Implications of Nonlinear Interaction of Signal and Noise in Low-OSNR Transmission Systems with FEC...

Implications of Nonlinear Interaction of Signal and Noise in Low-OSNR

Transmission Systems with FEC

A. Bononi, P. SerenaDepartment of Information Engineering, University of Parma, Parma, Italy

J.-C. Antona, S. BigoAlcatel Research & Innovation, Marcoussis, France

A. Bononi et al. OFC ’05 – paper OThW5 2/27

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


DM Terrestrial SystemsNotation

N

OF EF

RX

Bo Be

An z = N x zA km DM system is:

zA

AD

DispersionMap

In-line accumulated

dispersion


Experiments on DM Terrestrial Links

Booster

Preamplifier

M-Z

PRBS

215 -1FM

ECL

100 km

NZDSF

DCF

DCF

-10Sensitivity @ 10 BER

OF

EDFA 1 EDFA 2

0.4 nm

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=2.9ps/nm/km

0.4 nm

OF EF

RxBe

Tx1.

White ASE

source

EDFA 3

2.



[G. Bellotti et al., ECOC ’00, P.3.12]

end-line OSNR25 dB/0.1 nm

2

4

6

8

10

12

14

2 4 6 8 10 12 14 16

Launched power [dBm]

Se

ns

itiv

ity

pe

na

lty

[d

B]

at

BE

R=

10^

(-1

0)

-220 ps/nm

+150 ps/nm

-35 ps/nm

1. With PGIn-line

accumulated dispersion

2. No PG

power threshold



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

Ramanpumps

Tx

DGE

Rx

100 kmDCF

x3

x5

end-lineOSNR

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)


4 5 6 7 8 9 10

13

15

17

19

21

Launched power [dBm]

1. end-line OSNR>30 dB

Rec

eive

d O

SN

R @

BE

R 1

0

[dB

]-5


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


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.


OOK-NRZ Signal

Im[E]

Re[E]

JointPDF

Im[E]

Re[E]

P(t)

t

P(t)

tP

NL

AverageNonlinear

phase

span average

< >


Im[E]

Re[E]In a rotated reference systemwe express the Rx field as:

Rx Field

In-phaseASE

quadratureASE


ASE Spectrum

P(t)

t

N0

PS

D [

dB

]

frequency f

Si(f)

Sr(f)

-4

0

4

8

frequency f

No

rmal

ized

PS

D [

dB

]

Sr(f)

Si(f)Parametric

Gain

P

)2(2 0 oBN

POSNR end-line


0

ASE Statistics

end-line OSNR= 25 dB/0.1nmNL = 0.15 rad

Din =0 Dpre=0 Dpost=0

2 341

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]


Linear PG Model

L in ea rize d N L S E

C Wt

C Wt

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 ]


Linear PG Model

Red : quadrature ASENo pre-, post-comp.

A decreasing map hasnormally less in-phase ASEthan an increasing map

Blue: in-phase ASE

»

ASE gain comes at expense of CW depletion (negligible up to performance disruption)


Linear PG Model

... mixes in-phase and quadrature ASE from the line a large Dpost worsens PG impact on BER

Red : quadrature ASEBlue: in-phase ASE

Post-compensationhowever...

Otimized pre-, post-comp.

Pre-compensation no effecton ASE


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


In-phase ASE PSD at f=0

reason is that ASE-ASE beat is larger when increasing map tilt

20100 km, OSNR=11 dB/0.1nmD=8 ps/nm/km

In-p

has

e P

SD

at

f=0

[dB

]

0 0.2 0.4 0.6 0.8avg nonlinear phase [rad/]

-2

0

2

4

6

8

Din=0 ps/nm

Din=-2000 ps/nm

Din=+2000 ps/nm


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 Rx3. White PSD on zeros4. PSD on ones estimated from Monte-Carlo BPM simulations5. No pump depletion on ones


BER Evaluation

Why use the KL method ?

