We extend a model for nonlinear propagation over lumped-amplified uncompensated links to setups using Raman amplification. We compare theoretical to simulative results for PM-16QAM Nyquist-WDM on PSCF links, showing an excellent agreement. We also show that Raman NLI enhancement gives limited practical impairments in realistic setup

Bosco, Gabriella

Carena, Andrea

Curri, Vittorio

Forghieri, F.

Poggiolini, Pierluigi

V. Curri

A. Carena

P. Poggiolini

G. Bosco

F. Forghieri

Crossref

Evaluation of Non-Linear Interference in Uncompensated Links using Raman Amplification

PORTO Publications Open Repository TOrino

Politecnico di Torino
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[Proceeding] Evaluation of Non-Linear Interference in Uncompensated Links
using Raman Amplification
Original Citation:
V. Curri; A. Carena; P. Poggiolini; G. Bosco; F. Forghieri (2012). Evaluation of Non-Linear
Interference in Uncompensated Links using Raman Amplification. In: European Conference on
Optical Communication (ECOC), Amsterdam, September 2012. pp. 1-3
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We.2.C.5.pdf ECOC Technical Digest © 2012 OSA
Evaluation of Non-Linear Interference in Uncompensated Links 
using Raman Amplification 
V. Curri
(1)
, A. Carena
(1)
, P. Poggiolini
(1)
, G. Bosco
(1)
, F. Forghieri
(2) 
(1)
 DET, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy. curri@polito.it 
(2)
 Cisco Photonics Italy srl, Via Philips 12, 20900, Monza, Italy. fforghie@cisco.com 
Abstract We extend a model for nonlinear propagation over lumped-amplified uncompensated links to 
setups using Raman amplification. We compare theoretical to simulative results for PM-16QAM 
Nyquist-WDM on PSCF links, showing an excellent agreement. We also show that Raman NLI 
enhancement gives limited practical impairments in realistic setups. 
Introduction 
Modern optical communications are fast 
evolving  towards the use of multilevel 
modulation formats using coherent receivers 
based on digital signal processing (DSP)
1
. For 
such system scenarios it has been 
demonstrated that optimal setups are highly-
dispersive uncompensated links
2
. To further 
increase spectral efficiency, a promising option 
is the use of Nyquist-WDM with channel spacing 
approaching the symbol-rate
3
. For this system 
category, it has been shown that fiber 
nonlinearities act introducing an additional 
Gaussian noise-like component called nonlinear 
interference (NLI)
4
. Theory allowing to 
analytically derive the amount of NLI in lumped-
amplified links has been described and validated 
by simulations
4
 and experiments
5
. 
With the increasing of cardinality of modulation 
formats, for instance moving from PM-QPSK to 
PM-16QAM, the use of hybrid Raman/EDFA 
amplification (HFA) seems to be the solution for 
achieving ultra long-haul distances
6
.  
In this work, we present the extension of NLI 
theory to setups based on Raman amplification. 
After introducing the theory, we validate it by 
comparing theoretical derivations to simulations 
of a Nyquist WDM PM-16QAM link made of pure 
silica-core fiber (PSCF). Simulation results 
display excellent agreement with theory.  
Theory 
We consider the transmission over a multi-span 
uncompensated link of Nch Nyquist WDM 
channels at symbol rate Rs with channel spacing 
f=Rs  It can be shown that the power spectral 
density GNLI of NLI on the center channel (worst-
case) at the receiver can be expressed as
4
: 
 
 
 
)1(d
2
log
2sin
2sin
27
256
2
222
2
222
0
32
2



 







 
opt
s
ss
effTxNLI
B
L
LN
LPG
optB
where  is the fiber nonlinear coefficient, PTx is 
the transmitted power per channel, Leff is the 
fiber effective length, 2 is the dispersion 
coefficient, Ls is the span length, Ns is the 
number of spans, Bopt=Nch·Rs and  is the FWM 
efficiency
7
. Eq. (1) is obtained from the general 
expression of GNLI reported in
4
 (evaluated at f= 
0), with a proper change of variables based on 
the use of hyperbolic coordinates (e.g. 
2
=f1·f2). 
that holds for f=Rs. 
In general, the FWM efficiency vs. phase-
mismatch is given by
7 
    )2(d4exp)(1
2
0
2
2
2
2 
sL
ch
eff
zzjzp
L

 
where pch(z) is the normalized power evolution 
that  depends on fiber loss coefficient s and on 
Raman pump evolution. Supposing counter-
propagating and undepleted pump, 
Pp(z)=Ppump·exp{-p(Ls-z)}, where p is the pump 
loss coefficient and Ppump is the launched pump 
power,  assumes the following close-form:  
    
