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. A. Bononi et al.OFC ’05 – paper OThW51/27 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

3. A. Bononi et al.OFC ’05 – paper OThW52/27 DM Terrestrial Systems Notation An z = N x z A km DM system is: zAzA A D Dispersion Map In-line accumulated dispersion

4. A. Bononi et al.OFC ’05 – paper OThW53/27 Experiments on DM Terrestrial Links Booster Preamplifier M-Z PRBS 2 15 FM ECL 100 km NZDSF DCF -10 Sensitivity @ 10 BER OF EDFA 1EDFA 2 0.4nm end-line OSNR 100 km NZDSF 100 km NZDSF DCF [G. Bellotti et al., ECOC ’00, P.3.12] At ECOC 2000 we reported on parametric gain (PG) effects in a short-haul (3x100 km) terrestrial 10Gb/s single-channel NRZ-OOK system D=2.9 ps/nm/km 0.4nm OFEF Rx BeBe Tx 1. White ASE source EDFA 3 2.

5. A. Bononi et al.OFC ’05 – paper OThW54/27 Experiments on DM Terrestrial Links [G. Bellotti et al., ECOC ’00, P.3.12] end-line OSNR 25 dB/0.1 nm 2 4 6 8 10 12 14 246810121416 Launched power [dBm] Sensitivity penalty [dB] at BER=10^(-10) -220ps/nm +150ps/nm -35ps/nm 1. With PG In-line accumulated dispersion 2. No PG power threshold

6. A. Bononi et al.OFC ’05 – paper OThW55/27 Experiments on DM Terrestrial Links Din = +450 ps/nm Optimized pre-, post-comp. We repeated experiment for a long-haul (15x100 km) terrestrial 10Gb/s single- channel NRZ-OOK system based on Raman pumps Tx DGE Rx 100 km DCF x3 x5 end-line OSNR post-comp. pre-comp. end-line OSNR >30 dB/0.1nm OSNR received ~ ~ ~ White ASE source BER=10 -5 1. Teralight D= 8 ps/nm/km Teralight White ASE source ~ ~ ~ 2. end-line OSNR 19 dB/0.1nm (16 dB/0.1nm)

7. A. Bononi et al.OFC ’05 – paper OThW56/27 45678910 13 15 17 19 21 Launched power [dBm] 1. end-line OSNR>30 dB Received OSNR @ BER 10 [dB] -5 Experiments on DM Terrestrial Links 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

8. A. Bononi et al.OFC ’05 – paper OThW57/27  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.

9. A. Bononi et al.OFC ’05 – paper OThW58/27 OOK-NRZ Signal Im[E] Re[E] Joint PDF Im[E] Re[E] P(t) t t P  NL Average Nonlinear phase span average < >

10. A. Bononi et al.OFC ’05 – paper OThW59/27 Im[E] Re[E] In a rotated reference system we express the Rx field as: Rx Field In-phase ASE quadrature ASE

11. A. Bononi et al.OFC ’05 – paper OThW510/27 ASE Spectrum P(t) t N0N0 PSD [dB] frequency f S i (f) S r (f) -4 0 4 8 frequency f Normalized PSD [dB] S r (f) S i (f) Parametric Gain P end-line

12. A. Bononi et al.OFC ’05 – paper OThW511/27 0 ASE Statistics end-line OSNR= 25 dB/0.1nm  NL = 0.15  rad D in =0 D pre =0 D post =0 2 34 1 Re[E] Im[E] Re[E] Im[E] D= ps/nm/km …but with some dispersion, PDF contours become elliptical  Gaussian PDF D comp. fiber It is known that, at zero dispersion, PDF on marks is strongly non-Gaussian *... * [K.-P. Ho, JOSA B, Sept. 2003]

