
2
C2
VHQo (t) = d(t) cos2 (ϕ) sin φe (t) sin φe (t − Tb ) (2.131)
2
C2
= d(t) cos2 (ϕ) cos φe (t) − φe (t − Tb ) − cos φe (t) + φe (t − Tb )
2
60. Chapter 2. State of the art 41
C2
VV Qo (t) = d(t) sin2 (ϕ) sin φe (t) + θ sin φe (t − Tb ) + θ (2.132)
2
C2
= d(t) sin2 (ϕ) cos φe (t) − φe (t) − cos φe (t) + φe (t − Tb ) + 2θ
2
thus, given Vo (t) = VHIo (t) + VV Io (t) + VHQo (t) + VV Qo (t), and after some algebra:
C2
Vo (t) = d(t)cos φe (t) − φe (t − Tb ) (2.133)
2
Now, identifying terms from the values calculated, it is easy to see that:
4 PS PLO
SNR = 4kB T
(2.134)
2q (PS + PLO ) + ID BE + RL
FN BE
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 polyphase
signals are mainly intended for core networks and longhaul 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 frontend 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 wellknown linear prediction techniques
by employing a Wiener ﬁlter design. This was done in [26], with very good results.
61. Chapter 2. State of the art 42
A Lorentzianshaped laser tone contains phase noise, such that, once digitized:
φ(n) = φ(n − 1) + w(n) (2.136)
2
where w(n) is a zeromean Gaussian noise sequence, having a variance of σw = 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
2
σp ). In order to remove the data modulation r(n) is raised to the M th power:
s(n) = rM (n) = exp jM φ(n) + M p (n) exp jM φ(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) + Im{p (n)} (2.139)
ˆ
Then, the problem of ﬁnding the best estimate of φ(n) (φ(n)) can be stated as Wiener
ﬁlter problem:
ˆ 1 ˆ
φ(n) = θ(n) (2.140)
M
The Wiener ﬁlter can be easily calculated, and, in terms of Ztransform it is [26]:
ˆ
θ(z) = H(z)θ(z) (2.141)
D
1−α
= αD + (1 − α) αD−k z −k θ(z) (2.142)
1 − αz −1 k=1
where D is the lag number of symbols, and
M 2 σw + 2σp − M σw
2 2
M 2 σw + 4σp
2 2
α= 2
2σp
For the particular case of the Wiener ﬁlter, the error of the estimator can be easily
calculated and found to be:
ˆ
e(z) = θ(z) − θ(z) = θ(z) 1 − H(z) (2.143)
62. Chapter 2. State of the art 43
Thus, the transfer function of the error can be written as:
e(z)
He (z) = = 1 − H(z) (2.144)
θ(z)
and the LMS error of this estimator can be calculated [14]:
π
2 1
E{e (n)} = He (ejω )2 θ(ejω )dω (2.145)
2π −π
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 nonoptimal 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,
63. Chapter 2. State of the art 44
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) BER
Wiener 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 estimated
from Q factor and assuming Gaussian statistics.
2.3.3.3 Mpower 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 signals
based in regenerative frequency dividers.
After the ADCs, the resulting digitized signal rH,V is raised to the M th 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 lowpass ﬁlter is placed in order to eliminate the broadband noise
and high frequency harmonics generated when raising to the M th power. Afterwards,
64. Chapter 2. State of the art 45
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 phasealigned frequencymultiplied carrier signals of both branches
are added before being passed through the lowpass 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 BERﬂoor of 10−3 .
2.3.3.4 ViterbiViterbi 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 polyphase optical signals and MQAM data.
In this case, the received complex samples r(n) are ﬁrst raised to the M th power to
remove the Mary phase modulation. To more accurately estimate the phase error out
of the shotnoise, 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:
N
1
θ(n) = arg rM (k) (2.146)
M k=1
To combat the arising Mary 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.
65. Chapter 2. State of the art 46
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 phaselocked loop concept has been introduced as a ﬁrst solution, some
wellknown 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. Mpower law phase estimation with regenerative frequency dividers
4. ViterbiViterbi 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 ViterbiViterbi 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.
66. Chapter 3
LockIn 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 LockIn 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 LockIn 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
67. Chapter 3. LockIn 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 phaselocked loop model scheme is depicted in ﬁgure 3.2. It is a homodyne balanced
receiver with a ProportionalIntegral (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:
eS (t) = PS exp(j(ωt + φS (t))) (3.1)
ES (t) = PS exp(jφS (t)) (3.2)
φS (t) = φD (t) + φN S (t) (3.3)
eLO (t) = PLO exp(j(ωt + φLO (t))) (3.4)
ELO (t) = PLO exp(jφLO (t)) (3.5)
AKV CO
φLO (t) = φC (t) + φN LO (t) + sin(ωc t) (3.6)
ωc
AKV CO
φLO (t) = φT LO (t) + sin(ωc t) (3.7)
ωc
68. Chapter 3. LockIn ampliﬁer OPLL architecture 49
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, φN S (t) is the transmitter laser phase noise, φN LO (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: LockIn 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:
1
V1 (t) = RL PS + PLO − 2 PS PLO cos(φS (t) − φLO (t)) (3.8)
2
1
V2 (t) = RL PS + PLO + 2 PS PLO cos(φS (t) − φLO (t)) (3.9)
2
So the output signal is:
V3 (t) = V2 (t) − V1 (t) (3.10)
AKV CO
= 2 RL PS PLO cos φS − φT LO (t) + sin(ωc t) (3.11)
ωc
= 2 RL PS PLO · η (3.12)
AKV CO
being η = cos φS − φT LO (t) + ωc
sin(ωc t) .
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
69. Chapter 3. LockIn ampliﬁer OPLL architecture 50
related to the sum of arguments:
AKV CO
η = cos φS (t) − φT LO (t) cos sin(ωc t) −
ωc
AKV CO
− sin φS (t) − φT LO (t) sin sin(ωc t) (3.13)
ωc
The term AKωcCO is the dithering amplitude, and it is a parameter to be designed and
V
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 AKωcCO
V
1.
In this case, sine and cosine terms containing the dithering amplitude can be expanded in
TaylorMcLaurin series and truncated after the ﬁrst and second term respectively. Hence,
η can be rewritten as:
η =
A2 KV CO
2
cos φS (t) − φT LO (t) 1− 2
+ (3.14)
4ωc
A2 KV CO
2
+ 2
cos φS (t) − φT LO (t) cos(2ωc t) + (3.15)
4ωc
AKV CO
+ sin φS (t) − φT LO (t) sin(ωc t) (3.16)
ωc
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
3.14 3.16 3.15

ωc 2ωc ω
Figure 3.3: Spectral distribution of the terms 3.14, 3.15, and 3.16.
70. Chapter 3. LockIn ampliﬁer OPLL architecture 51
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 bandpass ﬁlter hf 1 (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 PS PLO · η ∗ hf 1 (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 PS PLO · γ (3.18)
where
AKV CO
γ = η ∗ hf 1 (t) = sin φS (t) − φT LO (t) sin(ωc t) (3.19)
ωc
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 hf 2 (t), a low pass
ﬁlter with square ideal response, giving V6 (t):
V6 (t) = [V4 (t) · V5 (t)] ∗ hf 2 (t) (3.20)
= [2 RL PS PLO · γ · A sin(ωc t)] ∗ hf 2 (t) (3.21)
√
RL PS PLO A2 KV CO
= sin φS (t) − φLO (t) (3.22)
ωc
and V5 (t) is deﬁned as A sin(ωc t).
