1. Signal Processing Techniques for Coherent Fiber- Optic Communication Systems in Presence of Kerr Nonlinearity Ph.D. Thesis Defense Department of Electrical Engineering Stanford University March 10, 2008 Alan Pak Tao Lau

2. 2 Outline Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced system impairments Kerr nonlinearity induced system impairments Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) Summary Summary

3. 3 Long-haul fiber-optic communication systems Terrestrial link (1500 ~ 3000 km) Submarine link (5000 ~ 10000 km)

4. 4 Tech. Evolution: Optical amplifiers, Wavelength Division Multiplexing (WDM), Wavelength Division Multiplexing (WDM), Forward Error Correction (FEC) Forward Error Correction (FEC) Long-haul fiber-optic communication systems TAT-8: 280 Mb/s, (1988) TAT-12/13: 5 Gb/s, (1996) TAT-14: 64 x 10 Gb/s, (2001) TPC5: 5Gb/s (1996) Bit Rate: 2.5 Gb/s ->10 Gb/s -> 40 Gb/s -> 100 Gb/s Spectral Efficiency: 0.0005 b/s/Hz -> 0.2 b/s/Hz -> 0.8 b/s/Hz Next technological breakthrough: Electronic signal processing!

5. 5 Coherent detection Traditionally in fiber-optics, information encoded in pulse energy – On-Off Keying (OOK) Traditionally in fiber-optics, information encoded in pulse energy – On-Off Keying (OOK) Differentially coherent detection – information encoded in phase difference between neighboring symbols: DPSK, DQPSK Differentially coherent detection – information encoded in phase difference between neighboring symbols: DPSK, DQPSK Coherent detection – information encoded in both phase and amplitude: QPSK, 16-QAM Coherent detection – information encoded in both phase and amplitude: QPSK, 16-QAM Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM modulation format in future. Currently, most interested in QPSK, DQPSK for 100 Gb/s. 16-QAM modulation format in future. LO 3-dB coupler BPSK MPSK/QAM 90° LO D-MPSK 90° Delay Receiver 90° Transmitter Laser MZ– Mach Zehnder Modulator

6. 6 Digital Signal Processing Currently available: 40 Gb/s FEC encoder/decoder Currently available: 40 Gb/s FEC encoder/decoder 40 Gb/s clock/data recovery 40 Gb/s clock/data recovery 10 Gb/s MLSD 10 Gb/s MLSD Arbitrary signal generation/detection, arbitrary signal processing Arbitrary signal generation/detection, arbitrary signal processing Communication theory / signal processing Communication theory / signal processing techniques becomes practically techniques becomes practically relevant and important !! relevant and important !! Information theory is also getting more attention Information theory is also getting more attention Fiber-optic channel is different from wireless / wireline communications Fiber-optic channel is different from wireless / wireline communications

7. 7 Signal propagation in optical fibers Erbium Doped Fiber Amplifiers (EDFA) Erbium Doped Fiber Amplifiers (EDFA) Nonlinear Schrödinger Equation (NLSE) Mode Pulse envelope Carrier frequency (~193 THz or 1550 nm) Japan USA Dispersion Compensating Fibers (DCF) Dispersion Compensating Fibers (DCF) amplifier Attenuation Chromatic Dispersion SMF DCF Kerr nonlinearity Kerr nonlinearity – not a LTI effect Kerr nonlinearity – not a LTI effect Dominant transmission impairment in long-haul systems! Dominant transmission impairment in long-haul systems!

8. 8 Kerr Nonlinearity in optical fibers induced intensity dependent refractive index induced intensity dependent refractive index Electric Polarization of molecules Electric Polarization of molecules Kerr induced nonlinear phase shift Kerr induced nonlinear phase shift Linear Regime EIEI EQEQ E Nonlinear Regime EIEI EQEQ E

9. 9 Impairments in long-haul systems with coherent detection Noise limits communication system performance Noise limits communication system performance BPSK / QPSK / DQPSK – phase noise BPSK / QPSK / DQPSK – phase noise Laser phase noise Laser phase noise Amplified Spontaneous Emission (ASE) noise from inline amplifiers Amplified Spontaneous Emission (ASE) noise from inline amplifiers Receiver shot/thermal noise Receiver shot/thermal noise Noise and inter-symbol interference (ISI) resulting from Kerr nonlinearity and its interaction with amplifier noise and other propagation effects Amplitude noise and phase noise are generally different Amplitude noise and phase noise are generally different

10. 10 Outline Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) Summary Summary