    
    
)3(
23.0,23.0,
23.0,23.0,
23.0
2
2
22
2
RAA
G
RAA
G
j
A
G
Gkk
Gjkjk
fp
RA
fp
RA
fp
RA







where s,xis the upper-incomplete gamma-
function
8
, GRA is the Raman on-off gain 
expressed in dB, Afp=exp{p·Ls}, k=s/p, 
=(2
2
2
2
/p. Eq. (3) depends only on the 
overall Raman gain, therefore it is valid also for 
Rx
X Ns
EDFA
80 km
PSCF
PM-16QAM
Nyquist WDM
Tx
(a)
(b)
RA pumps
GFF
(c)
0 200 400 600 800 1000 1200
0
2
4
6
8
10
12
14
P
pump
[dBm]
G
R
A
[k
m
]
0 200 400 600 800 1000 1200
-4
-3
-2
-1
0
1
2
3
4
5
6
P
pump
[dBm]
F
e
q
[k
m
]
 
Fig. 1: Layout of the analyzed system setup (a), 
Raman on-off gain (b) and HFA equivalent noise 
figure (c) vs. overall pump power. 
We.2.C.5.pdf ECOC Technical Digest © 2012 OSA
multi-pump counter-propagating Raman setups 
provided that pump depletion is negligible. In 
case of relevant pump depletion, the analysis 
holds using Eq. (2) for  evaluation. 
The system BER can then be derived from the 
non-linear OSNR
4
, defined as: 
 
)4(
nNLIASE
Tx
NL
BGG
P
OSNR

  
where GASE is the overall ASE noise power 
spectral density and Bn is the OSNR reference 
bandwidth. 
Validation setup 
In order to test the theoretical derivations, we 
analyze the system setup shown in Fig.1a. It is a 
Ns spans link carrying 11 PM-16QAM Nyquist-
WDM channels at Rs=32 Gbaud and channel 
spacing f=Rs. Channels are electrically shaped 
using a Nyquist raised-cosine filter with roll-
off=0.02 and an ideal DAC. The required OSNR 
in 0.1 nm in order to obtain the target BER=10
-3
 