Next, V6 (t) is introduced to the loop ﬁlter f (t), a standard proportionalintegral 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 PS PLO · γ ∗ hf 2 (t) ∗ f (t) + A cos(ωc t) (3.23)
Ideally, the local laser gives a frequency proportional to V7 (t), being φLO (t):
φLO (t) = KV CO V7 (t)dt + φN LO (t) (3.24)
AKV CO
= 2KV CO RL PS PLO · γ ∗ hf 2 (t) ∗ f (t)dt + sin(ωc t) + φN LO (t)
ωc
Then, identifying terms, the loop can be closed and its its behavior can be modeled with
the following diﬀerential equation:
dφC (t)
= K sin(φS (t) − φLO (t)) ∗ f (t) (3.25)
dt
71. Chapter 3. LockIn ampliﬁer OPLL architecture 52
√
A2 RL PS PLO KV CO
2
where K = ωc
Thus, while the local laser is controlled in lowpass response, the deviation measure signal
is in bandpass. 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 LockIn
ampliﬁer ﬁlters hf 1 (t), hf 2 (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:
ΦLO (S) KF (S)
H(S) = = (3.26)
ΦS (S) S + KF (S)
Hence the expressions deduced for generic linearizable loops are applicable in the LockIn
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:
2 ωn 1
σAN = ξ+ 2 (3.27)
2SNRBe 4ξ
2 2π∆ν
σP N = (3.28)
2ξωn
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:
2 A2 KV CO
2
σd = 2
(3.29)
2ωc
72. Chapter 3. LockIn ampliﬁer OPLL architecture 53
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:
2 2 2
σ = σAN + σP N + σd
2
ωn 1 2π∆ν A2 KV CO
= ξ+ 2 + + 2
(3.30)
2SNRBe 4ξ 2ξωn 2ωc
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 2ξωn τ product under 1.6 [16]. Also, the theoretical limit for 1 dB penalty at
BER 10−9 will be of 0.74 for the 2ξωn τ 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 proportionalintegral 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.
73. Chapter 3. LockIn ampliﬁer OPLL architecture 54
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:
8 2
∆ωP = 2ξK − ωn (3.32)
π
And the locking time can be expressed as:
(∆ωp )2
Tp ≈ 3
(3.33)
2ξωn
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 4ξωn τ
= 2ξωn τ J1 (3.34)
τ2 π
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
LockIn 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 phaselock crosstalk, a
full wave rectiﬁer has to be placed between the balanced receiver and the bandpass ﬁlter
of ﬁgure 3.2. But this produces a non desired eﬀect: πperiodic 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.
74. Chapter 3. LockIn ampliﬁer OPLL architecture 55
In order to avoid the eﬀects of this undesired slipcycling 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 πperiodic slip cycles is
expected to be in the same order.
3.2 Simulations
The LockIn 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 bandpass 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 PhaseLocked 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 LockIn loop limitations for minimizing the
75. Chapter 3. LockIn ampliﬁer OPLL architecture 56
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 decisiondriven 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 BERﬂoor 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.
BERﬂoor 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
76. Chapter 3. LockIn ampliﬁer OPLL architecture 57
Figure 3.5: Loop natural frequency versus damping factor relationship for optimal
conﬁgurations (transient response and phase noise) with 10 ns main loop delay.
Linewidth 1 ns delay 5 ns delay 10 ns delay
1 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 function
of 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 BERﬂoor 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.
77. Chapter 3. LockIn ampliﬁer OPLL architecture 58
Figure 3.6: BERﬂoor for optimal conﬁgurations as a function of the laser linewidth
evaluated 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 decisiondriven 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.
78. Chapter 3. LockIn ampliﬁer OPLL architecture 59
Figure 3.7: OPLL time response for a phase step of 1 rad. Inset ﬁgure is a zoom
between 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.
79. Chapter 3. LockIn ampliﬁer OPLL architecture 60
Figure 3.9: Rise time of the optimal conﬁgurations for several loop main delays.
Loop delay Setting time Rise time
10 ns 49.8 ns 45.2 ns
5 ns 31.6 ns 28.9 ns
1 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 LockIn ampliﬁed oPLL performances were compared to other oPLL architectures:
Balanced, Costas, and SubCarrier Modulated loops.
The four oPLL conﬁgurations were simulated, estimating their phase noise cancellation.
Several conﬁgurations of damping factor, natural frequency and dithering amplitude have
80. Chapter 3. LockIn ampliﬁer OPLL architecture 61
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 LockIn loop implemented, using nonintegrated
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
81. Chapter 3. LockIn ampliﬁer OPLL architecture 62
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 LockIn ampliﬁed loop mostly has an intermediate performance between the
Costas loop and the balanced loop. Thus when using the LockIn 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 LockIn ampliﬁed loop clearly outperfoms the most advanced loops, such
as the subcarrier modulated loop.
This behaviour is due to the inclusion of the LockIn 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 LockIn 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.
82. Chapter 3. LockIn ampliﬁer OPLL architecture 63
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 LockIn 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 LockIn ampliﬁed loop,
and up to 7.68 GHz for the subcarrier.
83. Chapter 3. LockIn ampliﬁer OPLL architecture 64
Balanced Costas SCM LockIn ampliﬁed
Linewidth tolerance BER 10−9 420 kHz 1.15 MHz 1.35 MHz 675 kHz
Linewidth 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 MHz
Hold 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 selfhomodining 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 Linewidth
30 mA 1.66 MHz 150 mA 1 MHz
50 mA 1 MHz 165 mA 1 MHz
70 mA 916 kHz 175 mA 1 MHz
90 mA 916 kHz 200 mA 1 MHz
100 mA 833 kHz 225 mA 1.1 MHz
120 mA 833 kHz 250 mA 1.17 MHz
135 mA 916 kHz 300 mA 1.36 MHz
Table 3.4: Measured values of the local oscillator linewidth.
84. Chapter 3. LockIn ampliﬁer OPLL architecture 65
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 LockIn 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 phaselocking 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 RL PS PLO . As all these
values where known, it was easy to ﬁnd the phase error deviation. Precisely, it was of
85. Chapter 3. LockIn ampliﬁer OPLL architecture 66
Figure 3.17: Electrical power spectrum after photodetection.
11.49◦ , for a measurement bandwidth of 200 MHz. This value ﬁts perfectly into the
LockIn 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 LockIn
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 phasecritical 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 4.55 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
86. Chapter 3. LockIn ampliﬁer OPLL architecture 67
(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.
87. 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 timeswitched 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 KarhunenLo`ve series expansion [40],
e
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
88. Chapter 4. Advances in phase and polarization diversity architectures 70
diversity [46]. Also, simulations and proofofconcept 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 KarhunenLo`ve series expansion phase estimation
e
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 ViterbiViterbi 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 KarhunenLo`ve series expansion is presented.
e
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 freerunning 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 AnalogtoDigital 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.
89. Chapter 4. Advances in phase and polarization diversity architectures 71
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 KarhunenLo`ve (KL) series form:
e
∞
w(t) = cn ϕn (t) (4.1)
n=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]:
2
ϕn (t) = sin(ωn t) (4.2)
T
T
2
cn = w(t) sin(ωn t) (4.3)
T 0
2π∆ν (2n+1)π
where ωn = λn
= 2T
being the eigenvalues deﬁned as the variance of the series coeﬃcients:
8T 2 ∆ν
λn = E{c2 } =
n (4.4)
(2n + 1)2 π
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:
ϕ1
ϕ2
w(t) = c ϕ = c1 c2 c3 . . . cn ϕ3
ˆ ¯ ¯ (4.5)
.
.
.
ϕn
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
90. Chapter 4. Advances in phase and polarization diversity architectures 72
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 spectral
width 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
91. Chapter 4. Advances in phase and polarization diversity architectures 73
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
92. Chapter 4. Advances in phase and polarization diversity architectures 74
(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 photoreceiver 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 postprocessing.
The coherent photoreceiver mixes the incoming optical ﬁeld with the local laser carrier
in the balanced photodetector 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 photoreceiver 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 postprocessing 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
93. Chapter 4. Advances in phase and polarization diversity architectures 75
Figure 4.5: Timeswitched diversity diﬀerential homodyne receiver scheme.
can assure its recovery. This operates like a phasediversity 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 nearzero
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 postprocesing, the signal can be obtained at the receiver output, where
the laser phase noise is considered as the limiting impairment,
C2
Vout (t) = d(t) cos φe (t) − φe (t − Tb ) + cos φe (t) + φe (t − Tb ) +
2
+ cos φe (t − Tb /2) − φe (t − 3Tb /2) − cos φe (t − Tb /2) + φe (t − 3Tb /2)
(4.6)
√
where C = 2 RL PS PLO is the peak voltage available at the output of the photoreceiver
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
94. Chapter 4. Advances in phase and polarization diversity architectures 76
not aﬀected by the loop delay: the I/Q postprocessing 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 lockin ampliﬁed
OPLL homodyne receiver. In these two cases, the output parameter measured was the
statistical eyeopening of the received data, accounted as the mean amplitude minus twice
the standard deviation, which provides a fair measure of the sensitivity penalty.
