1. Design Rules for Reach Maximization in Uncompensated Nyquist-WDM Links
V. Curri(1), A. Carena(1), G. Bosco(1), P. Poggiolini(1),
A. Nespola(2), F. Forghieri(3)
(1) DET, Politecnico di Torino, Torino, Italy.
(2) Istituto Superiore Mario Boella, Torino, Italy.
(3) Cisco Photonics Italy srl, Monza, Italy.
ECOC 2013 Paper Th.1.D.1

2. Motivation and outline
Design strategies aimed at a system optimization
Scaling laws with main system parameters
Max reach design strategy
A closed-form for design strategy based on the GN-model
Scaling laws based on a GN-model approx
Validation using experimental results
Application examples
Comments and conclusions
ECOC 2013 Paper Th.1.D.1

3. System scenario NyWDM X Ns NyWDM Coherent Tx EDFA Rx …… D,a,g AEL Ls
Any PM-multilevel mod format
RS: symbol rate
Df: channel spacing
KS: normalized channel spacing
Ech: channel PSD (energy)
Nch: number of channels
Bopt: overall bandwidth
Coherent Rx
X Ns
EDFA Ls
NyWDM Tx
D,a,g
G=As F
AEL
ECOC 2013 Paper Th.1.D.1

4. The Non-Linear Interference
Propagation of a NyWDM signal comb over an uncompensated link induces an additive Gaussian disturbance called non-linear interference (NLI)
NLI can be approximated as white in a single-channel bandwidth
Linear accumulation with distance is a good approximation for large Nch
Equivalent linear link
Coherent Rx
X Ns
G=As
NyWDM Tx
AEL +
ASE
NLI As
ASE PSD
NLI PSD
Channel PSD
ENL: nonlinear energy threshold depending on system parameters
ECOC 2013 Paper Th.1.D.1

5. Transmission performance
Back-to-back performance
Depends on modulation format and Tx/Rx performance
It is the optical signal-to-noise ratio in the symbol rate noise bandwidth
The NLI can be assumed to be an AWGN, so the Rx BER is:
Generalized SNR
ECOC 2013 Paper Th.1.D.1

6. Max reach design strategy (I)
Given the target performance
Among the others, a possible design strategy is aimed at the maximization of the reach, given the target performance
ECOC 2013 Paper Th.1.D.1

7. Max reach design strategy (II)
ECOC 2013 Paper Th.1.D.1

8. Is it available a closed-form for ENL?
The GN-Model
In Nmax and Eopt, dependence on link and NyWDM parameters is “hidden” in the nonlinear energy threshold parameter ENL
Is it available a closed-form for ENL?
Using the GN-model for the NLI modeling, we can apply an accurate approximation of ENL for the propagation of a NyWDM channel comb
where Ks=Df/Rs, adB [dB/km] is the fiber loss parameter, D [ps/nm/km] is the dispersion parameter, g [1/W/km] is the nonlinear coefficient, Leff is the fiber-span effective length, and c is the speed of the light.
ECOC 2013 Paper Th.1.D.1

9. GN-Model: an approximation
The closed-form expression for ENL is a powerful analytical tool but fails in giving quick scaling law of max reach with all system parameters
KNL: system-independent constant
Approximated expression for ENL with a tolerable maximum inaccuracy
Rs ∈ [15;40] Gbaud
Ks ∈ [1;1.5]
FdB ∈ [3;6] dB
SNRT,dB ∈ [10;20] dB
adB ∈ [0.15;0.25] dB/km
D ∈ [4;24] ps/nm/km
g ∈ [0.5;2] 1/W/km
Suitable approx for quick scaling laws
Max 0.5 dB inaccuracy in Nmax evaluation
ECOC 2013 Paper Th.1.D.1

10. … using the GN-model approx
Differential variations for Popt and Nmax
Referring Nmax and Eopt to a reference scenario characterized by Nmax=Nref and Eopt=Eref , KNL and c/f0 are simplified out
ECOC 2013 Paper Th.1.D.1