Im [E]

Re [E]

DecisionThreshold(in optical

domain)

PG stretchesQuadrature ASE

Marcuse’s QFactorformula

erroneouslypredicts large

BER worsening


Theory vs. Experiment

0 0.5 1 1.5-2

0

2

4

6

8

OS

NR

pen

alty

[d

B]

ΦNL

[rad/ ]

Symbols: Experiment

Lines: TheoryOSNR=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

0 0.5 1 1.50

3

6

In-p

has

e P

SD

at f=

0 [

dB

]

ΦNL

[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


We define PG doubling as the condition at which the in-phase ASE PSD at f=0 doubles (+ 3dB)

PG doubling


ΦNL [rad/]ΦNL [rad/]

Extrapolate15x100km, Din=0Optimized Dpre, Dpost

D=2.9NZDSF D=17SMF

0 1 2 3-2

0

2

4

6

8

OS

NR

pen

alty

[d

B]

0 0.5 1 1.5-2

0

2

4

6

8

OSNR=16 dBOSNR=16 dB

OSNR=19 dBOSNR=19 dB

Inp

has

e P

SD

at

f=0[

dB

]

0 1 2 30

3

6

9

0 0.5 1 1.50

3

6

9

ΦNL [rad/]ΦNL [rad/]


In-phase PSD at f=0

N L S E

C Wt

C Wt

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!

Large perturbations Small OSNR


At full in-line compensation (Din=0), analytical approximation is:

In-phase PSD at f =0

where

10 20 30 40 500

0.2

0.4

0.6

0.8

1

spans N

(N

)Map

StrengthT0

=1

At PG doubling


Region below red curve:< ~1dB penalty by PG in

optimized mapdeep 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 systemswith Din=0.

N large

0 0.2 0.4 0.6 0.8Map strength Sn

0

0.2

0.4

0.6

0.8

1

1.2

1.4

NL [r

ad/

]

end-line OSNR (dB/0.1nm)

40 Gb/s

NZDSF

0 1 2 30

3

6

9

0 0.5 1 1.50

3

6

9

SMF

0 1 2 3-202468

0 0.5 1 1.5-202468


10 Gb/s single-channel NRZ system, 20100 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/]0.2 0.4 0.6 0.8

end-line OSNR=11 dB/0.1nm

10

12

1

8Q F

acto

r

[dB

]

6

14

0 Q factor [dB]

log

(BE

R)

with FEC

Uncoded

CG


10 Gb/s NRZ system, 20100 km, D=8 ps/nm/km, Din=0.

Optimizing Dpost

Nonlinear phase [rad/]0 0.2 0.4 0.6 0.8 1

Pos

t di

sper

sion

[ps

/nm

]

noiseless optimized Dpost

Nonlinear phase [rad/]


0.6 0.8 10.4

Q F

acto

r

[dB

]

6

10

8

12

14

0 0.2

with PG-optimized Dpost

PG-optimized Dpost


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.


Gaussian ASE assumption

Beyond PG doubling the assumption of Gaussian ASE gives overestimation of BER

ΦNL = 0.7 rad (beyond PG doubling)

0.4 nm

OF EFRx

Be

Y

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real

Ima

g

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Real

Ima

gMonteCarlo

Gaussian, exact PSD

10 Gb/s NRZ system, 20100 km, D=8 ps/nm/km, OSNR=16 dB, Din=0.

0.5 0.7 0.9 1.1 1.3 1.5-6

-5

-4

-3

-2

-1

0

normalized decision threshold y

10

Gaussian, small-signal PSD

MonteCarlo

Gaussian, exact PSD

CD

F o

f Y

on

Mar

ks

[lo

g

]


10 Gb/s NRZ system, 20100 km, D=8 ps/nm/km, Din=0. Optimized Dpre, Dpost

Q-Factor Q

Fac

tor

[d

B]

6

10

8

12

14

18

16Standard method

(ignores PG)

Nonlinear phase [rad/]0 0.2 0.4 0.6 0.8 1


OSNR=11 dB/0.1nm

noiseless optimized Dpost


0 0.2 0.4 0.6 0.8 19

10

11

12

13

14

15

16

Nonlinear phase [rad/]

Q F

acto

r

[dB

]

end-line OSNR=15 dB/0.1 nm

10 Gb/s NRZ system, 20100 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

Implications of Nonlinear Interaction of Signal and Noise in Low-OSNR Transmission Systems with FEC...

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