1. Signal Design and Analysis in Presence of Nonlinear Phase Noise
Alan Pak Tao Lau
Department of Electrical Engineering,
Stanford University
November 30, 2006

2. Outline
Kerr nonlinearity induced nonlinear phase noise in coherent communication systems
Analytical derivation of Maximum Likelihood decision boundaries and Symbol Error Rate for PSK/DPSK systems
Signal design and detection for 16 QAM systems with low/high nonlinearity
Signal Constellation optimization

3. Kerr Nonlinearity induced intensity dependent refractive index
Nonlinear Phase Shift

4. Nonlinear phase noise
Fiber
Opt. Amp.
overall length L with N spans
ASE from inline amplifiers generate Gaussian noise
Random power of signal plus noise produce random nonlinear phase shift -- Gordon-Mollenauer effect
L=3000 km, N=30, = 0dBm

5. Phase Noise for coherent systems
Optical Amp.
Fiber
Optical Amp.
Fiber
Optical Amp.
Fiber
Linear Phase Noise
Nonlinear Phase Noise

6. Nonlinear Phase Noise Experiments
ECOC ’06
Post-Deadline Paper

7. Joint PDF of Received Amplitude and Phase
For distributed amplification scheme,
PDF given by K.P. Ho “Phase modulated Optical Communication Systems,” Springer 2005

8. PDF and Decision Boundaries for 40G Symbols/s QPSK Signals
L=5000 km, P=-4 dBm,

9. Maximum Likelihood Detection
To implement ML detection, need to know the ML boundaries
Need to know center phase
With ,can either de-rotate the received phase or use a lookup table

10. Center Phase The center phase satisfy the relation Let
Equation (1) becomes

11. Center Phase
With approximations
it can be shown that

12. Center Phase rotation Before rotation After rotation
Straight line ML decision boundaries after rotation!

13. For Comparison Center phase rotation Ho and Kahn (JLT vol.
22 no. 3, Mar. 2004)

14. Symbol Error Rate (SER)
With , can also derive the SER
For N-ary PSK,

15. Symbol Error Rate

16. SER for D-NPSK
We can also analytically derive the SER for DPSK modulation with coherent detection

17. QAM Signal Design
Typical 8, 16-QAM Signal Constellation

18. Received PDF and decision boundaries for 16-QAM signals

19. QAM Signal Detection : Low Nonlinearity
Cannot rotate the received signal phase by since we need to know the transmitted signal power!
Alternative approach: Signal design/processing to approximate ML boundaries with straight lines
Signal Processing Techniques
Signal phase pre-compensation: pre-rotate signal phase by mean nonlinear phase shift
Nonlinear Phase noise (NLPN) post-compensation: rotate received phase by (Kahn and Ho 2004)

20. Phase Pre-comp. and NLPN post-comp.
Phase Pre-comp. with NLPN post-comp
L=3000 km
Pavg= -13 dBm

21. QAM Signal Detection : High Nonlinearity
ML boundaries separate into 3 intervals
Can associate to the three input powers, then rotate by corresponding
For input power and noise power ,

22. Signal Constellation Optimization
Not a convex optimization problem for non-Gaussian noise (Johnson and Orsak (T.comm. 1993), Kearsley (NIST 2001), Foschini, Gitlin and Weinstein (Bell Sys. Tech. Journal 1973)
4 signal points optimization
1-3
2-2

23. Signal Constellation Optimization

24. Conclusions
ML decision boundaries is derived for PSK/DPSK systems in presence of nonlinear phase noise with distributed amplification
Allow easy implementation of optimal ML detection and allow analytical derivation of the SER for N-ary PSK/DPSK schemes and QAM systems with high nonlinearity
Phase rotation techniques to enhance performance using straight line decision boundaries for QAM systems with low nonlinearity
Preliminary optimization results

25. Future Work Further study on constellation optimizations
Dispersion effects
Experiments~~~~~~~

26. Acknowledgements
Prof. Kahn
Ezra
Dany
Thank You!