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Investigation of the Nonlinear Characteristic of Costas Loop based Carrier Recovery Systems
Semjon Schaefer
International Workshop on
Optical Phase-locked-Loop Techniques
16.06.2015
Kiel
Lehrstuhl für Nachrichten- und ÜbertragungstechnikTechnische Fakultät
Christian-Albrechts-Universität zu Kiel
-2-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Motivation
Main focus:
1) Carrier recovery system nonlinear OPLL characteristic
2) Influence of the carrier recovery (OPLL) on the data recovery
TransmitterChannel Coherent
Receiver
Carrier
Recovery(=PLL)
Data
Recovery
Receiver
..010110.. ..010110..
Data Data
e.g.
Fiber
Free-space
Atmosphere
-3-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Content
1. Introduction
2. Optical Phase-Locked Loop
3. Nonlinear OPLL Characteristic
4. Noise Sources & Cycle Slip Phenomena
5. Conclusion
-4-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Content
1. Introduction
2. Optical Phase-Locked Loop
3. Nonlinear OPLL Characteristic
4. Noise Sources & Cycle Slip Phenomena
5. Conclusion
-5-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Introduction
Why coherent detection?
Pros:
Full amplitude and phase recovery
High flexibility
Cons:
Requires local oscillator with same
carrier frequency as transmitter
High complexity
Carrier recovery structures:
Digital carrier frequency estimation (D. Clausen)
Phase-locked loop techniques
University of Kiel: Optical PLL based on Costas-loop in optical intersatellite links
-6-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Optical Intersatellite Link (OISL)
Current RF Scenario: OISL Scenario:
LEO GEO GS:
High data rate (LEO GEO)
Long time window (GEO GS)
LEO GS:
Low data rate
Short time window
LEO: Low-Earth Orbit
GEO: Geostationary Orbit
-7-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
OISL Transmission System
Typical Laser Communication Terminal (LCT) Setup:
Data modulation:
Binary phase shift keying (BPSK)
Phase of the laser is switched: Bit ‘1’ 180°
Bit ‘0’ 0°
Frequency mismatch between LO and input signal due to
Natural frequency drift
Phase noise
Doppler shift
PM: Phase modulator
YDFA: Ytterbium-doped fiber amplifier
OPLL: Optical phase-locked loop
LO: Local oscillator
Transmitter
Receiver
Optical
Electrical
Digital
OPLL
I
QData Recov.Diff. Decod.
OPLLElectronic
CoherentReceiver
Fast Tuneable LO(VCO)
Data
1064 nm YDFA
Free-spaceChannel
Tx/Rx Antenna
PM
Diff.Encoding
PulseShaper
-8-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Caused by the relative velocity between the satellites
Maximum frequency offset of approx. 7 GHz
Coarse compensation by using satellite trajectory data
Fine compensation by optical phase-locked loop (OPLL)
Residual Doppler shift, natural frequency drift and phase noise
Doppler Frequency Shift
2
21
1 cos
v
c
Tx vc
Rxf f
: Transmitted frequency
: Received frequency
: Speed of light in vacuum
: Relative velocity
Tx
Rx
f
f
c
v
-9-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Content
1. Introduction
2. Optical Phase-Locked Loop
3. Nonlinear OPLL Characteristic
4. Noise Sources & Cycle Slip Phenomena
5. Conclusion
-10-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Optical PLL based on Costas loop
Fundamentals of Costas PLL
with
1 2
( ) ( )· ( )
~ sin 2 ( ) ( )
I Qt I t I t
t t
Error signal:
1 1 0 1
2 2 0 2
ˆ sin ( )
ˆ sin ( )
s t s t t
s t s t t
1 2,0( )t t
Frequency offset
Phase offset
2,0
1 2
1 21 2 0 1 2
1 21 2 0 1 2
ˆ ˆcos ( ) ( ) cos 2 ( ) ( )
2
ˆ ˆsin ( ) ( ) sin 2 ( ) ( )
2
I
Q
I t s t s t
s st t t t t
s sI t t t t t t
LP Filter
-11-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Optical Phase-Locked Loop
Optical phase-locked loop for BPSK transmission based on Costas loop
1 2
1 2
( ) ~ cos ( ) ( ) ( )
( ) ~ sin ( ) ( ) ( )
I M
Q M
U t t t t
U t t t t
AGC: Automatic gain control
TIA: Transimpedance amplifier
LO: Local oscillator
( ) 0,M t
Demodulated data signal after coherent detection:
BPSK modulation:
1 2
( ) ( )· ( )
~ sin 2 ( ) ( )
I Qt U t U t
t t
Phase error
Coherent Receiver