The eyeopening estimation was made at several linewidths from 225 kHz to 1 GHz. Bit
rate was set at 10 Gb/s; and a 4thorder 7.5 GHz Bessel lowpass 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 eyediagrams 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 postprocessing 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).
95. Chapter 4. Advances in phase and polarization diversity architectures 77
Figure 4.7: I, Q, and I+Q outputs Eyediagrams, at 50 MHz total laser linewidth.
Figure 4.8: Statistical normalized eye opening (20Log) for the I/Q receiver (both ﬁrst
and second approach) and a lockin 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 timeswitch 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
photoreceiver with added clocksynchronous phase switching (0◦ − 90◦ ). The second part
is an electronic postprocessing of the signal demodulation and synchronous combination
96. Chapter 4. Advances in phase and polarization diversity architectures 78
Figure 4.9: Statistical normalized eyeopening (20log) for the I/Q receiver (both ﬁrst
and 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 delayandadd 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 dutycycle and the correspondingly increased electrical bandwidth produces
a 3dB signaltonoise ratio penalty.
After the photodetection 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
97. Chapter 4. Advances in phase and polarization diversity architectures 79
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:
C2
Vout = 2
d(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 PS PLO 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 phasenoise diﬀerence. After some trigonometric
algebra, this expression can be properly expanded for evaluating the phase noise eﬀects:
C2 ∆φ1 (t) + ∆φ2 (t) ∆φ2 (t) + ∆φ3 (t)
Vout = d(t) 1 − sin2 − sin2 + (4.8)
2 2 2
1 ∆φ1 (t) + ∆φ3 (t)
+ cos 2φe (t) 2 cos ∆φ1 (t) + ∆φ2 (t) sin2 +
2 2
+ sin ∆φ1 (t) + ∆φ2 (t) sin ∆φ1 (t) + ∆φ3 (t) +
1 ∆φ1 (t) + ∆φ3 (t)
+ sin 2φe (t) 2 sin ∆φ1 (t) + ∆φ2 (t) sin2 −
2 2
− cos ∆φ1 (t) + ∆φ2 (t) sin ∆φ1 (t) + ∆φ3 (t)
where the phase error on each half bit has been deﬁned as:
Tb
∆φ1 (t) = φe (t) − φe t −
2
Tb
∆φ2 (t) = φe t − − φe (t − Tb )
2
3Tb
∆φ3 (t) = φe (t − Tb ) − φe t −
2
98. Chapter 4. Advances in phase and polarization diversity architectures 80
Figure 4.11: BERﬂoor of several cases: theoretical (dashed line), theoretical but
including 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 bittime 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 timeswitched architecture
is used instead of the architecture proposed in [24]. So, in the ∆φ3 (t) = 0 limiting case,
a BERﬂoor 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
99. Chapter 4. Advances in phase and polarization diversity architectures 81
noise eﬀects, low linewidth lasers were initially used; the total linewidth was 350 kHz,
much smaller than the bit rate. Two externalcavity 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 MachZehnder 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 pseudorandom 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 delayandmultiply mod
ule plus a delayandadd stage, as shown in ﬁgure 4.10). A microwave doublebalanced
mixer (Marki Microwave M20004) was used as a fourquadrant 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 BERﬂoor 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.
100. Chapter 4. Advances in phase and polarization diversity architectures 82
Figure 4.13: Sensitivity results and output eyediagram
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:
C2
Vout = 2
d(t) cos 2πfd Tb − (4.9)
− cos 4πfd t + 2πfd (t − Tb ) +
+ cos 4πfd Tb +
+ cos 2πfd (t − Tb /2) + 2πfd (t − 3Tb /2)
After some algebra, the expression can be rearranged as:
C2
Vout = 2
d(t) 2 cos 2πfd Tb − (4.10)
− cos 2πfd t + 2πfd Tb +
+ cos 4πfd t − 4πfd Tb
Note that the cos(2πfd t + 2πfd Tb ) and cos(4πfd t − 4πfd Tb ) 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:
C2
Vout ≈ d(t)2 cos 2πfd Tb (4.11)
2
101. Chapter 4. Advances in phase and polarization diversity architectures 83
Using the proposed model and taking into account that data is diﬀerentially encoded, the
probability of error can be written as:
1 −SNR · cos2 2πfd Tb
Pe = exp (4.12)
2 2
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 ).
102. Chapter 4. Advances in phase and polarization diversity architectures 84
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:
SNR
penalty(dB) = −10 · log 1 − (4.13)
SIR
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 timeswitched phasediversity diﬀerentially
encoded BPSK receiver under study. In an equallyspaced multiple channel environment,
it satisﬁes the following set of equations:
N
eS (t) = PS exp(j(ωt + 2πDit + φSi (t))) (4.14)
i=−N
eLO (t) = PLO exp(j(ωt + φLO (t))) (4.15)
103. Chapter 4. Advances in phase and polarization diversity architectures 85
Figure 4.16: TimeSwitched PhaseDiversity DPSK receiver for channel spacing
study.
π
φLO (t) = p(t) (4.16)
2
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 bitrate 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 photodetected current can be written as:
N
π
Ip (t) = 2 PSi PLO cos φSi (t) + 2πiDt − p(t) + n(t) (4.17)
i=−N
2
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:
N
Ip (t) = 2 PSi PLO cos g1 (t)φSi (t) · cos 2πiDt + n(t) (4.18)
i=−N
104. Chapter 4. Advances in phase and polarization diversity architectures 86
1 0≤t≤ T
2
where g1 (t) is deﬁned as when t ∈ [0, T ], g1 (t) = 1 T g1 (t + T ) = g(t)
2 2
<t≤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:
N
Ip (t) = 2 PSi PLO · g2 (t) · d · cos 2πiDt + n(t) (4.19)
i=−N
where d is deﬁned to be 1 when φSi (t) = 0; and 1 when φSi (t) = 0.
1 0≤t≤ T
2
Also g2 (t) is deﬁned as: when t ∈ [0, T ], g2 (t) = g2 (t + T ) = g(t)
0 T <t≤T
2
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 doublesided PSD of Ip (t) is found to be:
N
2 T πT (f − iD)
Gp (f ) = 4 PS0 PLO sinc2 + N (f ) (4.20)
i=−N
4 2
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
105. Chapter 4. Advances in phase and polarization diversity architectures 87
Figure 4.18: Spectrum after photodetection: Ideal homodyne reception (a) and using
timeswitched phasediversity (b)
calculated from If (t):
+∞ πT f
−∞
H(f )2 sinc2 2
df
SIR ≈ +∞
(4.21)
πT (f −D)
−∞
H(f )2 sinc2 2
df
where H(f ) is the transfer function of the channel ﬁlter placed after photodetection stage,
depicted in ﬁgure 4.16. Here the total SIR is approximated to the signaltostrongest
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:
π
θ(t) = φS1 (t) + 2πDt + p(t) (4.22)
2
where the signaltostrongestinterference 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 Inphase straight line. Thus, the decision variable, X, can be expressed
as:
1 ˆ
X ∝d 1+ √ cos(θ) (4.23)
SIR
106. Chapter 4. Advances in phase and polarization diversity architectures 88
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.
ˆ
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
ˆ
θ in the optimum sampling instant is found to be:
2
ˆ 1 SNR 1 ˆ
Pe (θ) = exp − 1+ √ cos(θ) (4.24)
2 2 SIR
107. Chapter 4. Advances in phase and polarization diversity architectures 89
Finally, the overall bit error rate can be written as:
+π 2
1 SNR 1 ˆ ˆ
Pe = exp − 1+ √ cos(θ) dθ (4.25)
4π −π 2 SIR
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 4thorder 2 GHz Bessel
lowpass ﬁlter was placed after photodetection stage. For the ideal system, that ﬁlter
was also 4thorder 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
108. Chapter 4. Advances in phase and polarization diversity architectures 90
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
MachZehnder Modulator (MZM, Fujitsu FTM7921ER) properly biased to work in the
0◦ − 180◦ range. This modulator was driven by the complementary PseudoRandom
Binary Sequence (PRBS).