11. 11 Outline Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced phase noise Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Nonlinear Phase Noise (NLPN) Summary Summary

12. 12 Intra-channel four-wave mixing (IFWM) Pulse trains Pulse trains First-order perturbation theory First-order perturbation theory Linear solution to NLSE IFWM: not FWM! IFWM: not FWM! Nonlinear perturbation Pulse shape Phase modulated info IFWM is ISI caused by interaction of dispersion and Kerr nonlinearity IFWM is ISI caused by interaction of dispersion and Kerr nonlinearity (NLSE)

13. 13 IFWM - induced phase noise IFWM-induced phase noise on time slot 0 IFWM-induced phase noise on time slot 0 Highly nonlinear ISI Highly nonlinear ISI Each term in summation is a triple product of info. symbols Each term in summation is a triple product of info. symbols Triple product comes from future and past symbols combined in a strange way Triple product comes from future and past symbols combined in a strange way Too complicated to be fully exploited (at present) Too complicated to be fully exploited (at present) Considered noise most of the time Considered noise most of the time

14. 14 Probability distribution of Need to know the probability distribution of to analytically characterize system bit error ratio (BER) Need to know the probability distribution of to analytically characterize system bit error ratio (BER) Empirical distribution of only. BER obtained by numerical methods Empirical distribution of only. BER obtained by numerical methods Is it possible to at least approximate the probability distribution ? Is it possible to at least approximate the probability distribution ? Ho, PTL vol. 17, no. 4, Apr. 2005, pp. 789-791

15. 15 Insight: terms in are pairwise independent. For example, Insight: terms in are pairwise independent. For example, are independent are independent A consequence of modulo addition in phase of A consequence of modulo addition in phase of Not jointly independent Not jointly independent Approximate probability distribution Approximation:

16. 16 for QPSK/DQPSK systems QPSK DQPSK DQPSK: Group terms from that are correlated with each other DQPSK: Group terms from that are correlated with each other

17. 17 Tail Probability of QPSKDQPSK

18. 18 are correlated are correlated Exploiting Correlation structure of Wei and Liu, Optics Letters, Vol. 28, no. 23, pp. 2300-2302, 2003 No analytical knowledge of correlation structure of IFWM-induced phase noise No analytical knowledge of correlation structure of IFWM-induced phase noise

19. 19 Correlation MPSK BPSK

20. 20 for 40 GSym/s QPSK systems for 40 GSym/s QPSK systems L (km) SMF80.25171.2 DCF16.6-855.3 Sampling points SMF DCF Pulse shape: 33% RZ Gaussian Pulse shape: 33% RZ Gaussian

21. 21 Exploiting Optimal linear prediction of Optimal linear prediction of 1.8 dB improvement when dominates 1.8 dB improvement when dominates 0.8-1.2 dB improvement in presence of amplifier noise 0.8-1.2 dB improvement in presence of amplifier noise

22. 22 IFWM-induced phase noise and amplitude noise Received amplitude uncorrelated with phase noise for QPSK/DQPSK systems Received amplitude uncorrelated with phase noise for QPSK/DQPSK systems A.P.T. Lau, S. Rabbani and J.M. Kahn, to appear in OSA/IEEE JLT

23. 23 Outline Long-haul fiber-optic communication systems Long-haul fiber-optic communication systems Coherent detection, DSP, communication theory Coherent detection, DSP, communication theory Kerr nonlinearity induced phase noise Kerr nonlinearity induced phase noise Intra-channel four-wave mixing (IFWM) Intra-channel four-wave mixing (IFWM) Nonlinear Phase Noise (NLPN) Summary Summary

24. 24 Nonlinear phase noise (NLPN) Kerr nonlinearity induced nonlinear phase shift: Kerr nonlinearity induced nonlinear phase shift: corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiers corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiers EIEI EQEQ Linear Regime EIEI EQEQ Nonlinear Regime EIEI EQEQ Linear Regime E n E tot Nonlinear Regime EIEI EQEQ E tot  NL  |E tot | 2 Nonlinear phase noise or Gordon-Mollenauer effect Nonlinear phase noise or Gordon-Mollenauer effect

25. 25 Joint probability distribution (PDF) of received amplitude and phase K.P. Ho “Phase modulated Optical Communication Systems,” Springer 2005 Transmitted signal with power, phase Transmitted signal with power, phase

26. 26 PDF and maximum likelihood (ML) decision boundaries for 40G Sym/s QPSK Signals L=5000 km, P=-4 dBm, L=5000 km, P=-4 dBm,

