Electronic Compensation of Nonlinear Phase Noise for Phase-Modulated Signals

1. 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

2. Outline • What causes nonlinear phase noise • How nonlinear phase noise is distributed • Methods of electronic compensation • Performance analysis

3. Fiber Optical Amp. Nonlinear coefficient Effective length Power With amplifier noise: Nonlinear Phase Noise • Kerr effect-induced phase shift • 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

4. 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.)

5. ISPM+IXPM ISPM Only Nonlinear Phase Noise vs. IFWM 40-Gb/s RZ-DPSK, T0 = 5 & 7.5 ps (33% & 50%), L = 100 km, a = 0.2 dB/km Normalized to mean nonlinear phase shift of 1 rad Note: For low-loss spans, recent results from Bell Labs show far larger IFWM than above.

6. 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

7. 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 = 32 • Color grade corresponds to density • Red line is the decision boundary

8. ER iI I 90OpticalHybrid EL Q iQ LOLaser PLL iI Spiral- Boundary Detector DetectedData iQ iI Straight- Boundary Decision Device Compen- sator DetectedData iQ Two Electronic Implementationsfor PSK Signals Yin-Yang detector Receiver front end Compensator Either linear or nonlinear

9. Operation of Linear CompensatorFor PSK Signals • With detected phase using a linear combiner • Estimate the received phase fR • Subtract off scaled intensity to obtain compensated phase fR-aP • With the quadrature components cosfR and sinfR • Use the formulas • cos(fR-aP) = sinfRsin(aP) + cosfRcos(aP) • sin(fR-aP) = sinfRcos(aP) - cosfRsin(aP) • Optimal compensation factor is

10. Coupler Coupler P(t) Compensator iI(t) Er iQ(t) +p/2 Electronic CompensatorFor DPSK Signals

11. Operation of Linear CompensatorFor DPSK Signals • In principle • Use fR(t+T) -fR(t) -a[P(t+T) -P(t)] for signal detection • In practice • What you obtain is • Some simple math operations are required. • Optimal value of a same as for PSK signals

12. Nonlinear Phase NoiseLinear Compensator for PSK Signal Before compensation After compensation fr - ar2

13. Linear/Nonlinear CompensatorVariance of Nonlinear Phase Noise • Linear compensator • fr-ar2 • Nonlinear compensator • fr -E{fNL|r} • Linear and nonlinear compensators perform the same • Standard deviation is approximately halved • Transmission distance is approximately doubled

14. 5 MAP MMSE 4 Approx. w/o comp 3 SNR Penalty (dB) 2 w/ comp 1 0 0 0.5 1 1.5 2 2.5 3 F Mean Nonlinear Phase Shift < > (rad) NL 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

15. 3 linear nonlinear 2.5 2 w/o comp 1.5 SNR Penalty (dB) 1 MMSE 0.5 MAP 0 0 1 2 3 F Mean Nonlinear Phase Shift < > (rad) NL 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

16. 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, yielding1/3 standard deviation Phase Mod. tap Driver TIA

17. 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)