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