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Performance Evaluation of DPSK Optical Fiber Communication Systems

Performance Evaluation of DPSK Optical Fiber Communication Systems. DPSK: D ifferential P hase- S hift K eying, a modulation technique that codes information by using the phase difference between two neighboring symbols. Jin Wang April 22, 2004. Outline. Introduction

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Performance Evaluation of DPSK Optical Fiber Communication Systems

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

  2. Outline • Introduction • Bit Error Analysis in DPSK Systems • Transmission Impairments in DPSK Systems • Electrical Equalizer in DPSK Systems • Nonlinear DPSK Systems

  3. Introduction

  4. Information Bits Photodetector Laser Optical signal OpticalFilter Decoder Symbols Optical signal Bits Elec.Filter Encoder Modulator Communication Channel Optical Receiver Optical Transmitter One Span ~ 80 km for terrestrial system Optical Fiber Optical Amplifier Typical Long-Hual Optical Communication System 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.

  5. Modulation Formats Electric field of optical carrier: E(t) = êAexp(jwt+f) 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 Frequency Phase

  6. DPSK in Optical Systems • 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 • 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) • 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. Opticalfilter LaserMod. i 0 1 On-Off Keying (OOK) OOK System: Bits E(t) G i Electricalfilter 1 0 1 1 E(t) Bit set {0, 1}  symbol set {0, 1}. One symbol transfers one bit information. Easy to modulate and detect. Non-return-to-zero (NRZ) OOK Signal E(t) t Return-to-zero OOK Signal t Detected Signal: Symbol constellation for OOK Signal-ASE beat noise is dominant noise Im{E} Probability density function of i Re{E} 0 1

  8. +  1 0 Im{E} 1 0 -1 1 i Re{E} 0 1 Binary DPSK (2-DPSK) 2-DPSK System: i Ts Elec.Filter E(t) Bits Differential Encoder Optical Filter Laser Mod. G Es Interferometer 1 0 0 1 E(t) Bit set {0, 1}  symbol set {-1, 1} i.e. {ej , ej0} One symbol transfers one bit information Bit 0: leave phase alone, bit 1: introduce a p- phase change NRZ-2-DPSK signal t E(t) RZ-2-DPSK signal t Symbol constellation

  9. 4-DPSK System: Ts Elec.LPF iI E(t) Bits Optical BPF Differential Encoder Laser Mod. G Ts iQ Elec.LPF 90o EQ iQ 00 00 11 01 10 11 01 01 10 EI 00 iI 11 10 01 11 10 11 01 00 00 10 Quadrature DPSK (4-DPSK) Bit-pair set {00,01,10,11}  symbol set {e± j/4, e± j3/4} One symbol transfers TWO bits of information. Ts= 2Tb. Signal bandwidth is only one half of the bit rate.

  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). CD Parameter, 3 ~ 17 ps/km/nm Fiber length 1 1 1 0 40 km D=17 ps/km/nm 40 km D =17 ps/km/nm 10 Gb/s signal

  11. CD FNL Fiber Loss 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 .  No analytic solutions for general input, numerical approach necessary (split-step FFT)

  12. fast axis slow axis ideal fiber real fiber 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  D. Input field E0(t) D : power splitting ratio. D: differential group delay.

  13. Challenges for Optical Communication Systems

  14. DPSK vs. OOK (ASE dominated) 4 • 2-DPSK vs. OOK: Power   FNL , Power variation   FNL  • 4-DPSK vs. OOK: Spectrum efficiency , CD  , PMD  , FNL . 16 16 8 8 3 DPSK Relative Bandwidth (Hz) Spectral Efficiency (bits / symbol) PAM (Pulse Amplitude Modulation) OOK is 2-PAM 4 4 2 2 2 1 1 0 3 6 9 -3 12 15 18 Relative Required Light Power (dB) to Achieve 10-9 BER in Ideal System

  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. Bit Error Analysis in DPSK Systems

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

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

  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 u0 where the phase is stationary, i.e, q(u) u u0

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

  21. Transmission Impairments in DPSK Systems

  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 . RZ-2-DPSK NRZ-OOK RZ-OOK NRZ-2-DPSK 4-DPSK R: Bit rate, D: CD parameter, L: fiber length R2DL D: CD parameter, R: Bit rate, L: fiber length

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

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

  25. Df Power Penalty of Interferometer Phase Error Ts 0.1 mm path error  15º phase error 4-DPSK 2-DPSK

  26. Electrical Equalizer in DPSK Systems

  27. Electrical Equalizer in Optical Systems Feed-forward equalizer (FFE) … Td Td Td From electrical low-pass filter c1 c2 cM  Decided bits d1 d2 dN Data-feedback equalizer (DFE) … Ts Ts Ts Td may be symbol duration or a fraction of it. 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.

  28.      Equalizer based on LMS algorithm FFE ek 1 v(t)  … T T ek c0 _ c1 cM + + + + 0  yk + + kT Ik dN d1 … T T <ek2> is minimized DFE or

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

  30. Nonlinear DPSK Systems

  31. Nonlinear 2-DPSK and OOK Systems E(t) Bits Post-Compensator Receiver Pre-Compensator Transmitter DL= 1176 ps/nm DL= 1176 ps/nm DCF fiber DL= 258 ps/nm Pulses: Chirped RZ (phase varies with power) noise G Light loss in fiber: 0.2 dB/km Nonlinear parameter : 1.5 /W/km 80 km, LEAF fiber DL = 280 ps/nm 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.

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

  34. Fiber Fiber Current Work 4-DPSK long-haul transmission experiment EDFA +21 dBm Coupler VOA 100 km Raman DCF Pol Scr EDFA Fiber +21 dBm Coupler Fiber VOA 100 km DCF Raman 4-10 dB 5.6 dB 3 dB SW 2 Coupler Preamp • Recirculating Loop DMUX / RX SW 1 TX / MUX BERT

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