1. Performance Evaluation of DPSK Optical Fiber Communication Systems Jin Wang April 22, 2004 DPSK: Differential Phase-Shift Keying, a modulation technique that codes information by using the phase difference between two neighboring symbols.

2. 2 Outline 1.Introduction 2.Bit Error Analysis in DPSK Systems 3.Transmission Impairments in DPSK Systems 4.Electrical Equalizer in DPSK Systems 5.Nonlinear DPSK Systems

3. 3 1.Introduction

4. 4 Typical Long-Hual Optical Communication System Optical Transmitter Communication Channel Optical Receiver One Span ~ 80 km for terrestrial system Optical Amplifier Optical Fiber  Performance measure: Bit Error Ratio (BER). Required: 10 -9 ~ 10 -14.  Dominant noise is Amplified-Spontaneous-Emission (ASE) noise from optical amplifiers.  Capacity record (2002): 40 Gb/s/channel, 64 channel, 4000 km, BER < 10 -12. Using DPSK. Optical Filter Elec. Filter Photodetector Decoder Optical signal Bits Information Bits Laser Modulator Optical signal Encoder Symbols

5. 5 Modulation Formats One or more field properties can be modulated to carry information. Example:  On-off keying (OOK): binary amplitude modulation  Binary DPSK, Quadrature DPSK : phase modulation  Quadrature Amplitude Modulation (QAM): amplitude and phase modulation Amplitude Polarization PhaseFrequency Electric field of optical carrier: E(t) = êAexp(j  t+ 

6. 6 DPSK in Optical Systems 1.Early Experiments ( ~ 1990)  For the improvement of receiver sensitivity (At BER 10 -9, 1000 photons/bit for OOK v.s. < 100 photons/bit for DPSK)  Low bit rate: ~ 1 Gb/s 2.Cooling ( 90’s ) After the Advent of Optical Amplifiers  High sensitivity OOK receiver (<100 photons/bit) can be realized with the aid of optical amplifier (Ex. Erbium-Doped Fiber Amplifier)  Complicated DPSK transmitter and receiver  Stringent requirements on laser linewidth (< 1% of data rate) 3.Recent Revival ( ~ 2002)  For the improvement of receiver sensitivity (< 50 photons/bit), reduction of fiber nonlinearity and increase of spectrum efficiency  Interferometric demodulation + direct detection  Data rates of 10 Gb/s and 40 Gb/s  relaxed linewidth requirements

7. 7 On-Off Keying (OOK) Symbol constellation for OOK Im{E} Re{E} 0 1 Bits E(t)E(t) Optical filter Electrical filter G Laser Mod. i i 01 Probability density function of i E(t)E(t) t t Non-return-to-zero (NRZ) OOK Signal Return-to-zero OOK Signal 1 0 1 1  Bit set {0, 1}  symbol set {0, 1}.  One symbol transfers one bit information.  Easy to modulate and detect. Signal-ASE beat noise is dominant noise OOK System: E(t)E(t) Detected Signal:

8. 8 Binary DPSK (2-DPSK) Laser Mod. Differential Encoder Bits Elec. Filter Optical Filter TsTs Interferometer 0 0 10 Re{E} Im{E} 11 1 i 1 1 E(t)E(t) G NRZ-2-DPSK signal t 1 0 0 1 t RZ-2-DPSK signal  Bit set {0, 1}  symbol set {-1, 1} i.e. {e j , e j0 }  One symbol transfers one bit information  Bit 0: leave phase alone, bit 1: introduce a  phase change i +  2-DPSK System: EsEs E(t)E(t) E(t)E(t) Symbol constellation

9. 9 Quadrature DPSK (4-DPSK) 10 01 10 11 01 00 11 00 EIEI EQEQ iIiI iQiQ  Bit-pair set {00,01,10,11}  symbol set {e ± j  /4, e ± j3  /4 }  One symbol transfers TWO bits of information. T s = 2T b.  Signal bandwidth is only one half of the bit rate. Elec. LPF TsTs TsTs 90 o Elec. LPF iIiI iQiQ Laser Mod. Differential Encoder Bits Optical BPF E(t)E(t) G 4-DPSK System:

10. 10 Transmission Impairments - I Chromatic Dispersion (CD)  Origin: The refractive index of fiber is frequency dependent.  Analogy:  Linear effect. Baseband TF of fiber:  Phenomenon: pulse broadening  intersymbol interference (ISI). 40 km D=17 ps/km/nm 11 0 1 40 km D =17 ps/km/nm CD Parameter, 3 ~ 17 ps/km/nm Fiber length 10 Gb/s signal

11. 11 Transmission Impairments - II Fiber Nonlinearity (FNL)  Origin: The refractive index of fiber is power dependent.  Nonlinear Schrödinger equation (wave equation in fiber):  Effects:  Self-phase modulation (SPM)  spectrum broadening.  Cross-phase modulation (XPM)  spectrum broadening.  Four-wave mixing (FWM)  noise amplification. interchannel crosstalk.  Spectrum broadening + CD  intersymbol interference. CD Fiber Loss FNL  No analytic solutions for general input, numerical approach necessary (split-step FFT)

12. 12 Transmission Impairments - III Polarization Mode Dispersion (PMD)  Origin:  Principal states model  Linear effect in optical domain. Baseband TF of fiber with PMD:  PMD stochastic. PMD causes ISI. Impact  . ideal fiber real fiber slow axis fast axis  Input field E 0 (t)  : power splitting ratio.  : differential group delay.

13. 13 Challenges for Optical Communication Systems ChallengesSolutions Transmission at ultra high bit rate requires extremely low CD. Reduce signal bandwidth by transmitting multi- bits with one symbol. (4-DPSK) Long transmission distance causes significant FNL. Reduce FNL by decreasing signal power and its variation. (2-DPSK and 4-DPSK) Ultra short bit period implies high sensitivity to PMD. Increase symbol period transmitting multi-bits with one symbol. (4-DPSK) Fixed channel bandwidth, increasing bit rate. Improve spectrum efficiency by transmitting multi-bits with one symbol. (4-DPSK)

14. 14 DPSK vs. OOK (ASE dominated)  2-DPSK vs. OOK: Power   FNL , Power variation   FNL   4-DPSK vs. OOK: Spectrum efficiency , CD , PMD , FNL . 0369 1 2 3 4 Relative Required Light Power (dB) to Achieve 10 -9 BER in Ideal System 121518-3 2 4 2 8 16 DPSK PAM (Pulse Amplitude Modulation) OOK is 2-PAM 16 8 4 Spectral Efficiency (bits / symbol) 1 Relative Bandwidth (Hz)

15. 15 How Robust is DPSK? CD PMD Impacts on DPSK not quantified before. FNL Reasons for the dearth of impact analysis:  The BER of DPSK systems has been difficult to calculate, because of the squaring effect of photodetector.  The interaction of CD and FNL in fiber increases the difficulty of modeling optical noise in fiber.

16. 16 2.Bit Error Analysis in DPSK Systems

17. 17 BER Calculation using Eigenfunction Expansion Bits e(t)e(t) Optical BPF Electrical LPF G Laser Mod. i |.| 2 i(t)i(t)  Square in time domain  Convolution in frequency domain  The 2nd kind of homogeneous Fredholm integral equation:  Eigenfunction expansion:  2 distribution  Neglect fiber nonlinearity K(f, f’) Hermitian {  m (f)} is a complete orthornormal function set Signal Noise

18. 18 BER calculation in DPSK system – II Moment generating function (MGF) of i(t) is  (s), i.e.,  (s) = E[e si ] = Laplace transform of PDF of i(t) L -1 PDF of i(t)BER (CDF of i(t)) We use saddle point integration method to calculate the integral of MGF.saddle point integration method One more step to obtain BER:  di One Integral

19. 19 Saddle Point Integration  Also called stationary phase method, especially in physics.  Basic idea: For the calculation of line integral : If amplitude f(u) changes slowly compared to phase q(u), the main contribution to the integral comes from very near u 0 where the phase is stationary, i.e, u q(u) u0u0