27. 27 Maximum Likelihood (ML) Detection To implement ML detection, need to know the ML boundaries To implement ML detection, need to know the ML boundaries Need to know Need to know With,can either de- rotate the received phase or use a lookup table With,can either de- rotate the received phase or use a lookup table

28. 28 With approximations With approximations ML decision boundary it can be shown that it can be shown that

29. 29 Received phase rotation by Before rotation Before rotation After rotation After rotation Straight line ML decision boundaries after rotation Straight line ML decision boundaries after rotation

30. 30 Symbol Error Rate (SER) for MPSK Systems Numerical results Analytical

31. 31 SER for D-MPSK Systems

32. 32 16-QAM modulation formats High spectral efficiency. Together with coding, approach information- theoretic limits. High spectral efficiency. Together with coding, approach information- theoretic limits. For a given bit rate, reduce inter-symbol interference compared to 2-PSK or 4-PSK. For a given bit rate, reduce inter-symbol interference compared to 2-PSK or 4-PSK.

33. 33 16-QAM transmitter Laser

34. 34 Maximum likelihood detection for 16- QAM systems in presence of NLPN No analytical formula for ML decision boundaries for 16- QAM system as power of signal points not constant No analytical formula for ML decision boundaries for 16- QAM system as power of signal points not constant Boundaries distorted from straight lines Boundaries distorted from straight lines Can we design/process the signals at the transmitter and/or receiver such that ML detection can be better approximated by straight lines?

35. 35 16-QAM signal phase pre-compensation With phase pre- comp. Without phase pre-comp. P avg = -2.5 dBm Modes of conditional probability distribution corresponding to each signal point do not form a square constellation Modes of conditional probability distribution corresponding to each signal point do not form a square constellation Pre-rotate phase by the negative of mean nonlinear phase shift Pre-rotate phase by the negative of mean nonlinear phase shift

36. 36 NLPN post-compensation Rotate the received phase by proportional to received intensity for phase noise variance minimization Rotate the received phase by proportional to received intensity for phase noise variance minimization With phase pre- comp. only Phase pre- comp. with NLPN post-comp. Ho and Kahn, JLT vol.22 no. 3, Mar. 2004 Ly-Gagnon and Kikuchi, Paper 14C3-3, OECC 2004

37. 37 Performance of phase rotation methods in 16-QAM systems (No phase comp.)

38. 38 Signal Constellation Optimization in Presence of NLPN QPSK 1-2-1 1-3 2-2 A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, pp. 3008-3016, Oct 2007

39. 39 Design of inline amplifier gains and spacings to mitigate phase noise Amplifier Conventionally, amplifiers uniformly spaced along the link and the their gain exactly compensates for the signal loss in the previous span Conventionally, amplifiers uniformly spaced along the link and the their gain exactly compensates for the signal loss in the previous span Better design of amplifier gains/spacings in the link to mitigate phase noise? Better design of amplifier gains/spacings in the link to mitigate phase noise?

40. 40 Design of inline amplifier gains and spacings to mitigate phase noise Linear Phase Noise Linear Phase Noise Amplifier Nonlinear Phase Noise Nonlinear Phase Noise EIEI EQEQ E n

41. 41 Variance of phase noise Linear phase noise variance – for high SNR, Linear phase noise variance – for high SNR, Nonlinear phase noise variance Nonlinear phase noise variance Signal after amplifier: Signal after amplifier: where

42. 42 Minimization of joint phase noise variance When, the optimization problem can be shown to be convex in. When, the optimization problem can be shown to be convex in. are uncorrelated are uncorrelated Minimize the variance of total phase noise Minimize the variance of total phase noise

43. 43 Uniformly spaced amplifiers with per- span loss compensation Distributed amplification is not optimal ! Distributed amplification is not optimal ! (contrary to Yariv, Opt. Lett., vol. 15, no. 19,1990 ) (contrary to Yariv, Opt. Lett., vol. 15, no. 19,1990 )

44. 44 Optimal amplifier spacing in presence of NLPN Define span length Y*=L/N*. As A.P.T. Lau and J.M. Kahn, paper JWB23, OSA COTA, June 2006 Overall phase noise variance reduction by 40%. Overall phase noise variance reduction by 40%. Optimal N Optimal N

45. 45 Amplifier gain optimization in presence of NLPN Reduction in variance: 23% (3000 km), 81% (10000 km) Reduction in variance: 23% (3000 km), 81% (10000 km) Terrestrial link (3000 km) Submarine link (10000 km)