Afterwards, these two branches were coupled and launched in to a 27 km standard G652
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 4thorder 2 GHz BesselThomson 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 timeswitched phasediversity 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 nonlinear eﬀects are generated.
4.2.2 Fuzzy data estimation
This section aims to change the combination (delayandadd) 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 nonlinear 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 oﬀthe
shelf electrical components: digital gates and other simple digital components.
109. Chapter 4. Advances in phase and polarization diversity architectures 91
4.2.2.1 Receiver scheme
As previously shown, in the proposed phase diversity homodyne receiver, the coherent
photoreceiver mixes the incoming optical ﬁeld with the local laser carrier in the balanced
photodetector 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 cycleslipping 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 fuzzylogicbased 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
110. Chapter 4. Advances in phase and polarization diversity architectures 92
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 )
Tb 3Tb Tb 3Tb
VQ (t) ∝ cos φd t − − φd t − + φN t − − φN t − −
2 2 2 2
Tb 3Tb Tb 3Tb
− cos φd t − + φd t− + φN t − + φN t −
2 2 2 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 after
diﬀerential 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, moderatepositive 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
111. Chapter 4. Advances in phase and polarization diversity architectures 93
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 Positive
Negative Positive
Negative Zero Zero Zero Zero 
Moderate Negative Zero Zero Zero  One
Null Zero Zero  One One
Moderate 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 lookup table. Based on these member
ship functions, simple rules like ”If [(I is moderatepositive) and (Q is moderatepositive)
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
112. Chapter 4. Advances in phase and polarization diversity architectures 94
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 timeswitched 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 BERﬂoor 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 BERﬂoor 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 BERﬂoor. 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 timeswitching diversity (3 dB penalty due to the halfbit 0◦ − 90◦
modulation).
113. Chapter 4. Advances in phase and polarization diversity architectures 95
Figure 4.26: BERﬂoor 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.
4.2.3.1 Receiver scheme
The proposed diversity receiver has also two main parts: the ﬁrst is a coherent photo
receiver with added clocksynchronous sinusoidal phase switching (0◦ − 90◦ ). The sec
ond part is an electronic postprocessing 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.
The coherent photoreceiver mixes the incoming optical ﬁeld with the local laser carrier
in the balanced photodetector stage. The local laser is controlled by the ﬁltered data
clock producing a sinusoidal phase change, to obtain the Inphase (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 = Ac γ cos(2πfc t); 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.
114. Chapter 4. Advances in phase and polarization diversity architectures 96
Figure 4.27: Generic receiver module
The photocurrent present at the output of the balanced detector can be written as:
π Ac γKLO
Ipd (t) = 2 PS PLO cos φS (t) − φLO (t) + φd (t) + + sin(2πfc t)
4 2πfc
(4.28)
where A2πfLO is assumed to be π ; is the photodetector responsivity, PS the transmitter
cK
c 4
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◦ peaktopeak modulation; but a better performance is obtained when gain
√
factor of about 2 is used (Figure 4.28). It is assumed to be the bestﬁt 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 lowpass equivalent data power spectrum. As a consequence, this ﬁrst ﬁlter must be
twice as broad as usual. This produces 3 dB SignaltoNoise Ratio penalty with respect to
an ideal phaselocked homodyne receiver. However, as seen in the previous subsections,
it has much higher linewidth tolerance, about two orders of magnitude.
After ﬁltering, a postprocessing 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
postprocessing module is implemented by a delay andmultiply block followed by a delay
andadd 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 cycleslipping in
115. Chapter 4. Advances in phase and polarization diversity architectures 97
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
116. Chapter 4. Advances in phase and polarization diversity architectures 98
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)):
2 π Ac γKLO
Im (t) = 4 PS PLO d(t) cos φe (t) +
+ sin(2πfc t) · (4.29)
4 2πfc
π Ac γKLO
· cos φe (t − Tb ) + + sin 2πfc (t − Tb )
4 2πfc
= 2 2 PS PLO d(t) cos φe (t) − φe (t − Tb ) +
π
+ cos φe (t) + φe (t − Tb ) + + β sin(2πfc t)
2
where the phase error is expressed as φe (t) = φS (t) − φLO (t).
Then, the expression can be rearranged as,
∞
2
Im (t) = 2 PS PLO d(t) cos θ1 (t) − Jn (β) sin θ2 (t) (4.30)
n=−∞
with β = Ac γKLO ; θ1 (t) = φe (t) − φe (t − Tb ) and θ2 (t) = φe (t) + φe (t − Tb ) + 2πnfc t.
πfc √
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 delayanadd module, can
be written as:
Tb
Id (t) = Im (t) + Im t − (4.31)
2
2 Tb
= 2 PS PLO d(t) cos θ1 (t) + cos θ1 t − −
2
Tb
−2J2 (β) sin θ2 (t) − 2J2 (β) sin θ2 t−
2
117. Chapter 4. Advances in phase and polarization diversity architectures 99
√
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
= 2 PS PLO d(t) cos(∆φ1 + ∆φ2 ) + cos(∆φ2 + ∆φ3 ) +
3∆φ1 + 2∆φ2 + ∆φ3 ∆φ1 + ∆φ2
+2J2 (β) sin 2φe (t) ± 2π2fc t − cos
2 2
where
Tb
∆φ1 (t) = φe (t) − φe t −
2
Tb
∆φ2 (t) = φe t − − φe (t − Tb )
2
3Tb
∆φ3 (t) = φe (t − Tb ) − φe t −
2
as when talking about the ﬁrst timeswitching 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 bittime 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
118. Chapter 4. Advances in phase and polarization diversity architectures 100
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 delayandadd, DAD) and
Im (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:
2
Id (t) ≈ PS PLO d(t) cos(∆φ1 + ∆φ2 ) + cos(∆φ2 + ∆φ3 ) (4.33)
119. Chapter 4. Advances in phase and polarization diversity architectures 101
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:
2 π Ac γKLO
Im (t) = 4 PS PLO d(t) cos φe (t) + 2πfd t +
+ sin(2πfc t) ·
4 2πfc
π Ac γKLO
· cos φe (t − Tb ) + 2πfd (t − Tb ) + + sin(2πfc (t − Tb ))
4 2πfc
= 2 2 PS PLO d(t) cos φe (t) − φe (t − Tb ) + 2πfd Tb +
π
+ cos φe (t) + φe (t − Tb ) + 4πfd t − 2πfd Tb + + β sin(2πfc t)
2
∞
2
= 2 PS PLO d(t) cos θ1 (t) − Jn (β) sin θ2 (t) (4.34)
n=−∞
being β = Ac γKLO ; θ1 (t) = φe (t) − φe (t − Tb ) + 2πfd Tb and θ2 (t) = φe (t) + φe (t − Tb ) +
πfc
2π(2fd + nfc )t − 2πfd Tb .
For the correct development of the model, no phase noise is assumed. Then:
2 π
Im (t) = 2 PS PLO d(t) cos 2πfd Tb ) + cos 4πfd t − 2πfd Tb + + β sin(2πfc t)
2
∞
2
= 2 PS PLO d(t) cos 2πfd Tb − Jn (β) sin 2π(2fd + nfc )t − 2πfd Tb
n=−∞
(4.35)
Next, the output of the delayandadd module can be calculated, obtaining:
Id (t) = Im (t) + Im (t − Tb /2) (4.36)
∞
2
= 2 PS PLO d(t) cos(2πfd Tb ) − Jn (β) sin 2π(2fd + nfc )t − 2πfd Tb −
n=−∞
∞
− Jn (β) sin 2π(2fd + nfc )t − 2π(6fd + nfc )Tb /2
n=−∞
2
= 2 PS PLO d(t) cos(2πfd Tb ) −
∞
2π(4fd + 2nfc )t − 2π(10fd + nfc ) Tb
2 −2π(2fd + nfc )Tb
−2 Jn (β) sin( ) cos( )
n=−∞
2 4
Revisiting the assumptions made in the last subsubsection, 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
120. Chapter 4. Advances in phase and polarization diversity architectures 102
approximated as:
2
Id (t) ≈ PS PLO d(t) cos(2πfd Tb ) (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 timeswitching phase
diversity receiver by means of numerical simulation with MonteCarlo 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◦ peaktopeak 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 nearoptimum, 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
121. Chapter 4. Advances in phase and polarization diversity architectures 103
Figure 4.32: Maximum tolerated linewidth per bit rate ratio at BER 10−3 as a
function 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 MachZehnder 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 pseudorandom binary sequence (PRBS) generator used to
provide data at the ﬁrst branch. These two optical signals are coupled and detected by a
122. Chapter 4. Advances in phase and polarization diversity architectures 104
balanced detector followed by an electrical processing stage (a delayandmultiply mod
ule plus a delayandadd stage). A microwave doublebalanced mixer (Marki Microwave
M20004) was used as a fourquadrant multiplier.
