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Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato...
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![Page 1: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/1.jpg)
Electronic Compensation of Nonlinear Phase Noise for Phase-
Modulated Signals
Keang-Po Ho
Plato Networks, Santa Clara, CA
and
National Taiwan University
Taipei, Taiwan
Joseph M. Kahn
Dept. of Electrical Engineering
Stanford University
Stanford, CA
Workshop on Mitigating Linear and Non-Linear Optical Transmission Impairments by Electronic Means
ECOC ’05, 15/9/05, Glasgow, Scotland
![Page 2: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/2.jpg)
Outline
What causes nonlinear phase noise
How nonlinear phase noise is distributed
Methods of electronic compensation
Performance analysis
![Page 3: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/3.jpg)
Nonlinear Phase Noise
Kerr effect-induced phase shift
PLeffNL
Optical Amp.
Fiber
Nonlinear coefficient
Effective length
Power
With amplifier noise:2
0effNL || NEL
Often called Gordon-Mollenauer effect
Causes additive phase noise
Variance inversely proportional to SNR
Variance increases quadratically with mean nonlinear phase shift
There exists an optimal mean nonlinear phase shift
![Page 4: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/4.jpg)
Intrachannel Four-Wave-Mixing
Intensity at the transmitter without pulse overlap
Intensity after propagation with dispersion-induced pulse overlap
+1 Identical phases +1
+1 Opposite phases 1
Different intensities different nonlinear phase shifts and phase noises.(Actual electric field is complex, rather than real, as shown here.)
![Page 5: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/5.jpg)
Nonlinear Phase Noise vs. IFWM
40-Gb/s RZ-DPSK, T0 = 5 & 7.5 ps (33% & 50%), L = 100 km, = 0.2 dB/kmNormalized to mean nonlinear phase shift of 1 radNote: For low-loss spans, recent results from Bell Labs show far larger IFWM than above.
ISPM Only
ISPM+IXPM
![Page 6: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/6.jpg)
Distribution of Signals with Nonlinear Phase Noise
SNR = 18 (12.6 dB) Number of Spans = 32 Transmitted Signal = (1, 0) Color grade corresponds to density
Why the helical shape?– Nonlinear phase noise
depends on signal intensity
– Phase rotation increases with intensity
How we can exploit the correlation?– To compensate the
phase rotation by received intensity
![Page 7: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/7.jpg)
Yin-Yang Detector
Spiral decision boundary for binary PSK signals
Use look-up table to implementdecision boundaries
Transmitted signal of (±1, 0)SNR = 18 (12.6 dB)Number of Spans = 32Color grade corresponds to densityRed line is the decision boundary
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Two Electronic Implementationsfor PSK Signals
Compen-sator
DetectedData
Straight-BoundaryDecisionDevice
iI
iQ
Spiral-BoundaryDetector
DetectedData
iI
iQER
EL
I
Q
LOLaser
90OpticalHybrid
PLL
iI
iQ
Receiver front end
Yin-Yang detector
CompensatorEither linear or nonlinear
![Page 9: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/9.jpg)
Operation of Linear CompensatorFor PSK Signals
With detected phase using a linear combiner– Estimate the received phase R
– Subtract off scaled intensity to obtain compensated phase R P
With the quadrature components cosR and sinR
– Use the formulas cos(R P) = sinRsin(P) + cosRcos(P)
sin(R P) = sinRcos(P) cosRsin(P)
Optimal compensation factor is 2
1eff
NL
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Electronic CompensatorFor DPSK Signals
Coupler
Er
iI(t)
Coupler iQ(t)
+/2
P(t)
Com
pen
sato
r
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Operation of Linear CompensatorFor DPSK Signals
In principle– Use R(t+T) R(t) P(t+T) P(t)] for signal detection
In practice– What you obtain is
– Some simple math operations are required.– Optimal value of same as for PSK signals
)()(sin)()(
)()(cos)()(
tTttPTtP
tTttPTtP
RR
RR
![Page 12: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/12.jpg)
Nonlinear Phase NoiseLinear Compensator for PSK Signal
Before compensation After compensation
r - r2
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Linear/Nonlinear CompensatorVariance of Nonlinear Phase Noise
Linear compensator
r r2
Nonlinear compensator
r E{NL|r}
Linear and nonlinear
compensators perform the same
Standard deviation is
approximately halved
Transmission distance is
approximately doubled
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
Mean Nonlinear Phase Noise, <NL
> (rad)
Sta
nd
ard
Dev
iati
on
,
(ra
d)
NL
NL
- r
2
NL - E{
NL|
r}
![Page 14: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/14.jpg)
Linear CompensatorSNR Penalty for DPSK Signals
Exact BER has been derived MMSE compensator (minimizing variance) has been derived MAP compensator (minimizing BER) has been derived
0 0.5 1 1.5 2 2.5 30
1
2
3
4
5
Mean Nonlinear Phase Shift <NL
> (rad)
SN
R P
ena
lty (
dB)
w/o comp
w/ comp
MAPMMSEApprox.
20effNL || ELN
![Page 15: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/15.jpg)
0 1 2 30
0.5
1
1.5
2
2.5
3
Mean Nonlinear Phase Shift < NL
> (rad)
SN
R P
enal
ty (
dB)
w/o comp
linear nonlinear
MMSE
MAP
Linear/Nonlinear CompensatorSNR Penalty for PSK Signals
Exact BER has been derived MMSE compensator has been derived MAP compensator has been found numerically Linear and nonlinear MAP compensators perform similarly
20effNL || ELN
![Page 16: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/16.jpg)
Electro-Optic Implementation
Tap out part of the signal to drive a phase modulator Can be used for both PSK and DPSK signals Requires polarization control for the phase modulator Enables mid-span compensation Optimal location is at 2/3 of the span length, yielding
1/3 standard deviationPhase Mod.
Driver
tap
TIA
![Page 17: Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals Keang-Po Ho Plato Networks, Santa Clara, CA and National Taiwan University.](https://reader035.fdocuments.in/reader035/viewer/2022062309/56649ed85503460f94be6723/html5/thumbnails/17.jpg)
Summary
Nonlinear Phase Noise– Caused by interaction of signal and noise via Kerr effect
– Correlated with received intensity compensation possible
Two Equivalent Compensation Schemes– Yin-Yang detector or compensator
– Standard deviation is approximately halved
– Performance analysis yields analytical BER expressions
To probe further– K.-P. Ho and J. M. Kahn, J. Lightwave Technol., 22 (779) 2004.
– C. Xu and X. Liu, Opt. Lett. 27 (1619) 2002.
– K.-P. Ho, Phase-Modulated Optical Communication Systems (Spring, 2005)