13. A. Bononi et al.OFC ’05 – paper OThW512/27 Linear PG Model Small perturbation   Large OSNR [ C. Lorattanasane et al., JQE July 1997 ] [ A. Carena et al., PTL Apr. 1997 ] Rx ASE is Gaussian DM [ M. Midrio et al., JOSA B Nov. 1998 ]

14. A. Bononi et al.OFC ’05 – paper OThW513/27 Linear PG Model Red : quadrature ASE No pre-, post-comp. A decreasing map has normally less in-phase ASE than an increasing map Blue: in-phase ASE » ASE gain comes at expense of CW depletion (negligible up to performance disruption)

15. A. Bononi et al.OFC ’05 – paper OThW514/27 Linear PG Model... mixes in-phase and quadrature ASE from the line  a large Dpost worsens PG impact on BER Red : quadrature ASE Blue: in-phase ASE Post-compensation however... Otimized pre-, post-comp. Pre-compensation no effect on ASE

16. A. Bononi et al.OFC ’05 – paper OThW515/27 Failure of Linear PG Model 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 avg  =0.55 rad/  D=8 ps/nm/km

17. A. Bononi et al.OFC ’05 – paper OThW516/27 In-phase ASE PSD at f=0 reason is that ASE-ASE beat is larger when increasing map tilt 20  100 km, OSNR=11 dB/0.1nm  D=8 ps/nm/km

18. A. Bononi et al.OFC ’05 – paper OThW517/27 We decided to use and extend a known analytical BER evaluation method*. Main assumptions are: How do we estimate the bit error rate (BER) with strong PG? BER Evaluation *[ G. Bosco et al., Trans. Commun. Dec. 2001 ] Then a Karhunen-Loeve (KL) BER evaluation method is used for quadratic detectors in Gaussian noise. 1.Rx NRZ signal obtained by noiseless BPM propagation (ISI) 2.Gaussian ASE at Rx 3.White PSD on zeros 4.PSD on ones estimated from Monte-Carlo BPM simulations 5.No pump depletion on ones

19. A. Bononi et al.OFC ’05 – paper OThW518/27 BER Evaluation Why use the KL method ? Decision Threshold (in optical domain) PG stretches Quadrature ASE  Marcuse’s QFactor formula erroneously predicts large BER worsening

20. A. Bononi et al.OFC ’05 – paper OThW519/27 Theory vs. Experiment 00.511.5 -2 0 2 4 6 8 OSNR penalty [dB] Φ NL [rad/  ] Symbols: Experiment Lines: Theory OSNR=16 dB OSNR=19 dB We note a strong correlation between the growth of the in-phase PSD at f=0 and the growth of the OSNR penalty. 9 00.511.5 0 3 6 In-phase PSD at f= 0 [dB] Φ NL [rad/  ] OSNR=16 dB OSNR=19 dB 15x100km, Teralight, Din = +450 ps/nm, Optimized Dpre, Dpost ~ 1dB penalty when it doubles (+ 3 dB) OSNR>30 dB

21. A. Bononi et al.OFC ’05 – paper OThW520/27 We define PG doubling as the condition at which the in-phase ASE PSD at f=0 doubles (+ 3dB) PG doubling

22. A. Bononi et al.OFC ’05 – paper OThW521/27 Φ NL [rad/  ] Φ NL [rad/  ] Extrapolate 15x100km, Din=0 Optimized Dpre, Dpost D=2.9 NZDSF D=17 SMF 0123 -2 0 2 4 6 8 OSNR penalty [dB] 00.511.5 -2 0 2 4 6 8 OSNR=16 dB OSNR=19 dB Inphase PSD at f=0[dB] 0 1 2 3 0 3 6 9 00.511.5 0 3 6 9 Φ NL [rad/  ] Φ NL [rad/  ]

23. A. Bononi et al.OFC ’05 – paper OThW522/27 In-phase PSD at f=0 We managed to get an analytical approximation of the in-phase ASE PSD at f=0, S r (0) even in the large-signal regime (in the linear case S r (0)=1) We note in passing that S r (0) does not depend on post-compensation, since there is no GVD phase rotation at f=0! Large perturbations   Small OSNR