Figure 4.34: Experimental setup for the direct drive timeswitching.
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 photoreceiver
with added clocksynchronous phase (0◦ − 90◦ ) and polarization (HV) scrambling at the
local laser output. The second part is an electrical postprocessing 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 nearzero intermediate frequency.
123. Chapter 4. Advances in phase and polarization diversity architectures 105
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.
The coherent photoreceiver mixes the incoming optical ﬁeld with the local laser carrier
in the balanced photodetector stage. These components are no coincident with the
Txgenerated ones due to the unlocked transmission phase, but, with postprocessing
performing the operations in [24], the phasemodulated 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.
124. Chapter 4. Advances in phase and polarization diversity architectures 106
Figure 4.37: I, Q, H, V time distribution of each bit
Correspondingly, the photoreceiver 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
resynchronize the data clock signal with the signals introduced to the postprocessing
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 phaseswing 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.
125. Chapter 4. Advances in phase and polarization diversity architectures 107
To achieve the best performances in polarization diversity terms, the scrambler must in
troduce a clocksynchronous 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 dutycycle 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)ˆ + sin(ϕ)e−jθ y ) exp jω0 t + φS (t)
x ˆ (4.38)
eLO (t) = PLO (ˆ + y ) exp jω0 t + φLO (t)
x ˆ (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:
C2
IHIo (t) = d(t) cos2 (ϕ) (4.45)
2
C2
IV Io (t) = d(t) sin2 (ϕ) 1 + cos(2θ) (4.46)
2
C2
IHQo (t) = d(t) cos2 (ϕ) (4.47)
2
C2
IV Qo (t) = d(t) sin2 (ϕ) 1 − cos(2θ) (4.48)
2
And after combination it leads to:
C2
Io (t) = IHIo (t) + IV Io (t) + IHQo (t) + IV Qo (t) = d(t) (4.49)
2
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 timeswitching diversity receiver analyzed. So it can
be better implemented with the simpliﬁed scheme presented in ﬁgure 4.39. Please note
126. Chapter 4. Advances in phase and polarization diversity architectures 108
Figure 4.39: Alternative implementation for achieving timeswitched 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 subsubsection 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 KarhunenLo`ve series expan
e
sion for standard full phase diversity receivers, a simple timeswitching phase diversity
architecture, a Fuzzy logic data estimation algorithm, and a timeswitching polarization
diversity architecture.
For the phase estimation algorithm based on KarhunenLo`ve series expansion, the con
e
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 timeswitching phase diversity architecture has been discussed. Here the objec
tive was to obtain a phase diverse coherent receiver, using standard oﬀtheshelf 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 (BERﬂoor 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
127. Chapter 4. Advances in phase and polarization diversity architectures 109
broadens the signal bandwidth and introduces a nonnegligible penalty of 3 dB respect
to a theoretical coherent receiver.
In between, the concept of combining Fuzzy logic data estimation and timeswitching was
proposed and analyzed. It is an interesting approach that also combines lowcomplexity
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 BERﬂoor, equivalent to a 10−9 when FEC codes
are used.
Finally, a timeswitching 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 dutycycle and the
correspondingly increased electrical bandwidth produces a 3dB SNR penalty, like in the
timeswitching phase diversity architecture.
128. Chapter 5
ONU and OLT architectures
5.1 Summary of techniques and issues to take into
account
Homodyne systems today are mainly investigated toward longhaul 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 directdetection 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 PhaseLocked 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 + photodetection stages)
introduces a nonnegligible loop delay [17], resulting in a signiﬁcant penalty. In order to
avoid it, extremely low linewidth external cavity lasers had to be used.
111
129. 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 zeroIF/intradyne diversity receivers. The main goal of
these receivers is to replace the feedback loop (oPLL) by a feedforward postprocessing.
For full phase diversity schemes (using a 90◦ Hybrid), the architecture is based on an
intradyne system, using a freerunning local oscillator which is nominally at the same fre
quency as the incoming signal. Several relevant postprocessing approaches, depending on
the estimation/decoding performed are: diﬀerential detection in the analog domain [24],
digital Wiener ﬁltering [26], regenerative frequency dividers [28], ViterbiViterbi 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 lowtemperature processes and low cost packaging
based on passive alignment [54].
A third approach is timeswitching 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 postprocessing. 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 timeswitching diversity performances.
Technique Linewidth Penalty Required key Complexity
tolerance component
Decisiondrive loop 5 MHz 0 dB 90◦ hybrid High
Costas loop 4.9 MHz 0 dB 90◦ hybrid Medium/High
Subcarrier loop 5.1 MHz 0 dB 90◦ hybrid High
Balanced loop 2.4 MHz 2 dB Optical coupler Low
Heterodyne loop 6.4 MHz 1 dB Optical coupler Low
Full phase diversity 5% bitrate 0 dB 90◦ hybrid Medium
Timeswitch (Scrambler) 1.8% bitrate 4 dB Phase modulator Medium
Timeswitch (Direct drive) 5.4% bitrate 4 dB Highchirp laser Low
Table 5.1: Phase noise cancellation techniques summary table. The linewidth toler
ance is for a 10−3 BERﬂoor, 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
130. Chapter 5. ONU and OLT architectures 113
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 timeswitching 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 postprocessing 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 switching
Penalty 0 dB 0 dB 3 dB
Key component Polarization actuator Pol. beam splitter Pol. scrambler/switch
Response 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 downstream
and upstream 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
131. Chapter 5. ONU and OLT architectures 114
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 tradeoﬀ 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 4quadrant 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 photodetectors. The
electronic postprocessing 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.
132. Chapter 5. ONU and OLT architectures 115
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 highspeed analogtodigital converters (ADCs).
Inside digital I and Q postprocessing 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 wellknown
techniques, like Wiener ﬁlter [26] or ViterbiViterbi [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 postprocessing is now
composed by two parallel delayandmultiply 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
133. Chapter 5. ONU and OLT architectures 116
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 postprocessing is com
posed by four parallel delayandmultiply blocks, for diﬀerential detection, as proposed
in [24].
Figure 5.4: Analog conﬁguration scheme using 90◦ hybrid combined with PBS.
134. Chapter 5. ONU and OLT architectures 117
5.2.2 Transceivers based in timeswitching 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
timeswitching 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
135. Chapter 5. ONU and OLT architectures 118
Figure 5.6: Analog conﬁguration scheme using phase switch.
for obtaining a sinusoidal signal, which drives directly the laser, performing the 0127
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 delayandadd
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.
136. Chapter 5. ONU and OLT architectures 119
Figure 5.8: Analog conﬁguration scheme using standard balanced detector.
5.2.3 Transceiver based in Optical PhaseLocked 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 proportionalintegral 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
downconverted in a proper way [33]. At data detection branch, a delayandmultiply
block performs diﬀerential demodulation, and next a delayandadd 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.