is 23 dB. 
The system is composed of several spans of 
PSCF with length Ls=80 km. Each fiber span is 
followed by a coupler enabling counter-
propagating Raman pumping, a gain flattening 
filter (GFF) that ideally compensates for the 
Raman gain tilting and an EDFA with noise-
figure F=6 dB that recovers the residual loss. 
The PSCF parameters are: s,dB=0.185 dB/km, 
p,dB=0.3 dB/km, D=20.6 ps/nm/km (2=-26.2 
ps
2
/km) and =0.81 1/W/km. We include 5.2 dB 
of extra losses due to passive components and 
connectors in the span, hence we assume an 
overall span loss Aspan=20 dB that is completely 
recovered by the HFA.  
Raman amplification is obtained using three 
unpolarized counter propagating pumps at 1425, 
1436 and 1459 nm. The overall pump power 
Ppump ranges from 200 mW up to 1200 mW. We 
limit Ppump to 1200 mW in order to have negligible 
depletion. As a reference, we also consider 
EDFA only lumped amplification (Ppump=0 mW). 
Fig. 1b displays the Raman on-off gain GRA vs. 
the overall pump power. The maximum value of 
GRA is 13.1 dB for Ppump=1200 mW and it almost 
completely recovers the fiber loss that is 14.8 
dB. Fig. 1c shows the values of the equivalent 
noise figure Feq of the HFA for the different Ppump 
levels. While increasing Ppump,  Feq decreases 
from 6 dB for the case of EDFA only 
amplification to -4 dB for Ppump=1200 mW: it 
corresponds to an OSNR improvement of 10 dB. 
We first apply the theory in order to evaluate the 
NLI enhancement GNLI/GNLI,EDFA of the NLI in 
cases of HFA with respect to EDFA-only 
amplification. Results are plotted in Fig. 2 as  
vs. Ppump for Ns=5 and Ns=30: the maximum 
value of   is 2 dB, for Ppump=1200 mW. From 
these results it can also be deduced that the 
presence of Raman amplification, besides 
enhancing the NLI, slightly increases its 
accumulation along the line and does not 
increase linearly with Ppump. Such an effect is 
shown by the larger value of  after 30 spans 
with respect to the one after 5 spans. We 
verified however that in all practical scenarios 
such an effect is limited to a small fraction of dB, 
as for the presented results, with a negligible 
impact on system performance.  
Simulative results 
In order to validate the presented theory, we 
simulate the propagation of 11 PM-16QAM 
Nyquist-WDM channels in the link setup 
described in the previous section. 
We use a polarization diversity Rx based on 90° 
hybrids and balanced photodetectors. The Rx 
electric bandwidth is ½·Rs=16 GHz and the local 
oscillator is supposed to be ideal, without phase 
noise. The Rx DSP placed after photodetectors 
operates at 2 samples/symbol and implements 
ideal electronic dispersion compensators and a 
butterfly equalizer based on 51-tap FIR filters. 
The filter coefficients are adjusted through a 
least mean squares (LMS) algorithm. Simulation 
results are obtained by simulating 2
16
 symbols 
(2
19
 bits) per channel  and performing direct 
error counting on the center channel.  
We vary the transmitted power per channel PTx 
from -5 up to +3 dBm. For each Ppump and PTx we 
derive the maximum reachable distance Lmax still 
allowing BER10
-3
. In order to isolate the effect 
of NLI enhancement due to Raman 
amplification, we also consider the unrealistic 
systems based on equivalent-EDFAs with noise-
figures equal to the ones of the HFAs. 
For each setup we also apply the proposed 
theory to derive the power PNLI of NLI and  
consequently evaluate Lmax at which OSNRNL=23 
dB (corresponding to BER=10
-3
). 
0 200 400 600 800 1000 1200
0
0.5
1
1.5
2
P
pump
[mW]

