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

Outline

What causes nonlinear phase noise

How nonlinear phase noise is distributed

Methods of electronic compensation

Performance analysis

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

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.)

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

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

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

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

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

Electronic CompensatorFor DPSK Signals

Coupler

Er

iI(t)

Coupler iQ(t)

+/2

P(t)

Com

pen

sato

r

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

Nonlinear Phase NoiseLinear Compensator for PSK Signal

Before compensation After compensation

r - r2

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}

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

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

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

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)