137. Chapter 5. ONU and OLT architectures 120
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 Cost
handling handling processing penalty tolerance
5.2.1.1 90◦ hybrid Switch at CO Digital 3 dB 5 MHz Med./High
5.2.1.2 90◦ hybrid Switch at CO Analog 4 dB 5 MHz Med./High
5.2.1.3 90◦ hybrid PBS Digital 0 dB 5 MHz Very high
5.2.1.4 90◦ hybrid PBS Analog 1 dB 5 MHz Very high
5.2.2.1 Switch (Scr.) Switch at CO Digital 6 dB 1.8 MHz Medium
5.2.2.2 Switch (Scr.) Switch at CO Analog 7 dB 1.8 MHz Medium
5.2.2.3 Switch (Dir.) Switch at CO Digital 6 dB 5.4 MHz Low
5.2.2.4 Switch (Dir.) Switch at CO Analog 7 dB 5.4 MHz Low
5.2.3.1 OPLL Switch at CO Analog 4 dB 525 kHz Low
Table 5.3: Transceiver architectures summary table. The linewidth tolerance is for 1
dB 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 directdrive time
switching in combination with timeswitching 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
frontend (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
138. Chapter 5. ONU and OLT architectures 121
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 polarization
switch.
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 highspeed modulator, which is driven with a highspeed
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
139. Chapter 5. ONU and OLT architectures 122
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 polarization
switch.
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 passthrough 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.
140. Chapter 5. ONU and OLT architectures 123
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 directdrive timeswitching in combination with timeswitching 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.
141. 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 1020 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 subbands, that ﬁt several ultradensely spaced channels
allocated in the subPON 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 ultradense wavelengths to a power splitter. Such a power
splitter distributes the signal to each of the ONUs connected to the branch.
125
142. Chapter 6. Network topologies 126
Figure 6.1: Pure coupler splitting network scheme.
Figure 6.2: Network scheme and routing proﬁle.
Ultradense 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
2GHz channel spacing and 1 Gb/s data rate, 32 channels can be easily accommodated in
an ITUT G.694.1 100GHz DWDM channel. So the network can potentially serve 1280
users, oﬀering a total capacity of slightly more than 1 Tb/s.
143. Chapter 6. Network topologies 127
6.3 Advanced: WDM ringtree SARDANA network
This network is based in a WDM doubleﬁbrering with singleﬁbre wavelengthdedicated
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 AddDrop 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 (inline EDFs are also possible). Two singleﬁber PON trees are connected to each
RN; a 1:32 TDM PON is considered at each treePON 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,
144. Chapter 6. Network topologies 128
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 timeswitching 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].
• Ringtree ultradense WDMPON, with transparent remote nodes [68].
Both networks are based on the ultradense 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 ITUT G.694.1 100GHz DWDM channel. On the Cband, 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
145. Chapter 6. Network topologies 129
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 phaselocked 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, subMegaHertz (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 DWDM 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 2GHz 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.
146. Chapter 6. Network topologies 130
Figure 6.5: Upand Downstream transmission results.
Figure 6.6: Sensitivity penalty as a function of channel spacing.
6.4.2 Ringtree ultradense WDM PON
As shown in ﬁgure 6.7, the network topology ﬁber, is based on a twostage outside plant,
with a primary couplerbased feeder ring and a secondary powersplitterbased distribu
tion stage. The central ring multicasts all the wavelengths transmitted on the trunk ﬁber
to the diﬀerent networks subsegments. Subsequently, the secondary powersplitters 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 pointtopoint
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
147. Chapter 6. Network topologies 131
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 headend 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.
148. Chapter 6. Network topologies 132
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 postprocessing, 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 4node (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 = Lf iber + (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), Lf iber 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 Cband. 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, proofofconcept network experiments were
carried out using the network setup detailed in ﬁgure 6.9.
At the CO, a 1550 nm Distributed FeedBack (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 UDWDM scenario, a 4GHzspaced signal was
149. Chapter 6. Network topologies 133
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 3dB coupler to connect to two access trees.
Insertion losses of this device were measured to be 1.6 dB for passthrough 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 headend 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
headend 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 BERﬂoor.
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) errorfree data for a raw BER below 10−3 [11]. So,
150. Chapter 6. Network topologies 134
Figure 6.10: Sensitivity results
Normal operation Resilient mode
RN1 RN2 RN4 RN1 RN2 RN4
Sensitivity −43 dBm −41.3 dBm  −49.1 dBm −49.3 dBm −49.1 dBm
Link 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 4GHz 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.
151. Chapter 6. Network topologies 135
6.5 Chapter summary
In this chapter, several advanced UDWDM access solutions have been presented. Among
them, two case studies have been experimentally demonstrated: A subband WDM tree,
and a Ringtree ultradense WDM network architectures.
In both cases, the networks potentially oﬀers terabit transmission capabilities, and are
based on the transmission of narrowedspaced 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 RingTree ultradense 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.
152. Chapter 7
Conclusions and future work
7.1 General conclusions
The use of coherent systems in access networks appear as a promising mid to longterm
solution to the highspeed 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: KarhunenLoeve series expansion phase es
timation, Fuzzy logic data estimation, timeswitched phase diversity, and timeswitched
polarization diversity.
Among them, the KarhunenLo`ve series expansion phase estimation should be high
e
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 timeswitching
phase diversity and tolerating linewidths up to 1.8% of the bitrate. i. e. at 1 Gb/s it
137
153. Chapter 7. Conclusions and future work 138
can tolerate linewidths up to 18 MHz (BERﬂoor 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 (BERﬂoor 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 timeswitched polarization local diversity have been
analyzed, demonstrating the concept theoretically.
Furthermore, several transceiver architectures have been proposed and discussed, some
of them including wellknown techniques (as the full phase diversity receivers) whereas
others have been designed using the novel approaches previously reported in this thesis.
The tradeoﬀ between performances and cost has been diﬃcult to overcome, but ﬁnally
the decision of implementing the timeswitched diversity transceiver has been made. Ad
ditionally, OLT designs searching for a timeswitched 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
ultradense WDM networks. Laboratory testbeds have been developed for two of the
presented schemes (subband WDM tree and ring tree transparent ultradense 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.
154. Chapter 7. Conclusions and future work 139
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 nonnegligible 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.
155. Chapter 7. Conclusions and future work 140
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.
156. 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 costeﬀective due to the
components needed for the modulation and detection of the upstream and/or downstream
signals. A more costeﬀective 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 ﬁberscheme, the
tolerance against Rayleigh backscattering ratios is evaluated.
141
157. 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 delayandmultiply 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 (doublesided), the photodetection 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 PhotoDetector (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:
1
2
(mM PS ) 2
SNR = 4kT F ∆f
(A.1)
RL
+ 2qFa ( PS + Id )∆f
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
(onesided), 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]:
1 − ER
m= (A.2)
1 + ER
where ER is the Extinction Ratio, in linear units, deﬁned as the oﬀstate power over the
onstate 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]:
1
Pe = exp(−SNR) (A.3)
2
The next section shows the experimental implementation of the SCMsystem 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.
158. Appendix A. Passive optical network solution using a subcarrier multiplex 143
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, fullduplex 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 costeﬀective 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: Halfduplex 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 bandpass ﬁlter typically used at the transmitter
side is not required, thanks to the mixer’s frequency response, which ensures a bandpass
ﬁltering as shown in ﬁgure A.2. The mixer’s bandwidth has been measured by using the
threemixer 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 delayandmultiply 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 phaselocking 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.
159. Appendix A. Passive optical network solution using a subcarrier multiplex 144
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 baseband
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 OLTTX 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.
160. Appendix A. Passive optical network solution using a subcarrier multiplex 145
Figure A.4: Downstream power penalty at BER 10−10 due to extinction ratio. Square
points are experiments, whereas continuous line is derived from Eqs. 1 and 2.
A.3.2 Fullduplex 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
photodetection, a low pass ﬁlter was placed in order to properly reject remodulation
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
161. Appendix A. Passive optical network solution using a subcarrier multiplex 146
Figure A.5: Experimental setup for single ﬁbre fullduplex 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 Rayleighbackscattering
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
162. Appendix A. Passive optical network solution using a subcarrier multiplex 147
Figure A.6: Electrical power spectrums after photodetection 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 testbed 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.
