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Ph.D. Thesis Defense Department of Electrical Engineering Stanford University March 10, 2008

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

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Ph.D. Thesis Defense Department of Electrical Engineering Stanford University March 10, 2008

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

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

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

  4. Long-haul fiber-optic communication systems Tech. Evolution: Optical amplifiers, Wavelength Division Multiplexing (WDM), Forward Error Correction (FEC) TAT-14: 64 x 10 Gb/s, (2001) TAT-12/13: 5 Gb/s, (1996) TPC5: 5Gb/s (1996) TAT-8: 280 Mb/s, (1988) Next technological breakthrough: Electronic signal processing! 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

  5. LO 3-dB coupler Delay 90° 90° 90° Laser LO MZ– Mach Zehnder Modulator Transmitter Coherent detection • 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 • 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. BPSK D-MPSK MPSK/QAM Receiver

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

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

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

  9. Impairments in long-haul systems with coherent detection • Noise limits communication system performance • BPSK / QPSK / DQPSK – phase noise • Laser phase noise • Amplified Spontaneous Emission (ASE) noise from inline amplifiers • 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

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

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

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

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

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

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

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

  17. Tail Probability of QPSK DQPSK

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

  19. Correlation MPSK BPSK

  20. for 40 GSym/s QPSK systems • Pulse shape: 33% RZ Gaussian Sampling points DCF SMF

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

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

  24. EQ fNL|Etot|2 EI Etot Nonlinear Regime EQ Etot n E EI Linear Regime Nonlinear phase noise (NLPN) • corrupted by Amplified Spontaneous Emission (ASE) noise from inline amplifiers • Kerr nonlinearity induced nonlinear phase shift: • Nonlinear phase noise or Gordon-Mollenauer effect EQ EQ EI EI Linear Regime Nonlinear Regime

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

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

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

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

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

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

  31. SER for D-MPSK Systems

  32. 16-QAM modulation formats • 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.

  33. 16-QAM transmitter Laser

  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 • 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. 16-QAM signal phase pre-compensation • 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 Without phase pre-comp. With phase pre- comp. Pavg= -2.5 dBm

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

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

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

  39. Amplifier Amplifier Amplifier Design of inline amplifier gains and spacings to mitigate phase noise • 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?

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

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

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

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

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

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

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

  47. Comparison of various phase noises in long-haul systems

  48. Summary • 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 • System BER characterization in presence of IFWM, NLPN • Appropriate signal processing techniques and system designs for performance improvements • Much more work remains to understand/improve long-haul system performance!

  49. 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, “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. • 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,"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.

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

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