24. A. Bononi et al.OFC ’05 – paper OThW523/27 At full in-line compensation (Din=0), analytical approximation is: In-phase PSD at f =0 where 1020304050 0 0.2 0.4 0.6 0.8 1 spans N  (N) Map Strength T0T0 =1 At PG doubling

25. A. Bononi et al.OFC ’05 – paper OThW524/27 Region below red curve: < ~1dB penalty by PG in optimized map deep into region: 1)~Linear PG model 2)ASE Gaussian (No PG, optimized map) 1dB SPM penalty 15 10 Gb/s 17 19 21 15 @ PG doubling 1 DM systems with Din=0. N large 00.20.40.60.8 Map strength Sn 0 0.2 0.4 0.6 0.8 1 1.2 1.4  NL [rad/  ] end-line OSNR (dB/0.1nm) 40 Gb/s NZDSF 0123 0 3 6 9 00.51 1.5 0 3 6 9 SMF 0123 -2 0 2 4 6 8 00.511.5 -2 0 2 4 6 8

26. A. Bononi et al.OFC ’05 – paper OThW525/27 10 Gb/s single-channel NRZ system, 20  100 km, D=8 ps/nm/km, Din=0. Noiseless optimized Dpre, Dpost Q-Factor Standard method (ignores PG) Our method (with PG) Nonlinear phase [rad/  ] 0.20.40.60.8 end-line OSNR=11 dB/0.1nm 10 12 1 8 Q Factor [dB] 6 14 0 Q factor [dB] log(BER) with FEC Uncoded CG

27. A. Bononi et al.OFC ’05 – paper OThW526/27 10 Gb/s NRZ system, 20  100 km, D=8 ps/nm/km, Din=0. Optimizing Dpost Nonlinear phase [rad/  ] 00.20.40.60.81 Post dispersion [ps/nm] noiseless optimized Dpost with PG-optimized Dpost PG-optimized Dpost

28. A. Bononi et al.OFC ’05 – paper OThW527/27 Conclusions PG  significant factor in design of 10Gb/s NRZ DM long-haul terrestrial 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.

29. A. Bononi et al.OFC ’05 – paper OThW528/27 Gaussian ASE assumption Beyond PG doubling the assumption of Gaussian ASE gives overestimation of BER Φ NL = 0.7  rad (beyond PG doubling) 0.4nm OFEF Rx BeBe Y Monte Carlo Gaussian, exact PSD 10 Gb/s NRZ system, 20  100 km, D=8 ps/nm/km, OSNR=16 dB, Din=0. 0.50.70.91.11.31.5 -6 -5 -4 -3 -2 0 normalized decision threshold y 10 Gaussian, small-signal PSD Monte Carlo Gaussian, exact PSD CDF of Y on Marks [log ]

30. A. Bononi et al.OFC ’05 – paper OThW529/27 10 Gb/s NRZ system, 20  100 km, D=8 ps/nm/km, Din=0. Optimized Dpre, Dpost Q-Factor Q Factor [dB] 6 10 8 12 14 18 16 Standard method (ignores PG) Nonlinear phase [rad/  ] 00.20.40.60.81 end-line OSNR=16 dB/0.1nm OSNR=11 dB/0.1nm noiseless optimized Dpost

31. A. Bononi et al.OFC ’05 – paper OThW530/27 00.20.40.60.81 9 10 11 12 13 14 15 16 Nonlinear phase [rad/  ] Q Factor [dB] end-line OSNR=15 dB/0.1 nm 10 Gb/s NRZ system, 20  100 km, D=2.9 ps/nm/km, Din=0. Standard method (ignores PG) Bosco’s method (Linear PG model and KL) Our semi-analytical method (Monte-Carlo ASE PSD) Optimized Dpre, Dpost Q-Factor