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A. Bononi , P. Serena Department of Information Engineering, University of Parma, Parma, Italy

Implications of Nonlinear Interaction of Signal and Noise in Low-OSNR Transmission Systems with FEC. A. Bononi , P. Serena Department of Information Engineering, University of Parma, Parma, Italy J.-C. Antona, S. Bigo Alcatel Research & Innovation, Marcoussis, France. Outline.

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A. Bononi , P. Serena Department of Information Engineering, University of Parma, Parma, Italy

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  1. Implications of Nonlinear Interaction of Signal and Noise in Low-OSNR Transmission Systems with FEC A. Bononi, P. Serena Department of Information Engineering, University of Parma, Parma, Italy J.-C. Antona, S. Bigo Alcatel Research & Innovation, Marcoussis, France

  2. Outline • Experiments on Single-channel Dispersion Managed (DM) 10Gb/s non-return-to-zero (NRZ) on-off keying (OOK)Terrestrial systems with significant nonlinear signal-noise interaction, i.e., parametric gain (PG) • Modeling DM Terrestrial links • Amplified Spontaneous Emission (ASE) • Power Spectral Density (PSD) • Probability Density Function (PDF) • PG doubling • Issues in bit error rate (BER) evaluation with strong PG • Implications for systems with Forward Error Correction (FEC) • Conclusions OFC ’05 – paper OThW5

  3. RX OF EF Bo Be N D A Dispersion Map In-line accumulated dispersion DM Terrestrial SystemsNotation An z = N x zA km DM system is: zA OFC ’05 – paper OThW5

  4. OF EF 1. 2. Be 0.4 nm Rx EDFA 3 White ASE source Sensitivity @ 10 BER Experiments on DM Terrestrial Links At ECOC 2000 we reported on parametric gain (PG) effects in a short-haul(3x100 km) terrestrial 10Gb/s single-channel NRZ-OOK system PRBS 100 km 100 km FM 2 -1 15 Booster EDFA 1 EDFA 2 Tx NZDSF NZDSF ECL M-Z D=2.9 ps/nm/km DCF DCF OF 100 km DCF 0.4 nm NZDSF Preamplifier -10 end-line OSNR [G. Bellotti et al.,ECOC ’00, P.3.12] OFC ’05 – paper OThW5

  5. 2. No PG 14 12 +150 ps/nm 10 8 -35 ps/nm 6 -220 ps/nm 4 2 power threshold 2 4 6 8 10 12 14 16 Experiments on DM Terrestrial Links 1. With PG In-line accumulated dispersion Sensitivity penalty [dB] at BER=10^(-10) end-line OSNR 25 dB/0.1 nm Launched power [dBm] [G. Bellotti et al.,ECOC ’00, P.3.12] OFC ’05 – paper OThW5

  6. Teralight ~ ~ ~ ~ White ASE source ~ ~ received end-line 2. OSNR OSNR BER=10-5 end-line OSNR 19 dB/0.1nm (16 dB/0.1nm) White ASE source Teralight D=8 ps/nm/km Experiments on DM Terrestrial Links We repeated experiment for a long-haul (15x100 km) terrestrial 10Gb/s single-channel NRZ-OOK system based on • Din = +450 ps/nm • Optimized pre-, post-comp. pre-comp. 1. Rx Tx post-comp. end-line OSNR >30 dB/0.1nm x5 DGE DCF 100 km Raman pumps x3 OFC ’05 – paper OThW5

  7. 1. end-line OSNR>30 dB 2. end-line OSNR=19 dB end-line OSNR=16 dB Difference among curves due to PG-enhanced ASE giving more than 1dB decrease in power threshold Experiments on DM Terrestrial Links 21 19 -5 17 Received OSNR @ BER 10 [dB] 15 13 4 5 6 7 8 9 10 Launched power [dBm] OFC ’05 – paper OThW5

  8. These experiments triggered an intense modeling activity in order to understand the key degradation mechanisms and extrapolate the experimental results. • Such a modeling is the object of the rest of the talk. • We next introduce the key concepts in our modeling. OFC ’05 – paper OThW5

  9. P(t) P(t) P t t Im[E] Im[E] Average Nonlinear phase Re[E] Re[E] FNL < > Joint PDF span average OOK-NRZ Signal OFC ’05 – paper OThW5

  10. Im[E] Re[E] In-phase ASE quadrature ASE Rx Field In a rotated reference system we express the Rx field as: OFC ’05 – paper OThW5

  11. 8 Si(f) Parametric Gain 4 Normalized PSD [dB] 0 Sr(f) P -4 frequency f PSD [dB] Si(f) end-line N0 Sr(f) frequency f ASE Spectrum P(t) t OFC ’05 – paper OThW5