163. Appendix A. Passive optical network solution using a subcarrier multiplex 148
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 testbed 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
164. Appendix A. Passive optical network solution using a subcarrier multiplex 149
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 bidirectional fullduplex 2.5 Gb/s / 1.25 Gb/s was demonstrated in a SCM sin
gle ﬁbre PON. The downstream signal is DPSK coded and upconverted by using a 5
GHz subcarrier, while the upstream data is transmitted in burstmode NRZ. A simpliﬁed
165. Appendix A. Passive optical network solution using a subcarrier multiplex 150
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 testbeds,
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.
166. 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 ultrafast 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 oﬀline processing and the realtime approach.
For the oﬀline approach, the same receiver architecture is used, almost all times [63, 64].
There the challenge is the development of feedforward processing algorithms that can
compensate the frequency oﬀset between local laser and received signal.
This study presents a reliable, fast and realtime wavelength control for intradyne co
herent reception, based on a single sideband optical VCO; intended for, at least, 8PSK
modulation format.
151
167. 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 frontend, driven by a local optical Voltage Controlled Oscillator (VCO); a
delayandmultiply 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 phaselocking
can be found in [81].
Figure B.1: Scheme of the proposed analog frequency estimation loop.
Figure B.2: Optical SSBmodulation VCO.
Regarding the frequency discriminator, it was found that a good and reliable implemen
tation can be just a delayandmultiply 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
168. Appendix B. Automatic wavelength control design 153
ﬁrst set of simulations was conﬁgured for an RZ8PSK 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 oﬀline 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 powerofeight block is required
to remove the 8PSK modulation, and this puts a cycleslipping 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 and
received 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:
K · Kp · S + K · Ki
HS (S) = (B.1)
(1 + K · Kp )S + K · Ki
K = 8πKLO 2 RL PS PLO
2
(B.2)
1 + K · Kp
T = (B.3)
K · Ki
where S is the complex angular frequency, KLO is the sensitivity of the optical VCO
module (Hz/V), is the photodetector’s responsivity, RL is the load impedance, PS is
the received optical power, PL O is the local oscillator optical power, Kp is the proportional
169. Appendix B. Automatic wavelength control design 154
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 oﬀline 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
170. Appendix B. Automatic wavelength control design 155
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
171. Appendix B. Automatic wavelength control design 156
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 30009
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 Residual
linewidth speed range slope amplitude
SSBIQ mod. 100 kHz 10 MHz 2 GHz 260 MHz/V 2.8 dB
GCSR 60 MHz 100 MHz 18 GHz 320 MHz/V 0.1 dB
DFB 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
oﬀline experiments were carried out. The setup used is depicted in ﬁgure B.8. It is a
backtoback version of the 10 Gbaud RZ8PSK (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 MachZehnder Modulator (MZM) is used. Regarding the 8PSK
signal, it was generated by an IQmodulator, 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 pseudorandom bit sequence, given by a Pulse
Pattern Generator (PPG). These signals were given to the modulator inputs with diﬀerent
delays to ensure their independence.
172. Appendix B. Automatic wavelength control design 157
At the receiver side, the RZ8PSK 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
delayandmultiply, work as expected, but with a nonnegligible 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 highspeed optical VCO. First proofofconcept experiments have been performed,
showing the feasibility of the main components of the loop and a good agreement with
simulation results.
173. 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 modulatedgrating Ybranch (MGY) laser, Syntune
3500) was obtained; and next a highresolution 3dimensional wavelengthtimepower
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 modulatedgrating Ybranch 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
174. 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 (Iref 1 ), reﬂector 2 (Iref 2 ) 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 05mA range, while Iref 1 and Iref 2 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 (supermodes). Such supermodes 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
175. Appendix C. Static and dynamic wavelength characterization of tunable lasers 161
the supermodes can be easily identiﬁed. Furthermore, one can also depict that each
supermode 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 of
reﬂector currents. (b) Logic stable regions map in function of reﬂector currents. The
phase current for a) and b) is Iph = 2.4 mA.
The wavelength spacing between consecutive modes is much bigger between two consecu
tive modes placed in diﬀerent supermodes (∆λ in the order of 5 nm), than between two
consecutive modes placed in the same supermode (∆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 (bc)
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 (23 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 quasilinear wavelength increment while increasing the
176. Appendix C. Static and dynamic wavelength characterization of tunable lasers 162
Figure C.3: (a) Plot of the wavelength in function of the phase current. Reﬂector
currents are biased at Iref 1 = 22.8 mA and Iref 2 = 8.6 mA. (b, c) Wavelength region
map as a function of both reﬂector currents for a phase current of 1.8 and 2.2 mA,
respectively.
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 diﬀerent
reﬂector currents (Iph = 2.4 mA): (a) Ir ef 1 = 10.8 mA, Iref 2 = 29 mA; (b) Iref 1 = 12.4
mA, Iref 2 = 8.9 mA; (c) Iref 1 = 10.2 mA, Iref 2 = 11.9 mA.
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
3D wavelengthpowertime 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.
177. Appendix C. Static and dynamic wavelength characterization of tunable lasers 163
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 photodetector, 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 photodetector 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 MGY laser will be discussed for diﬀerent
kinds of wavelength switching. In the ﬁrst experiment (depicted in ﬁgure C.6 (a1)), 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 3D
WavelengthPowerTime 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).
178. Appendix C. Static and dynamic wavelength characterization of tunable lasers 164
Figure C.6: (a) Stable regions map for Iph = 2.4 mA. The black points denote working
points used to measure the transition between two modes. The white lines denote such
transitions, and the number is used as experiment identiﬁer. (b) Voltage versus time
plot of the signals driving reﬂector sections for experiment 4 (see table C.1).
The lines shown in ﬁgure C.6 (a2) and ﬁgure C.6 (a3) 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 nonconsecutive modes
(from 1559.49 to 1561.93 nm). Please note that the laser modes corresponding to each
test are located in the same supermode. 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 (noncontinuous) 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 modehopping occurs and such mode becomes the main mode (what
produces the noncontinuous 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 (a4, 5,
6 and 7), the measured transitions were between diﬀerent supermodes: experiment 4
consists in a transition between consecutive supermodes; in experiment 5 the transition
measured was between two supermodes separated by one supermode; the working points
in experiment 6 are separated by 4 supermodes; 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 MGY 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.
179. Appendix C. Static and dynamic wavelength characterization of tunable lasers 165
Figure C.7: (Id.a) WPT plot: Plot of the wavelength versus time, and power (gray
scale) versus both wavelength and time for experiment ’Id’ (see table C.1 and/or 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 supermode 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 supermodes between both
working points (see table C.1). Consequently, the fact of not having the continuous
wavelength shift makes the transitions between consecutive supermodes much faster
than the transition between consecutive modes (inside the same supermode).
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
180. Appendix C. Static and dynamic wavelength characterization of tunable lasers 166
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 Cband 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 ”nonlasing” 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 (logarithmic
colour 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 nonlasing 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 supermodes (mode 1 at 1534.16 nm and mode 2 at 1545.2
nm) separated by one supermode (intermode 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 modehopping between mode 1 and mode 2 when the device (main mode) is
181. Appendix C. Static and dynamic wavelength characterization of tunable lasers 167
lasing in the intermode; and a modehopping between the intermode and mode 1/mode
2, when the main mode is located in mode 2/mode 1. In addition, a modehopping of the
main mode is also observed in ﬁgure C.9 (c), which is a zoom of the transition between
the intermode and mode 2 of ﬁgure C.9 (b). Please note that this modehopping 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) Wavelength
versus time of the main and secondary modes of depicted in (a). (c) Zoom of (b) during
the transition between intermode (1539.8 nm) and mode 2 (1545.2 nm).
Experiment Kind of transition Wavelengths (nm) Switching SMSR
Identiﬁer time (ns) (dB)
1 InM 1560.08  1560.32 3.0 20.14
2 CM 1550.00  1550.80 4.0 23.63
3 NCM 1559.68  1562.08 7.0 22.28
4 CS 1550.00  1555.60 0.40 20.83
5 NCS (1 supermode in between) 1534.16  1545.20 5.0 22.27
6 NCS (4 supermodes between) 1534.16  1559.68 12.0 23.85
7 NCS (close wavelengths) 1534.16  1535.80 13.0 22.14
8 Iph : InM 1554.78  1554.86 12.0 23.15
9 Iph : CM 1554.80  1554.84 40.0 23.9
Table C.1: The acronyms read in ”kind of transition” column, have a brief explanation
of the working points location: InM (Inside the same Mode); CM (Consecutive Modes
in the same supermode); NCM (NonConsecutive modes in the same supermode);
CS (Consecutive Supermodes); NCS (NonConsecutive Supermodes); Iph (change in
phase current).
