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 Optical Amp. Fiber Nonlinear coefficientEffective length Power With amplifier noise:  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 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, T 0 = 5 & 7.5 ps (33% & 50%), L = 100 km,  = 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. 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 implement decision 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

Two Electronic Implementations for PSK Signals Compen- sator Detected Data Straight- Boundary Decision Device iIiI iQiQ Spiral- Boundary Detector Detected Data iIiI iQiQ ERER ELEL I Q LO Laser 90  Optical Hybrid PLL iIiI iQiQ Receiver front end Yin-Yang detector Compensator Either linear or nonlinear

Operation of Linear Compensator For 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 cos  R and sin  R –Use the formulas  cos(  R   P) = sin  R sin(  P) + cos  R cos(  P)  sin(  R   P) = sin  R cos(  P)  cos  R sin(  P)  Optimal compensation factor is

Electronic Compensator For DPSK Signals Coupler ErEr iI(t)iI(t) iQ(t)iQ(t) +  /2 P(t)P(t) Compensator

Operation of Linear Compensator For 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

Nonlinear Phase Noise Linear Compensator for PSK Signal Before compensation After compensation  r -  r 2

Linear/Nonlinear Compensator Variance of Nonlinear Phase Noise  Linear compensator –  r   r 2  Nonlinear compensator –  r  E{  NL |r}  Linear and nonlinear compensators perform the same  Standard deviation is approximately halved  Transmission distance is approximately doubled

Linear Compensator SNR Penalty for DPSK Signals  Exact BER has been derived  MMSE compensator (minimizing variance) has been derived  MAP compensator (minimizing BER) has been derived Mean Nonlinear Phase Shift <  NL > (rad) SNR Penalty (dB) w/o comp w/ comp MAP MMSE Approx.

Mean Nonlinear Phase Shift <  NL > (rad) SNR Penalty (dB) w/o comp linear nonlinear MMSE MAP Linear/Nonlinear Compensator SNR 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

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 deviation Phase 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) –C. Xu and X. Liu, Opt. Lett. 27 (1619) –K.-P. Ho, Phase-Modulated Optical Communication Systems (Spring, 2005)

Nonlinear Kerr Effects Kerr Effects Multiple Channels Four-Wave Mixing (FWM) Cross-Phase Modulation (XPM) Intra-Channel Cross-Phase Modulation (IXPM) Intra-Channel Four-Wave Mixing (IFWM) Single Channel Self-Phase Modulation (SPM) Nonlinear Intersymbol Interference Timing JitterAmplitude Jitter Pulse Distortion Coherent Cross-Talk Coherent Timing Jitter and Pulse Distortion With constant intensity, DPSK signals are affected by only IFWM and FWM.

Nonlinear Phase Noise  Nonlinear Refractive Index  Nonlinear Phase Shift With Amplifier Noise Power Nonlinear constant Effective fiber length Optical Amp. Fiber

Nonlinear Phase Noise Math Model  Discrete Model  Distributed Model Wiener process Nonlinear Phase Noise Linear Electric Field Received Electric Field N spans Opt. Amp. Fiber

Exact Error Probability Distributed Model, DPSK Signals  Both exact and approximation models –Non-Gaussian distributed nonlinear phase noise –Uncorrelated with the phase of amplifier noise  Exact model –With dependence between nonlinear phase noise and the phase of amplifier noise  Approximation model –Independent

Mean Nonlinear Phase Shift <  NL > (rad) Required SNR (dB) Exact Indep. (approx) Nicholson Q-factor SNR Penalty A Comparison of Different Models  All approximated models underestimate the BER and SNR penalty.  The independence model underestimates up to 0.23 dB.  The Nicholson model, for Gaussian-distributed phase noise, underestimates up to 0.27 dB.  Q-factor is complete failure except at high nonlinear phase noise

Error Probability Simulation SNR  s (dB) Error Probability Exact Simulation Approx. = 0.71 rad 32 spans DPSK signals Monte-Carlo error count

Small Number of Spans  Very complicated model  Depending on the eigenvalues and eigenvectors of the covariance matrix  More than 32 spans validates distributed model  Penalty decreases with the increase of fiber spans  For experimental verification

Experimental Verification  10 Gb/s NRZ-DPSK  Single-branch receiver  Single-span 20-km single-mode fiber Back-to-back BER ~ km of fiber = 0.5 rad BER ~ w/ 3.7 dB larger SNR

Measurement Results Difference: 3.0 dB single-branch Rx 1.7 dB fiber dispersion 0.4 dB orthogonal noise 0.7 dB thermal noise 1.2 dB optical filter 2.7 dB ??

SPM with Amplifier Noise  Without noise, IFWM nonlinear force is  Without noise, SPM nonlinear force is  SPM-induced nonlinear force including amplifier noise of n(z,t) Signal-noise beat induced nonlinear force only

SPM and IXPM Phase Noise The Dominant Terms  For the pulse at t = 0 of –SPM phase noise is from –IXPM phase noise is from –SPM is from –IXPM is from –IFWM is from SPM IXPM IFWM Phase noise scaled down by the SNR of 20 SPM IXPM 40-Gb/s RZ-DPSK, T 0 = 7.5 ps L = 100 km

IFWM & IXPM z = 0 km z = 5 km, opposite phase z = 5 km, same phase z = 5 km, difference z =10 km, difference T 0 = 5 ps D = 17 ps/km/nm T = 25 ps Cancel each other

Nonlinear Phase Noise vs. IFWM 40-Gb/s RZ-DPSK, T 0 = 5 & 7.5 ps, L = 100 km SPM Only SPM+IXPM

Dispersion Effect on Nonlinear Phase Noise  The nonlinear force is equal to Overall intensity z = 10 km z = 5 km z = 0 km 40-Gb/s RZ-DPSK, T 0 = 5 ps Overall intensity is very random You get the mean

DQPSK Signal SPM-Induced Nonlinear Phase Noise Required SNR for DPSK is 13.0 dB DQPSK is 17.9 dB

N spans EDFA Fiber TX 1 TX 2 TX 3 TX M RX 1 RX 2 RX 3 RX M    M Optical Spectrum Wavelength-Division Multiplexing (WDM) All DPSK Signals Self-phase modulation, the channel itself Cross-phase modulation, another channel Nonlinear phase noise from 2 channels

Cross-Phase Modulation Induced Nonlinear Phase Noise  Nonlinear phase noise – Channel walk-off The channel itself Another channel After some distance walk-off Nonlinear phase noise reduced by walk-off by averaging launched position

XPM-Induced Nonlinear Phase Noise SNR Penalty L W : Walk-off length the distance to walk of the bit-interval T