Signal Design and Analysis in Presence of Nonlinear Phase Noise

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

5. Fiber Fiber Fiber Optical Amp. Optical Amp. Optical Amp. Phase Noise for coherent systems • 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 Ho and Kahn (JLT vol. 22 no. 3, Mar. 2004) Center phase rotation

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 PDF Decision Boundaries

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. 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 2-2 1-3

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!