C.2 Conclusions
The topology of the wavelength modes has been fully characterized. The 3dimensional
(Iref 1 , Iref 2 , 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.
182. Appendix C. Static and dynamic wavelength characterization of tunable lasers 168
In addition, through the highresolution wavelengthpowertime 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.
183. 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:
t
φN (t) = ϕN (τ )dτ (D.1)
0
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:
∆ν
S(f ) = (D.2)
2πf 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:
j
φN [j] = ∆t · ϕN [i] (D.3)
i=1
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
184. 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
ΦN (z)
H(z) = (D.5)
ΓN (z)
and
ΦN (Ω) 1
H(z) = = (D.6)
ΓN (Ω) 1 − e−jΩ
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 AutoRegressive (AR) process. Now, one
can work without normalized frequencies and manipulate the expressions, resulting in:
Gγ (f ) Gγ (f )
Sφ (f ) = −j2πf ∆t 2
= (D.7)
1 − e 2 1 − cos(2πf ∆t)
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:
Gγ (f )
Sφ (f ) = (D.8)
4π 2 f 2 ∆t2
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)
185. Appendix D. Phase noise digital modeling 171
But Gγ (f ) is the PSD of γN ; while γN has an autocorrelation of:
γN [i] = ∆tϕN [i] (D.10)
rγ (l) = ∆t2 rϕ (l) = ∆t2 σϕ δ(l)
2
(D.11)
being rg amma the autocorrelation of γN and rϕ the autocorrelation of ϕN .
Thus, as Gγ (f ) is the DFT of rγ :
Gγ (f ) = DF T {rγ } = ∆t2 · σϕ
2
(D.12)
And such expression can be made the same as equation D.9:
∆t2 · σϕ = 2π∆ν∆t
2
(D.13)
2 2π · ∆ν
σϕ = (D.14)
∆t
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.
186. Appendix D. Phase noise digital modeling 172
Figure D.1: Phase of phase noise spectrum.
187. Appendix E
LockIn OPLL prototype scheme
and printed circuit board
Figure E.1: Printed circuit board outline of the LockIN OPLL prototype.
173
188. Appendix E. LockIn OPLL prototype scheme and printed circuit board 174
189. Appendix E. LockIn OPLL prototype scheme and printed circuit board 175
190. Appendix F
Research publications
F.1 Patents
1. J. Prat, J. M. F`brega, ”Homodyne receiver for optical communications with post
a
processing,” app. number US12521619, date 10/20/2009.
2. J. Prat, J. M. F`brega, ”Receptor homodino para comunicaciones ´pticas con
a o
procesado a posteriori,” app. number ESP200700041 (PCT/ES2007/000778), date
12/29/2006.
3. J. Prat, J. M. F`brega, J. M. Gen´, ”Receptor coherente homodino para comuni
a e
caciones opticas con demodulacion diferencial,” app. number ESP200500998, date
04/21/2005.
F.2 Book contributions
1. Contribution to the book ”Next Generation FTTH Passive Optical Networks,”
SpringerVerlag 2008 (Josep Prat Ed.), in the transmission techniques chapter.
F.3 Journal publications
1. J. M. F`brega, J. Prat, ”Experimental Investigation of Channel Crosstalk in a
a
TimeSwitched Phase Diversity Optical Homodyne Receiver,” OSA Optics Letters,
vol. 34, No. 4, February 2009.
2. J. M. F`brega, J. Prat, ”Homodyne receiver prototype with timeswitching phase
a
diversity and feedforward analog processing,” OSA Optics Letters, vol. 32, No. 5,
March 2007.
177
191. Appendix F. Research publications 178
3. J. M. F`brega, J. Prat, ”Fuzzy Logic Data Estimation Based PSK Receiver with
a
Timeswitched Phase Diversity,” IEE Electronics Letters, vol. 42, no. 16, August
2006.
F.4 Conference publications
1. J. M. F`brega, J. Prat ”Digital Phase Estimation Method based on KarhunenLo`ve
a e
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. F`brega, A. El Mardini, V. Polo, J. A. L´zaro, E. T. Lopez, R. Soila, Josep
a a
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. F`brega, V. Polo, E. T. L´pez, J. A. L´zaro, J. Prat ”Optical Network
a o a
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. F`brega, J. Prat, ”UltraDense, Transparent and Resilient RingTree Access
a
Network using Couplerbased 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. F`brega, J. Prat, L. Molle, R. Freund, ”Design of a wavelength control for
a
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. F`brega, J. Prat, ”Low Cost Homodyne Transceiver for UDWDM Access Net
a
works,” European Conference on Networks and Optical Communications NOC’09,
Invited Paper, Valladolid, Spain, June 2009.
7. J. M. F`brega, E. T. L´pez, J. A. L´zaro, M. Zuhdi, J. Prat, ”Demonstration of a
a o 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. F`brega, L. Vilabru, J. Prat, ”Experimental Demonstration of Heterodyne
a
Phaselocked loop for Optical Homodyne PSK Receivers in PONs,” International
Conference on Transparent Optical Networks ICTON’08, Paper We.C1.5, Athens,
Greece, July 2008.
192. Appendix F. Research publications 179
9. J. M. F`brega, J. Prat, ”Simple LowCost Homodyne Receiver,” European Confer
a
ence on Optical Communications ECOC’07, Paper 7.2.5, Berlin, Germany, Septem
ber 2007.
10. J. Prat, J. A. L´zaro, J. M. F`brega, V. Polo, C. Bock, C. Arellano, M. Omella,
a a
”Next Generation Architectures for Optical Access and Enabling Technologies,” 5a
Reunion espanola de Optoelectronica OPTOEL’07, Bilbao, July 2007.
11. J. M. F`brega, J. Prat, ”Channel Crosstalk in ultradense WDM PON using Time
a
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. F`brega, J. Prat, ”Homodyne PSK Receiver with ElectronicDriven Phase
a
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. F`brega, J. Prat, ”UltraDense WDM PON based on Homodyne
a
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. F`brega, J. Prat, ”Homodyne Receiver Implementation with Diversity Switch
a
ing and Analogue Processing”, European Conference on Optical Communications
ECOC’06, Paper We3.P.100, Cannes, France, September 2006.
15. J. M. F`brega, J. Prat, ”Optimization of Heterodyne Optical PhaseLocked Loops:
a
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. F`brega, J. Prat, ”New Intradyne Receiver with ElectronicDriven Phase
a
and Polarization Diversity”, Optical Fiber Communication OFC/NFOEC’06, paper
JThB45, Anaheim (CA), USA, March 2006.
17. J. Prat, J. M. F`brega, ”New Homodyne Receiver with Electronic I&Q Diﬀerential
a
Demodulation”,European Conference on Optical Communications ECOC’05, paper
We4.P.104, Glasgow, UK, September 2005.
193. Appendix F. Research publications 180
F.5 Submitted publications
F.5.1 Book contributions
• J. A. L´zaro, J. M. F`brega, A. L. J. Teixeira and J. Prat, ”Laboratory Setups
a a
and Methods for Teaching and Characterizing Optical Polarization Modulators,” in
EuroFOS project Handbook of Experimental Fiber Optics.
F.5.2 Journal publications
• J. M. F`brega, A. ElMardini, V. Polo, E. T. L´pez, J. A. L´zaro, M. Zuhdi, and J.
a o a
Prat, ”Demonstration of a single ﬁbre PON featuring 2.5 Gbps SubCarrier 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. F`brega, J. A. L´zaro, V. Polo, A. Djupsj¨backa, M. Forzati, P.J.
a a o
Rigole and J. Prat, ”Tuning Characteristics and Switching Speed of a Modulated
Grating Y Structure Laser for Wavelength Routed PONs,” submitted to OSAANIC
2010.
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