  12. Im[E] Im[E] Re[E] D= ps/nm/km comp. fiber Re[E] ASE Statistics It is known that, at zero dispersion, PDF on marks is strongly non-Gaussian*... …but with some dispersion, PDF contours become elliptical  Gaussian PDF 3 4 2 0 1 D end-line OSNR= 25 dB/0.1nm FNL = 0.15p rad Din =0 Dpre=0Dpost=0 *[K.-P. Ho, JOSA B, Sept. 2003] OFC ’05 – paper OThW5

  13. Rx ASE is Gaussian Small perturbation Large OSNR [ M. Midrio et al., JOSA B Nov. 1998 ] DM Linear PG Model [ C. Lorattanasane et al.,JQE July 1997] [ A. Carena et al.,PTL Apr. 1997] OFC ’05 – paper OThW5

  14. A decreasing map has normally less in-phase ASE than an increasing map Linear PG Model No pre-, post-comp. Red : quadrature ASE » Blue: in-phase ASE ASE gain comes at expense of CW depletion (negligible up to performance disruption) OFC ’05 – paper OThW5

  15. Linear PG Model Otimized pre-, post-comp. Red : quadrature ASE Blue: in-phase ASE Pre-compensation no effect on ASE Post-compensation however... ... mixes in-phase and quadrature ASE from the line  a large Dpost worsens PG impact on BER OFC ’05 – paper OThW5

  16. Failure of Linear PG Model avg F=0.55 rad/p, D=8 ps/nm/km • Go back to case without Dpost, with Din=0 (flat map). • At large end-line OSNR (25 dB/0.1 nm) good match between linear PG model (dashed) and Monte-Carlo simulations based on the beam propagation method (BPM) (solid, ~30 min simulation time per frame) What happens at smaller OSNRs? Failure is due to ASE-ASE beating during propagation OFC ’05 – paper OThW5

  17. 8 Din=0 ps/nm 6 Din=+2000 ps/nm 4 reason is that ASE-ASE beat is larger when increasing map tilt In-phase PSD at f=0 [dB] 2 0 Din=-2000 ps/nm -2 0 0.2 0.4 0.6 0.8 avg nonlinear phase F [rad/] In-phase ASE PSD at f=0 20100 km, OSNR=11 dB/0.1nm, D=8 ps/nm/km OFC ’05 – paper OThW5

  18. BER Evaluation How do we estimate the bit error rate (BER) with strong PG? We decided to use and extend a known analytical BER evaluation method*. Main assumptions are: • Rx NRZ signal obtained by noiseless BPM propagation (ISI) • Gaussian ASE at Rx • White PSD on zeros • PSD on ones estimated from Monte-Carlo BPM simulations • No pump depletion on ones Then a Karhunen-Loeve (KL) BER evaluation method is used for quadratic detectors in Gaussian noise. *[ G. Boscoet al., Trans. Commun. Dec. 2001 ] OFC ’05 – paper OThW5

  19. PG stretches Quadrature ASE ò Marcuse’s QFactor formula erroneously predicts large BER worsening Decision Threshold (in optical domain) BER Evaluation Why use the KL method ? OFC ’05 – paper OThW5

  20. 8 6 4 2 0 -2 9 f= 0 [dB] OSNR=16 dB 6 We note a strong correlation between the growth of the in-phase PSD at f=0 and the growth of the OSNR penalty. In-phase PSD at 3 OSNR=19 dB ~ 1dB penalty when it doubles (+ 3 dB) 0 0 0.5 1 1.5 Φ Φ   [rad/ [rad/ ] ] NL NL Theory vs. Experiment Symbols: Experiment Lines: Theory OSNR=19 dB OSNR=16 dB OSNR penalty [dB] OSNR>30 dB 15x100km, Teralight, Din = +450 ps/nm, Optimized Dpre, Dpost 0 0.5 1 1.5 OFC ’05 – paper OThW5

  21. PG doubling We define PG doubling as the condition at which the in-phase ASE PSD at f=0 doubles (+ 3dB) OFC ’05 – paper OThW5

  22. 15x100km, Din=0 Optimized Dpre, Dpost 8 6 4 2 0 -2 9 9 6 6 Inphase PSD at f=0[dB] 3 3 0 0 0 2 1 3 0 0.5 1 1.5 Φ Φ Φ Φ [rad/] [rad/] [rad/] [rad/] NL NL NL NL Extrapolate D=17 SMF D=2.9 NZDSF 8 OSNR=19 dB 6 OSNR=19 dB OSNR=16 dB 4 OSNR=16 dB OSNR penalty [dB] 2 0 -2 0 1 2 3 0 0.5 1 1.5 OFC ’05 – paper OThW5