-12-Chair
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Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Frequency Acquisition
Example: Residual frequency offset of 5 MHz
Error Signal Frequency Error( )t
0.7
2 6.5 MHzn
D
Damping:
Natural Frequency:
-13-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Content
1. Introduction
2. Optical Phase-Locked Loop
3. Nonlinear OPLL Characteristic
4. Noise Sources & Cycle Slip Phenomena
5. Conclusion
-14-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Mathematical description of Costas-PLL
Error signal:
Loop filter: e.g. passive PI filter (lag-lead)
Phase error:
Nonlinear differential equation system:
0 0
2 1 2
1 12 cos 2 sin 2D D
d
dt
dK K m K K m
dt T T T
( ) sin 2Dt K
1
1 1 1
2 2
1 1( )( ) , with
( ) 1 1T
m
sT sT TX sF s m
E s sT Ts
1 2 1 0
1
0
( ) ( ) ( ) ( ) ( )
1( )
t t t t K x t dt
ddx t
K dt dt
No analytical solutions exist
Numerical approximation
Phase plane
2 1
1 1( ) ( )
d dx t t m
dt T dt T
KD: Phase discriminator gain [V/rad]
K0: LO (VCO) gain [MHz/V]
-15-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Phase Plane Diagram
Each solution of the NLDE system is represented by a trajectory in the phase plane
All trajectories end in
a stable point P
L :
H Hold-in range
Lock-in rangeL
-16-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Phase Plane Diagram
Each solution of the NLDE system is represented by a trajectory in the phase plane
Not all trajectories end
in a stable point P
A stable periodic state
exists
L H :
H Hold-in range
Lock-in rangeL
-17-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Phase Plane Diagram
Each solution of the NLDE system is represented by a trajectory in the phase plane
No trajectories end in
a stable point P but in
the stable periodic state
H :
H Hold-in range
Lock-in rangeL
-18-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Content
1. Introduction
2. Optical Phase-Locked Loop
3. Nonlinear OPLL Characteristic
4. Noise Sources & Cycle Slip Phenomena
5. Conclusion
-19-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Noise Sources
Shot noise
Results from transformation of optical power into photo current
Phase noise
Due to laser linewidth (Tx and LO laser)
Main focus: noise influence on the phase error (i.e. carrier frequency offset)
noise distortion affects directly the carrier recovery1 2
(Ideal) (Measurement)
Laser spectrum:
-20-Chair
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Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Equivalent mathematical block diagram
Both noise sources influence the phase error
Phase error variance
PLL bandwidth BL influences the noise performance:
• Variance due to shot noise increases with BL
• Variance due to phase noise decreases with BL
Optimum bandwidth exists
2 L
L Rx
Phase noise Shot noise
Ba b
B P
a,b const.
-21-Chair
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Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Cycle Slip phenomena
High phase errors may drive the PLL
in the nonlinear regime
OPLL unlocks from stable point P and
relocks after several jumps
Caused by nonlinear OPLL characteristic:
( ) sin(2 )t
OPLL may lose lock
without relock
sin(2 ) 2
-22-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Noise Influence
Cycle slips will impair data demodulation
Phase jumps in will flip the data
Bit errors!
Solution:
Observe relative changes of bits
and not absolute values
Differential Encoding
T1<T2<T3
T: Observing time per simulation
n: No. of simulations
( ) ~ cos ( ) ( )
( ) ~ sin ( ) ( )
I M
Q M
U t t t
U t t t
( )t
-23-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Conclusions
Coherent detection requires carrier frequency recovery
OPLL as carrier recovery in optical communication systems
Investigation of the nonlinear characteristic
Shot and phase noise impair the (nonlinear) OPLL performance
Cycle slips influence the communication system and data recovery
-24-Chair
for Communications
Lehrstuhl für
Nachrichten- und Übertragungstechnik
Semjon Schaefer, PLL-Workshop, 16.06.2015
Thank you!