11. Scaling laws Differential variations for system parameters
Loss and span length:
Da = 10∙log10(adB/adB,ref)
dAs = As,dB- As,dB,ref
Dispersion: DD = 10∙log10(D/Dref)
Nonlinearity: Dg = 10∙log10(g/gref)
Mod. format and FEC: dSNRT = SNRT,dB - SNRT,dB,ref
Amplifier: dF = FdB - FdB,ref
Rate: DRs = 10∙log10(Rs/Rs ref)
Channel spacing: DKs = 10∙log10(Ks/Ks ref)
Scaling laws with system parameters
Optimal power per channel
Max reach
ECOC 2013 Paper Th.1.D.1

12. Validation: reference scenario
9 NyWDM channels 200G PM-16QAM
Ls = 80 km
adB,ref = 0.22 dB/km
As,dB,ref = 17.6 dB
Dref = 16.7 ps/nm/km
gref = 1.3 1/W/km
FdB,ref = 5 dB
Rs,ref =32 Gbaud
Ks,ref =1.05
SNRT,dB,ref =16.85 dB (BER = 10-3)
Reference simulation results
Nmax,ref = 15
Pch [dBm] Ns
ECOC 2013 Paper Th.1.D.1

13. Validation: results It works! Experiments Rs [Gbaud] Ks Fiber Nmax Exp
Scaling laws
Reference
NyWDM 200G
PM-16QAM
Rs=32
Ks=1.05
SSMF 15
(simulation result)
[1]
NyWDM 100G
PM-QPSK
Rs=30
Ks=1.1
NZDSF 8 7 20
PSCF 32 31
[2]
NyWDM
100G
Rs=15.625
Ks=1.024 12 11 38 39
PSCF80 44 45
PSCF110 58 57
PSCF130 62 63
PSCF150 70
[3]
PM-64QAM
Rs=10.4
Ks=1.15 28 30
It works!
[1] E. Torrengo et al., “Experimental validation of an analytical model ….,” OSA Optics Express, 19, B790-B798 (2011)
[2] A. Nespola et al., “Extensive fiber comparison and GN-model validation…”, OFC/NFOEC 2013, paper OTh3G.5
[2] A. Nespola et al., “1306-km 20x124.8-Gb/s PM-64QAM Transmission …”, ECOC 2013, paper Th.2.D.1

14. Scaling laws: some examples
Loss
Span length
Dispersion
Nonlinearity
Mod. Format
FEC
Amplifier
Channel
spacing
Hard to soft decision FEC » dSNRT ≈-2 dB » DNmax≈+2 dB <-> +60%
SSMF to PSCF with Ls = 80 km
D: 16 -> 20 ps/nm/km » DD ≈+1 dB »+1/3» DNmax≈+1/3 dB <-> +10%
Aeff: 80 -> 130 mm2 » Dg ≈-2.1 dB »-2/3» DNmax≈+1.4 dB <-> +40%
adB: 0.2 -> 0.16 dB/km:
Da ≈-1 dB »+1/3» DNmax≈-1/3 dB <-> -10%
dAs≈ -3.2 dB »-2/3» DNmax≈+2.1 dB <-> +63%
+53%
ECOC 2013 Paper Th.1.D.1

15. Comments and conclusions
A closed-form expression based on GN-model for max reach link design strategy has been proposed
A GN-model approximation has been proposed allowing to derive simple scaling laws with the main system parameters in max reach optimization
Scaling laws has been positively validated using already published results
They can be applied to different rates and different modulation formats
ECOC 2013 Paper Th.1.D.1

16. This work was supported by CISCO Systems within a SRA contract
Acknowledgements
This work was supported by CISCO Systems within a SRA contract
The simulator OptSimTM was supplied by Synopsys Inc.
ECOC 2013 Paper Th.1.D.1

17. Max reach scaling vs. main parameters
DNs,max [dB]
g [1/W/km]
FdB [dB] KS
SNRT [dB]
As,dB [dB]
D [ps/nm/km]
adB [dB/km]
ECOC 2013 Paper Th.1.D.1