46. 46 Joint amplifier spacing and gain optimization in presence of NLPN Reduction of variance: 45% (3000 km), 83% (10000 km) Reduction of variance: 45% (3000 km), 83% (10000 km) A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, Mar 2006, pp.1334-1341 Terrestrial link (3000 km) Submarine link (10000 km)

47. 47 Comparison of various phase noises in long-haul systems ASE induced (Linear) phase noise IFWM-induced phase noise Nonlinear Phase Noise Signal Power Amplifier noise power System Length Remarks Dominant in terrestrial links Dominant in Submarine links

48. 48 Summary Coherent detection and DSP technologies results in the relevance and importance of communication theory in next- generation long-haul communication system design Coherent detection and DSP technologies results in the relevance and importance of communication theory in next- generation long-haul communication system design Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, NLPN Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, NLPN System BER characterization in presence of IFWM, NLPN System BER characterization in presence of IFWM, NLPN Appropriate signal processing techniques and system designs for performance improvements Appropriate signal processing techniques and system designs for performance improvements Much more work remains to understand/improve long-haul system performance! Much more work remains to understand/improve long-haul system performance!

49. 49 Research Papers Research Papers A.P.T. Lau and J.M. Kahn, “Design of Inline Amplifiers Gain and Spacing to Minimize Phase Noise in Optical Transmission Systems,” OSA/IEEE Journal of Lightwave Technology, Mar 2006, pp.1334-1341. A.P.T. Lau and J.M. Kahn, “Design of Inline Amplifiers Gain and Spacing to Minimize Phase Noise in Optical Transmission Systems,” OSA/IEEE Journal of Lightwave Technology, Mar 2006, pp.1334-1341. A.P.T. Lau and J.M. Kahn, “Signal Design and Detection in Presence of Nonlinear Phase Noise,” OSA/IEEE Journal of Lightwave Technology, vol. 25, no. 10, pp. 3008-3016, Oct. 2007. A.P.T. Lau and J.M. Kahn, “Signal Design and Detection in Presence of Nonlinear Phase Noise,” OSA/IEEE Journal of Lightwave Technology, vol. 25, no. 10, pp. 3008-3016, Oct. 2007. A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the Statistics of Intra-channel Four-Wave Mixing in Phase-Modulated Optical Communication Systems,” to appear in OSA/IEEE Journal of Lightwave Technology. A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the Statistics of Intra-channel Four-Wave Mixing in Phase-Modulated Optical Communication Systems,” to appear in OSA/IEEE Journal of Lightwave Technology. E. Ip, A.P.T. Lau, D.J.F. Barros and J.M. Kahn (Invited), “Coherent Detection in Optical Fiber Systems,” to appear in OSA Optics Express, 2008. E. Ip, A.P.T. Lau, D.J.F. Barros and J.M. Kahn (Invited), “Coherent Detection in Optical Fiber Systems,” to appear in OSA Optics Express, 2008. A.P.T. Lau and J.M. Kahn, “Non-Optimality of Distributed Amplification in Presence of Nonlinear Phase Noise”, paper JWB23, OSA Coherent Optical Technologies and Applications (COTA), Whistler, BC, Canada, June 2006. A.P.T. Lau and J.M. Kahn, “Non-Optimality of Distributed Amplification in Presence of Nonlinear Phase Noise”, paper JWB23, OSA Coherent Optical Technologies and Applications (COTA), Whistler, BC, Canada, June 2006. A.P.T. Lau and J.M. Kahn,"16-QAM Signal Design and Detection in Presence of Nonlinear Phase Noise," Paper TuA4.4, 2007 IEEE/LEOS Summer Topical Meetings, Portland, OR, July 23-25, 2007. A.P.T. Lau and J.M. Kahn,"16-QAM Signal Design and Detection in Presence of Nonlinear Phase Noise," Paper TuA4.4, 2007 IEEE/LEOS Summer Topical Meetings, Portland, OR, July 23-25, 2007. A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the statistics of Intra-channel Four-Wave Mixing in phase modulated systems,” paper JThA52, OFC/NFOEC, San Diego, CA, Feb. 24-28, 2008. A.P.T. Lau, S. Rabbani and J.M. Kahn, “On the statistics of Intra-channel Four-Wave Mixing in phase modulated systems,” paper JThA52, OFC/NFOEC, San Diego, CA, Feb. 24-28, 2008.