[d
B
]
N
s
=5
N
s
=30
 
Fig. 2: NLI enhancement in Raman amplified links 
with respect to EDFA link for different overall Raman 
pumping  after 5 and 30 spans 
We.2.C.5.pdf ECOC Technical Digest © 2012 OSA
Fig. 3a shows results  in terms of  Lmax  vs. PTx 
for the EDFA-only link, for the 1200 mW HFA 
link and for its equivalent EDFA-only link. Lines 
refer to analytical results, while circles and 
diamonds are simulative results for EDFA-only 
and HFA links, respectively. The excellent 
agreement with simulative results confirms the 
accuracy of the proposed theoretical evaluation. 
On such a basis, together with other tests we 
have carried out and that are not reported here 
due to lack of space, we can conclude that the 
developed theory can reliably be applied to 
uncompensated links using Raman amplification 
and transmitting coherent modulation formats.  
From Fig. 3a it can be also observed that using 
EDFAs with F=6 dB, Lmax=600 km only, while, 
with 1200 mW HFAs, Lmax=2400 km, 
corresponding to 4-times (6 dB) on Lmax. It is due 
to 10 dB ASE noise reduction (Feq from 6 dB to -
4 dB) and NLI noise enhancement inducing the 
optimal power PTx,opt going from 1.5 dBm down 
to -2.5 dBm, i.e., 4 dB reduction. Moreover, we 
have seen in Fig. 2 that the 1200 mW HFA 
induces 2 dB NLI enhancement,  corresponding 
(compare in Fig 3a, Eq. EDFA to HFA) to 0.5 dB 
reduction on both PTx,opt and Lmax. Hence, even 
with =2 dB, effects of NLI enhancement due to 
Raman amplification are limited. 
Fig. 3b shows results as Lmax at PTx,opt for all the 
considered HFA setups and for their equivalent-
EDFA links. As well as in previous plots, lines 
refer to theory while circles and diamonds are 
obtained by simulation. The excellent agreement 
between theory and simulations for all pump 
levels gives a further confirmation to the validity 
of the theory. Moreover, it can be observed that 
up to Ppump=800 mW, corresponding to =1 dB, 
effects of NLI enhancement are practically 
negligible. It indicates  that, keeping the NLI 
enhancement below 1 dB, Raman amplification 
induces negligible impairments with respect to 
its equivalent-EDFA, i.e., we have benefits of 
noise reduction without excess NLI impact. 
Note that, in general, for a fixed Ppump,  
decreases with the increasing of Ls. The reason 
is a reduction of the power at the end of the fiber 
span, where the Raman gain has higher effects. 
As a practical consequence, in most long-span 
links  is smaller than 1 dB, giving a negligible 
impact on system performance. 
Conclusions 
We  presented  the extension of the theory of 
NLI for uncompensated links to systems based 
on Raman amplification. We showed general 
results and a specific close form for undepleted 
and counter-propagating pumps. Theory was 
successfully validated by simulation of Nyquist 
WDM PM-16QAM links on PSCF.  
Acknowledgements 
This work was supported by CISCO Systems 
within a SRA contract. The simulator OptSim
® 
was supplied by RSoft Design Group Inc. 
References 
1 M. G. Taylor, PTL, Vol. 16, p. 674, 2004 
2 M. S. Alfiad et al., JLT, Vol. 27, p. 3590, 2009 
3 G. Bosco et al., PTL, Vol. 22, p. 1129, 2010 
4 A. Carena et al., JLT, Vol. 30, p.1524, 2012 
5 E. Torrengo et al., Op.Exp., Vol. 19, p. B790, 2011 
6 Yamanaka et al., ECOC 2010, paper We.8.C.1 
7 N. Shibata, JQE, Vol. 23, p. 1205, 1987 
8 M. Abramowitz, I. A. Stegun, Handbook of 
mathematical functions, 1965 
-5 -4 -3 -2 -1 0 1 2 3
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
P
Tx
[dBm]
L
m
a
x
[k
m
]
(a) (b)
HFA 
Ppump= 1200 mW
Feq = -4 dB
EDFA
F = 6 dB
Equivalent  
EDFA
F = -4 dB
0 200 400 600 800 1000 1200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
P
pump
[mW]
L
m
a
x
@
L
P
T
x
,o
p
t
[k
m
]
HFA
Equivalent EDFA
 
Fig. 3: Maximum reach Lmax @ BER≤10
-3
 vs. the transmitted power (PTx) for EDFA only, HFA with Ppump= 1200 
mW and its equivalent EDFA with F = -4 dB (a). Maximum reach @ BER≤10
-3
 for the optimal transmitted power 
vs. the overall Raman pump for HFAs and equivalent EDFAs (b). In both figures lines refer to theory, circles and 
diamonds to equivalent EDFA and HFA simulative results, respectively. 
 


We extend a model for nonlinear propagation over lumped-amplified uncompensated links to setups using Raman amplification. We compare theoretical to simulative results for PM-16QAM Nyquist-WDM on PSCF links, showing an excellent agreement. We also show that Raman NLI enhancement gives limited practical impairments in realistic setups