  23. Large perturbations Small OSNR In-phase PSD at f=0 We managed to get an analytical approximation of the in-phase ASE PSD at f=0,Sr(0) even in the large-signal regime (in the linear case Sr(0)=1) We note in passing that Sr(0) does not depend on post-compensation, since there is no GVD phase rotation at f=0! OFC ’05 – paper OThW5

  24. =1 1 At PG doubling 0.8 0.6 (N) L 0.4 Map Strength 0.2 T0 0 10 20 30 40 50 spans N In-phase PSD at f =0 At full in-line compensation (Din=0), analytical approximation is: where OFC ’05 – paper OThW5

  25. 10 Gb/s end-line OSNR (dB/0.1nm) DM systems with Din=0. N large 1.4 21 1.2 19 NZDSF SMF 17 8 8 1 ] p 6 6 15 4 4 2 2 0.8 [rad/ 0 0 • Region below red curve: • < ~1dB penalty by PG in optimized map • deep into region: • ~Linear PG model • ASE Gaussian -2 -2 0 1 2 3 0 0.5 1 1.5 NL 9 9 F 0.6 1dB SPM penalty 6 6 (No PG, optimized map) 3 3 0.4 0 0 1.5 0 1 2 3 0 0.5 1 40 Gb/s 0.2 0 0 0.2 0.4 0.6 0.8 1 Map strength Sn @ PG doubling 15 OFC ’05 – paper OThW5

  26. 14 Standard method (ignores PG) Our method (with PG) with FEC 12 Uncoded log(BER) 10 Q Factor [dB] CG 8 Q factor [dB] 6 0 1 Q-Factor 10 Gb/s single-channel NRZ system, 20100 km, D=8 ps/nm/km, Din=0. Noiseless optimized Dpre, Dpost end-line OSNR=11dB/0.1nm 0.2 0.4 0.6 0.8 Nonlinear phase [rad/] OFC ’05 – paper OThW5

  27. 14 end-line OSNR=11dB/0.1nm 12 10 Q Factor [dB] 8 with PG-optimized Dpost PG-optimized Dpost 6 0 0.2 0.4 0.6 0.8 1 Nonlinear phase [rad/] Optimizing Dpost 10 Gb/s NRZ system, 20100 km, D=8 ps/nm/km, Din=0. noiseless optimized Dpost Post dispersion [ps/nm] 0 0.2 0.4 0.6 0.8 1 Nonlinear phase [rad/] OFC ’05 – paper OThW5

  28. Conclusions • PG significant factor in design of 10Gb/s NRZ DM long-haulterrestrial systems operated at “small” OSNR and thus needing FEC. MESSAGE:Do not rely on traditional simulation packages that neglect PG: too optimistic about the gain of your FEC. • Our PG doubling formula useful to tell when OSNR is “small” . • Up to PG doubling, BER can be found by our semi-analytical mehod. Well above PG doubling, however, Gaussian ASE assumption less accurate, and tends to underestimate BER. • When PG significant, less Dpost is needed than in noiseless optimization. • PG even more significant in low OSNR RZ systems. For OOK-RZ soliton systems classical noise analyses neglect ASE-ASE beating during propagation. OFC ’05 – paper OThW5

  29. OF EF Gaussian, exact PSD Monte Carlo Y Rx Be 0.4 nm Gaussian ASE assumption 10 Gb/s NRZ system, 20100 km, D=8 ps/nm/km, OSNR=16 dB, Din=0. • Beyond PG doubling the assumption of Gaussian ASE gives overestimation of BER ΦNL = 0.7 rad (beyond PG doubling) 0 Gaussian, exact PSD -1 10 -2 Monte Carlo -3 CDF of Y on Marks [log ] Gaussian, small-signal PSD -4 -5 -6 0.5 0.7 0.9 1.1 1.3 1.5 normalized decision threshold y OFC ’05 – paper OThW5

  30. 0 0.2 0.4 0.6 0.8 1 Q-Factor 10 Gb/s NRZ system, 20100 km, D=8 ps/nm/km, Din=0. Optimized Dpre, Dpost 18 end-line OSNR=16 dB/0.1nm Standard method (ignores PG) 16 14 OSNR=11 dB/0.1nm Q Factor [dB] 12 10 8 noiseless optimized Dpost 6 Nonlinear phase [rad/] OFC ’05 – paper OThW5

  31. 16 Standard method (ignores PG) Our semi-analytical method (Monte-Carlo ASE PSD) 15 Bosco’s method (Linear PG model and KL) 14 Q Factor [dB] 13 12 11 10 9 0 0.2 0.4 0.6 0.8 1 Nonlinear phase [rad/] Q-Factor 10 Gb/s NRZ system, 20100 km, D=2.9 ps/nm/km, Din=0. Optimized Dpre, Dpost end-line OSNR=15 dB/0.1 nm OFC ’05 – paper OThW5

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