50. 50 Acknowledgements Prof. Joseph Kahn Prof. Joseph Kahn Prof. Shanhui Fan Prof. Shanhui Fan Prof. David Miller Prof. David Miller Prof. John Gill Prof. John Gill Group members: Ezra, Rahul, Dany, Daniel, Mahdieh, Jeff, Sahand Group members: Ezra, Rahul, Dany, Daniel, Mahdieh, Jeff, Sahand

51. 51 Acknowledgements Prof. Frank Kschischang, University of Toronto Prof. Frank Kschischang, University of Toronto

52. 52 Acknowledgements Financial Support Financial Support National Science and Engineering Research Council (NSERC) of Canada National Science and Engineering Research Council (NSERC) of Canada Macau Special Administrative Region Post-Graduate Scholarship, Macau, China Macau Special Administrative Region Post-Graduate Scholarship, Macau, China

53. 53 Thank you!

54. 54 How good is the variance measure? BER/Capacity optimized at close vicinity of N that minimize phase noise variance BER/Capacity optimized at close vicinity of N that minimize phase noise variance

55. 55 Per-Span Loss Compensation (fixed N) Earlier amplifiers spaced closer together due to asymmetry of contribution of nonlinear phase noise Earlier amplifiers spaced closer together due to asymmetry of contribution of nonlinear phase noise Reduction of variance: 11% (3000 km) 49% (10000 km) Reduction of variance: 11% (3000 km) 49% (10000 km)

56. 56 Optimal Power Profile Power profile Power profile Let Let Phase noise variance Phase noise variance Euler Characteristic Equation Euler Characteristic Equation

57. 57 Optimal Power Profile A.P.T. Lau and J.M. Kahn, IEEE PTL, pp. 2514-2516 Dec. 2006. Phase noise variance reduction of 60% when Phase noise variance reduction of 60% when

58. 58 Received PDF and ML decision boundaries for 16-QAM signals Probability Distribution Decision Boundaries

59. 59 Research Outlook Advances in photonic/electronic devices allows one to start a research problem in fiber-optic communications by Advances in photonic/electronic devices allows one to start a research problem in fiber-optic communications by Underlying physics of signal transmission yet to be fully understood Underlying physics of signal transmission yet to be fully understood Fiber-optic communications will be even more interdisciplinary in the future! Fiber-optic communications will be even more interdisciplinary in the future! “Consider an arbitrarily modulated signal x(t)...”

60. 60 IFWM-induced phase noise IFWM induced phase noise on bit 0 IFWM induced phase noise on bit 0 IFWM induced perturbations IFWM induced perturbations

61. 61 overall length L tot with N spans SMF DCF DCM SMF DCF DCM

62. 62 Nonlinear Phase Noise Experiments ECOC ’06 Post-Deadline Paper OFC ‘07

63. 63 Cross phase modulation (XPM) in WDM systems Cross-phase modulation (XPM) Cross-phase modulation (XPM) Difference in group velocity -- Walk Off Effect Difference in group velocity -- Walk Off Effect Pulse waveform distortion negligible compared to walk off in modeling nonlinear phase noise variance Pulse waveform distortion negligible compared to walk off in modeling nonlinear phase noise variance

64. 64 XPM induced nonlinear phase noise Terrestrial system: 40Gb/s, 50 GHz spacing, D=17 ps/(km-nm): Lw=3.9 km Terrestrial system: 40Gb/s, 50 GHz spacing, D=17 ps/(km-nm): Lw=3.9 km Submarine system: Lw=15 km Submarine system: Lw=15 km

65. 65 Orthogonal Frequency Division Multiplexing (OFDM) Well-known in wireless/DSL Well-known in wireless/DSL Multiplexing of large number of low rate sub-carriers Multiplexing of large number of low rate sub-carriers FFT based processing FFT based processing … OFDM Single Carrier

66. 66 OFDM in Fiber-Optics Wireless / DSL Fiber-Optics Fiber-Optics Spectrum Confinement Much more confined than SC Same EqualizationComplexity in OFDM vs. in SC in OFDM vs. in SCSame Channel Equalization Bit loading to achieve info. theoretic capacity Dispersion: High signal peaks Peak-to-Avg Power Ratio (PAPR) Fiber nonlinearity! SC – Single Carrier

67. 67 Nonlinearity induced impairments in Optical OFDM Nonlinear perturbations originate from FWM products between sub- carriers with perfect phase matching Nonlinear perturbations originate from FWM products between sub- carriers with perfect phase matching For a system with K sub- carriers, noise variance at sub-carrier k is given by For a system with K sub- carriers, noise variance at sub-carrier k is given by A.P.T. Lau, D.J. Barros and J.M. Kahn, in preparation.