CURRI, Vittorio

CARENA, Andrea

POGGIOLINI, PIERLUIGI

BOSCO, GABRIELLA

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEEvaluation of Non-Linear Interference in Uncompensated Links using Raman Amplification / V. Curri; A. Carena; P.Poggiolini; G. Bosco; F. Forghieri. - ELETTRONICO. - (2012), pp. 1-3. ((Intervento presentato al convegno EuropeanConference on Optical Communication (ECOC) tenutosi a Amsterdam nel September 2012.OriginalEvaluation of Non-Linear Interference in Uncompensated Links using Raman AmplificationPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2503775 since:The Optical Society of America (OSA)We.2.C.5.pdf ECOC Technical Digest © 2012 OSAEvaluation of Non-Linear Interference in Uncompensated Links using Raman Amplification V. Curri(1), A. Carena(1), P. Poggiolini(1), G. Bosco(1), F. Forghieri(2) (1) DET, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy. curri@polito.it (2) Cisco Photonics Italy srl, Via Philips 12, 20900, Monza, Italy. fforghie@cisco.com Abstract We extend a model for nonlinear propagation over lumped-amplified uncompensated links to setups using Raman amplification. We compare theoretical to simulative results for PM-16QAM Nyquist-WDM on PSCF links, showing an excellent agreement. We also show that Raman NLI enhancement gives limited practical impairments in realistic setups. Introduction Modern optical communications are fast evolving  towards the use of multilevel modulation formats using coherent receivers based on digital signal processing (DSP)1. For such system scenarios it has been demonstrated that optimal setups are highly-dispersive uncompensated links2. To further increase spectral efficiency, a promising option is the use of Nyquist-WDM with channel spacing approaching the symbol-rate3. For this system category, it has been shown that fiber nonlinearities act introducing an additional Gaussian noise-like component called nonlinear interference (NLI)4. Theory allowing to analytically derive the amount of NLI in lumped-amplified links has been described and validated by simulations4 and experiments5. With the increasing of cardinality of modulation formats, for instance moving from PM-QPSK to PM-16QAM, the use of hybrid Raman/EDFA amplification (HFA) seems to be the solution for achieving ultra long-haul distances6.  In this work, we present the extension of NLI theory to setups based on Raman amplification. After introducing the theory, we validate it by comparing theoretical derivations to simulations of a Nyquist WDM PM-16QAM link made of pure silica-core fiber (PSCF). Simulation results display excellent agreement with theory.  Theory We consider the transmission over a multi-span uncompensated link of Nch Nyquist WDM channels at symbol rate Rs with channel spacing f=Rs  It can be shown that the power spectral density GNLI of NLI on the center channel (worst-case) at the receiver can be expressed as4:    )1(d2log2sin2sin27256222222220322  optssseffTxNLIBLLNLPGoptBwhere  is the fiber nonlinear coefficient, PTx is the transmitted power per channel, Leff is the fiber effective length, 2 is the dispersion coefficient, Ls is the span length, Ns is the number of spans, Bopt=Nch·Rs and  is the FWM efficiency7. Eq. (1) is obtained from the general expression of GNLI reported in4 (evaluated at f= 0), with a proper change of variables based on the use of hyperbolic coordinates (e.g. 2=f1·f2). that holds for f=Rs. In general, the FWM efficiency vs. phase-mismatch is given by7     )2(d4exp)(1202222 sLcheffzzjzpL where pch(z) is the normalized power evolution that  depends on fiber loss coefficient s and on Raman pump evolution. Supposing counter-propagating and undepleted pump, Pp(z)=Ppump·exp{-p(Ls-z)}, where p is the pump loss coefficient and Ppump is the launched pump power,  assumes the following close-form:              )3(23.0,23.0,23.0,23.0,23.022222RAAGRAAGjAGGkkGjkjkfpRAfpRAfpRAwhere s,xis the upper-incomplete gamma-function8, GRA is the Raman on-off gain expressed in dB, Afp=exp{p·Ls}, k=s/p, =(2222/p. Eq. (3) depends only on the overall Raman gain, therefore it is valid also for RxX NsEDFA80 kmPSCFPM-16QAMNyquist WDMTx(a)(b)RA pumpsGFF(c)0 200 400 600 800 1000 120002468101214Ppump[dBm]GRA[km]0 200 400 600 800 1000 1200-4-3-2-10123456Ppump[dBm]Feq[km] Fig. 1: Layout of the analyzed system setup (a), Raman on-off gain (b) and HFA equivalent noise figure (c) vs. overall pump power. We.2.C.5.pdf ECOC Technical Digest © 2012 OSAmulti-pump counter-propagating Raman setups provided that pump depletion is negligible. In case of relevant pump depletion, the analysis holds using Eq. (2) for  evaluation. The system BER can then be derived from the non-linear OSNR4, defined as:  )4(nNLIASETxNLBGGPOSNR  where GASE is the overall ASE noise power spectral density and Bn is the OSNR reference bandwidth. Validation setup In order to test the theoretical derivations, we analyze the system setup shown in Fig.1a. It is a Ns spans link carrying 11 PM-16QAM Nyquist-WDM channels at Rs=32 Gbaud and channel spacing f=Rs. Channels are electrically shaped using a Nyquist raised-cosine filter with roll-off=0.02 and an ideal DAC. The required OSNR in 0.1 nm in order to obtain the target BER=10-3 is 23 dB. The system is composed of several spans of PSCF with length Ls=80 km. Each fiber span is followed by a coupler enabling counter-propagating Raman pumping, a gain flattening filter (GFF) that ideally compensates for the Raman gain tilting and an EDFA with noise-figure F=6 dB that recovers the residual loss. The PSCF parameters are: s,dB=0.185 dB/km, p,dB=0.3 dB/km, D=20.6 ps/nm/km (2=-26.2 ps2/km) and =0.81 1/W/km. We include 5.2 dB of extra losses due to passive components and connectors in the span, hence we assume an overall span loss Aspan=20 dB that is completely recovered by the HFA.  Raman amplification is obtained using three unpolarized counter propagating pumps at 1425, 1436 and 1459 nm. The overall pump power Ppump ranges from 200 mW up to 1200 mW. We limit Ppump to 1200 mW in order to have negligible depletion. As a reference, we also consider EDFA only lumped amplification (Ppump=0 mW). Fig. 1b displays the Raman on-off gain GRA vs. the overall pump power. The maximum value of GRA is 13.1 dB for Ppump=1200 mW and it almost completely recovers the fiber loss that is 14.8 dB. Fig. 1c shows the values of the equivalent noise figure Feq of the HFA for the different Ppump levels. While increasing Ppump,  Feq decreases from 6 dB for the case of EDFA only amplification to -4 dB for Ppump=1200 mW: it corresponds to an OSNR improvement of 10 dB. We first apply the theory in order to evaluate the NLI enhancement GNLI/GNLI,EDFA of the NLI in cases of HFA with respect to EDFA-only amplification. Results are plotted in Fig. 2 as  vs. Ppump for Ns=5 and Ns=30: the maximum value of   is 2 dB, for Ppump=1200 mW. From these results it can also be deduced that the presence of Raman amplification, besides enhancing the NLI, slightly increases its accumulation along the line and does not increase linearly with Ppump. Such an effect is shown by the larger value of  after 30 spans with respect to the one after 5 spans. We verified however that in all practical scenarios such an effect is limited to a small fraction of dB, as for the presented results, with a negligible impact on system performance.  Simulative results In order to validate the presented theory, we simulate the propagation of 11 PM-16QAM Nyquist-WDM channels in the link setup described in the previous section. We use a polarization diversity Rx based on 90° hybrids and balanced photodetectors. The Rx electric bandwidth is ½·Rs=16 GHz and the local oscillator is supposed to be ideal, without phase noise. The Rx DSP placed after photodetectors operates at 2 samples/symbol and implements ideal electronic dispersion compensators and a butterfly equalizer based on 51-tap FIR filters. The filter coefficients are adjusted through a least mean squares (LMS) algorithm. Simulation results are obtained by simulating 216 symbols (219 bits) per channel  and performing direct error counting on the center channel.  We vary the transmitted power per channel PTx from -5 up to +3 dBm. For each Ppump and PTx we derive the maximum reachable distance Lmax still allowing BER10-3. In order to isolate the effect of NLI enhancement due to Raman amplification, we also consider the unrealistic systems based on equivalent-EDFAs with noise-figures equal to the ones of the HFAs. For each setup we also apply the proposed theory to derive the power PNLI of NLI and  consequently evaluate Lmax at which OSNRNL=23 dB (corresponding to BER=10-3). 