Ph.D. Candidate, Department of Electrical Engineering Stanford University

1. The Marriage of Photonics and Communication Theory for 100 Gb/s Long-Haul and Ethernet Fiber-Optic Transmissions presented at The Hong Kong University of Science and Technology Dec. 7th, 2007 Alan Pak Tao Lau Ph.D. Candidate, Department of Electrical Engineering Stanford University

2. Part I – 100 Gb/s long-haul • 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) • WDM effects and optical OFDM • 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 -> 100/160Gb/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. Part I – 100 Gb/s Long-haul • 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) • WDM effects and optical OFDM • Summary

11. Part I – 100 Gb/s Long-haul • 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) • WDM effects and optical OFDM • Summary

12. Intra-channel four-wave mixing (IFWM) • A form of inter-symbol interference (ISI) due to the term amplifier DCF SMF

13. 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!

14. 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

15. 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

16. 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:

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

18. Tail Probability of QPSK DQPSK

19. 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

20. Correlation MPSK BPSK

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

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

23. 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, subm. OSA/IEEE JLT Sept. 2007

24. Part I – 100 Gb/s Long-haul • 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) • WDM effects and optical OFDM • Summary

25. 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

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

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

28. 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

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

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

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

32. SER for D-MPSK Systems

33. 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.

34. 16-QAM transmitter Laser

35. 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?

36. 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

37. 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.

38. Performance of phase rotation methods in 16-QAM systems (No phase comp.) A.P.T. Lau and J.M. Kahn, OSA/IEEE JLT, pp. 3008-3016, Oct 2007

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

40. Part I – 100 Gb/s Long-haul • Long-haul fiber-optic communication systems • Coherent detection, DSP, communication theory • Kerr nonlinearity induced perturbations • Intra-channel four-wave mixing (IFWM) • Nonlinear Phase Noise (NLPN) • WDM effects and optical OFDM • Summary

41. Summary – 100Gb/s Long-Haul • Coherent detection and DSP technologies results in the relevance and importance of communication theory in long-haul system design for 100 Gb/s transmission • Performance of long-haul systems limited by Kerr nonlinearity induced system impairments such as IFWM, NLPN • System BER characterization • Appropriate signal processing techniques for performance improvements • Much more work remains to understand/improve long-haul system performance!

42. Part II – 100Gb/s Ethernet using multimode fiber • Motivation and background • Principal Modes and adaptive optics using spatial light modulator • System optimization framework and experimental results

43. Ethernet Roadmap • Who needs 100G Ethernet? • Not me (individual user) ~ • Data centers (e.g. Google) and other large enterprise/core switches • Multimode Fiber (MMF) widely deployed. Want to reuse it for cost effectiveness (just like DSL)

44. 100 Gb/s Ethernet • IEEE Higher Speed Study Group formed July ‘06 • Standards expected to be finalized by 2010 • 100Gb/s transmission over 100 m of multi-mode fiber

45. Multimode Fibers (MMF) MMF SMF Mode Pulse envelope Ideal Modes • Spatially orthogonal (typical MMF has 100 modes) having well-defined propagation speeds • Propagate without cross-coupling in ideal fiber • Significant mode coupling in real installed fibers

46. Modal Dispersion in MMF MMF t t Tx • MMF systems – OOK with direct detection • Different modes have different – different speed • Single pulse in – many pulses out (modal dispersion or ISI). • Linear ISI – identical to ISI in wireless/wireline

47. Part II – 100Gb/s Ethernet using multimode fiber • Motivation and background • Principal Modes and adaptive optics using spatial light modulator • System optimization framework and experimental results

48. Principal Modes in Multimode Fiber • Input electric field Propagation matrix that captures mode coupling • Group delay operator • Principal Modes (PM) – linear combinations of ideal modes • Single pulse in – single pulse out (well defined group delay ) • Insight – input electric field design to excite single PM! S. Fan and J. M. Kahn, Optics Letters, vol. 30, no. 2, pp. 135-137, 2005

49. Spatial Light Modulator (SLM) • 2-D array of mirrors with the reflectance of each mirror (vi) can be controlled. • Sort of a 2-D spatial filter ky y x kx MMF SLM Laser Collimating lens

50. Fourier Lens Iout(t) Photo-Detector AdaptiveAlgorithm Clock & DataRecovery Rec.Data Multimode Fiber Spatial LightModulator Iin(t) ISIEstimation Trans.Data OOKModulator ISI ObjectiveFunction Transmitter Receiver Low-Rate Feedback Channel Adaptive Transmission Scheme Impulse response Eye opening -0.4 -0.1 +0.3 +0.8