20. 20 Accuracy of BER calculation method  10 Gb/s system, with Gaussian optical filter and 5 th -order Bessel electrical filter. 2-DPSK 4-DPSK 2-DPSK 4-DPSK OSNR is optical signal-to-noise ratio

21. 21 3.Transmission Impairments in DPSK Systems

22. 22 Power penalty of CD Power Penalty: To account for the transmission impairments, the increase in the optical power to maintain a fixed BER such as 10 -9. D: CD parameter, R: Bit rate, L: fiber length 4-DPSK R: Bit rate, D: CD parameter, L: fiber length R 2 DL NRZ-2-DPSK RZ-OOK RZ-2-DPSK NRZ-OOK

23. 23 Power Penalty of PMD  : Differential group delay, T b : Bit period. RZ-4-DPSK NRZ-4-DPSK RZ-OOK and RZ-2-DPSK NRZ-OOK and NRZ-2-DPSK

24. 24 Link Distance Limitation due to PMD Fiber PMD parameter 0.25 ps/ NRZ-4-DPSK RZ-4-DPSK

25. 25 Power Penalty of Interferometer Phase Error TsTs   m path error  15º phase error 4-DPSK 2-DPSK

26. 26 4.Electrical Equalizer in DPSK Systems

27. 27 Electrical Equalizer in Optical Systems TdTd TdTd TdTd c1c1 c2c2 cMcM  From electrical low-pass filter Feed-forward equalizer (FFE) TsTs TsTs d 1 d2d2 Data-feedback equalizer (DFE) TsTs dNdN … … Decided bits  Electrical equalizer is used to reduce ISI caused by CD, PMD, etc.  Electrical equalizer is compact, flexbile, low-cost.  High speed electrical equalizers operate at 10 Gb/s and 40 Gb/s.  Tap weights can be adapted using Least-Mean-Square (LMS), Q-factor maximization and BER minimization schemes. T d may be symbol duration or a fraction of it.

28. 28 Equalizer based on LMS algorithm T + _  T …  c0c0 c1c1 cMcM ekek v(t)v(t) ++ +  kT T T … d1d1 dNdN DFE FFE + + ykyk IkIk     or 0 1 e k is minimized

29. 29 Performance of Electrical Equalizer DPSK - CD OOK - PMD OOK - CD DPSK - PMD

30. 30 5.Nonlinear DPSK Systems

31. 31 Nonlinear 2-DPSK and OOK Systems Transmitter Bits E(t)E(t) G 80 km, LEAF fiber DL = 280 ps/nm DCF fiber DL =  258 ps/nm Pulses: Chirped RZ (phase varies with power) NF: 4.5 dB  Total link distance 8000 km.  CD of green fiber + CD of blue fiber + CD of Pre, Post-Compensators  0 ( Local high dispersion, global low dispersion )  Pre-Compensator spreads pulses quickly, realizing quasi-linear transmission. Light loss in fiber: 0.2 dB/km Nonlinear parameter  : 1.5 /W/km noise Pre-Compensator Post-CompensatorReceiver DL =  1176 ps/nm

32. 32 BER Calculation in Nonlinear DPSK System  No noise model for general nonlinear DPSK or OOK system.  No BER calculation method for general nonlinear DPSK or OOK system.  Q-factor is not a reliable performance measure, especially for DPSK system (2~3 dB OSNR error).  In CRZ-DPSK or CRZ-OOK system, noise can be modeled as additive non-white Gaussian noise because of low fiber nonlinearity.  Non-white Gaussian noise model + eigenfunction expansion method yields accurate BER.

33. 33 Performance of Nonlinear OOK and DPSK  There exists an optimum optical power for both OOK and DPSK systems.  DPSK has lower BERs than OOK because of lower FNL. CRZ-OOK CRZ-DPSK Threshold

34. 34 Current Work 4-DPSK long-haul transmission experiment Fiber TX / MUX Coupler DMUX / RX 5.6 dB3 dB 4-10 dB SW 2 Raman DCF +21 dBm Coupler VOA 100 km BERT Preamp Raman Pol ScrDCF +21 dBm Coupler VOA SW 1 EDFA Recirculating Loop Fiber