0 200 400 600 800 1000 120000.511.52Ppump[mW][dB]Ns=5Ns=30 Fig. 2: NLI enhancement in Raman amplified links with respect to EDFA link for different overall Raman pumping  after 5 and 30 spans We.2.C.5.pdf ECOC Technical Digest © 2012 OSAFig. 3a shows results  in terms of  Lmax  vs. PTx for the EDFA-only link, for the 1200 mW HFA link and for its equivalent EDFA-only link. Lines refer to analytical results, while circles and diamonds are simulative results for EDFA-only and HFA links, respectively. The excellent agreement with simulative results confirms the accuracy of the proposed theoretical evaluation. On such a basis, together with other tests we have carried out and that are not reported here due to lack of space, we can conclude that the developed theory can reliably be applied to uncompensated links using Raman amplification and transmitting coherent modulation formats.  From Fig. 3a it can be also observed that using EDFAs with F=6 dB, Lmax=600 km only, while, with 1200 mW HFAs, Lmax=2400 km, corresponding to 4-times (6 dB) on Lmax. It is due to 10 dB ASE noise reduction (Feq from 6 dB to -4 dB) and NLI noise enhancement inducing the optimal power PTx,opt going from 1.5 dBm down to -2.5 dBm, i.e., 4 dB reduction. Moreover, we have seen in Fig. 2 that the 1200 mW HFA induces 2 dB NLI enhancement,  corresponding (compare in Fig 3a, Eq. EDFA to HFA) to 0.5 dB reduction on both PTx,opt and Lmax. Hence, even with =2 dB, effects of NLI enhancement due to Raman amplification are limited. Fig. 3b shows results as Lmax at PTx,opt for all the considered HFA setups and for their equivalent-EDFA links. As well as in previous plots, lines refer to theory while circles and diamonds are obtained by simulation. The excellent agreement between theory and simulations for all pump levels gives a further confirmation to the validity of the theory. Moreover, it can be observed that up to Ppump=800 mW, corresponding to =1 dB, effects of NLI enhancement are practically negligible. It indicates  that, keeping the NLI enhancement below 1 dB, Raman amplification induces negligible impairments with respect to its equivalent-EDFA, i.e., we have benefits of noise reduction without excess NLI impact. Note that, in general, for a fixed Ppump,  decreases with the increasing of Ls. The reason is a reduction of the power at the end of the fiber span, where the Raman gain has higher effects. As a practical consequence, in most long-span links  is smaller than 1 dB, giving a negligible impact on system performance. Conclusions We  presented  the extension of the theory of NLI for uncompensated links to systems based on Raman amplification. We showed general results and a specific close form for undepleted and counter-propagating pumps. Theory was successfully validated by simulation of Nyquist WDM PM-16QAM links on PSCF.  Acknowledgements This work was supported by CISCO Systems within a SRA contract. The simulator OptSim® was supplied by RSoft Design Group Inc. References 1 M. G. Taylor, PTL, Vol. 16, p. 674, 2004 2 M. S. Alfiad et al., JLT, Vol. 27, p. 3590, 2009 3 G. Bosco et al., PTL, Vol. 22, p. 1129, 2010 4 A. Carena et al., JLT, Vol. 30, p.1524, 2012 5 E. Torrengo et al., Op.Exp., Vol. 19, p. B790, 2011 6 Yamanaka et al., ECOC 2010, paper We.8.C.1 7 N. Shibata, JQE, Vol. 23, p. 1205, 1987 8 M. Abramowitz, I. A. Stegun, Handbook of mathematical functions, 1965 -5 -4 -3 -2 -1 0 1 2 34006008001000120014001600180020002200240026002800PTx[dBm]Lmax[km](a) (b)HFA Ppump= 1200 mWFeq = -4 dBEDFAF = 6 dBEquivalent  EDFAF = -4 dB0 200 400 600 800 1000 12004006008001000120014001600180020002200240026002800Ppump[mW]Lmax@LPTx,opt[km]HFAEquivalent EDFA Fig. 3: Maximum reach Lmax @ BER≤10-3 vs. the transmitted power (PTx) for EDFA only, HFA with Ppump= 1200 mW and its equivalent EDFA with F = -4 dB (a). Maximum reach @ BER≤10-3 for the optimal transmitted power vs. the overall Raman pump for HFAs and equivalent EDFAs (b). In both figures lines refer to theory, circles and diamonds to equivalent EDFA and HFA simulative results, respectively.  

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https://iris.polito.it/retrieve/handle/11583/2503775/58549/118_ecoc2012.pdf

Evaluation of Non-Linear Interference in Uncompensated Links using Raman Amplification

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