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IEEE GLOBECOM 2011, Houston, TX, December 7, 2011
Citation preview
Range of Influence of Physical Impairments inWavelength-Division Multiplexed Systems
Houbing Song and Maıte Brandt-Pearce
Charles L. Brown Department of Electrical and Computer EngineeringUniversity of Virginia, USA
[email protected], [email protected]
IEEE GLOBECOM 2011Houston, Texas, USA
Wednesday, 7 December 2011
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Outline
Introduction
2D Discrete-Time Model
Range of Influence
Conclusion
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 2/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Motivation
Performance of long-haul WDM systems limited byPhysical Impairments
Fiber LossDispersionFiber Nonlinearity
Amplified Spontaneous Emission (ASE) Noise
Fiber Modeling: Prerequisite for development of physicalimpairment mitigation techniques
2D
Time: IntrachannelWavelength: Interchannel
Discrete-Time
Digital CommunicationsDigital Signal Processing (DSP)
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 3/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Concept of Range of Influence (RoI)
1 ... 1 1 1 1... ... ...
1 ... 1 1 1 1... ... ...
1 ... 1 1 1 1... ... ...
1 ... 1 1 1 1... ... ...
1 ... 1 1 1 1... ... ...
Intrachannel RoI
Intrachannel RoI
Inte
rcha
nnel
RoI
Inte
rcha
nnel
R
oI
: : :
:::
: : :
: ::
Wav
elen
gth
Time
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 4/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Significance
Signal Processing for Optical Communications
PredistortionEqualizationConstrained Coding......
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 5/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Long-Haul WDM System
Laser 0
WDM
MUX
Dispersion
CompensatorAmplifier
( )ts ( )( )0,tA n ( )( )LtA n , ( )( )0,1 tA n +
n th span
Laser F-1
kFa 1−
ka0
( )ts F 1−
( )ts0
( )tr
Assumptions:
Chirped Gaussian pulses
Gaussian optical filters
No ASE noise
No predetection optical filtering
No photodetection
No postdetection electrical filtering
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 6/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Input and Output
Input-output model: {afk} ⇒ {rf (tk )}
... 1 1 ...
... 1 ...
... 1 1 ...
... ... ...
Wav
elen
gth
Time
0
0
0
... ...
... ...
.........
[ ]fka
... ? ? ...
... ? ...
... ? ? ...
... ... ...
Wav
elen
gth
Time
?
?
?
... ...
... ...
.........
( )[ ] ?=kf trGiven input matrix Output matrix
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 7/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Volterra Series Transfer Function (VSTF)
A(ω, L)≈H1(ω, L)A(ω, 0) +
∫ +∞
−∞
∫ +∞
−∞H3(ω1, ω2, ω−ω1+ω2, L)
A(ω1, 0)A∗(ω2, 0)A(ω − ω1 + ω2, 0)dω1dω2
where
H1(ω, L) = exp(−α2L + i
β2
2ω2L),
H3(ω1, ω2, ω − ω1 + ω2, L)=iγ
4π2H1(ω, L)
∫ L
0exp[−αz +
iβ2z(ω1 − ω)(ω1 − ω2)]dz
A(ω, z) : Fourier transform of A(t, z)H1(ω, L): linear transfer functionH3(ω1, ω2, ω − ω1 + ω2, L): nonlinear transfer function
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 8/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Optical Equalization:
H−11 (ω, L) = exp(
α
2L− i
β2
2ω2L)
Input Signal:
S(ω) =√
2πF−1∑f =0
K−1∑k=0
afkAf Tf
exp
[−
(ω − f ∆)2T 2f
2− i(ω − f ∆)kTs + iΦfk
]
where
Af =√Pf , where Pf is launched peak power
T 2f =
T 20f
1+iCf, where T0f is pulse width, Cf is chirp parameter
Φfk : pulse phase
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 9/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Model Development
Step 1: Extend VSTF to multispan multichannel multipulsecase to get R(ω)
Step 2: Simplify R(ω) from triple integral to simple integral
Step 3: Take inverse Fourier transform to get r(t)
Step 4: Sample r(t)
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 10/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
2D Model
r(t) =F−1∑f =0
K−1∑k=0
afkAf exp
[−(t − kTs)2
2T 2f
+ if ∆t + iΦfk
]
+ iNγF−1∑u=0
F−1∑v=0
F−1∑w=0
K−1∑l=0
K−1∑m=0
K−1∑n=0
aulavmawnAuAvAw TuTv Tw
× exp[i(Φul − Φvm + Φwn) + i∆Ts(ul − vm + wn)]
× E (t)
∫ L
0exp(−αz)J(t, z)dz
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 11/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
E(t) and J(t,z)
E (t) = exp
[−(u∆)2T 2
u
2− (v∆)2T 2
v
2− (w∆)2T 2
w
2
].
J(t, z) =
exp
{{u∆T 2
u +v∆T 2v +w∆T 2
w +A1+B1+i [t−(l−m+n)Ts ]}2
2(T 2u +T 2
v +T 2w +2A2)
}√[(
T 2u + T 2
v
)(T 2
v + T 2w
)−(T 2
v + iβ2z)2]
× exp(A0 + B0 + C )√T 2
u + T 2v + T 2
w + 2A2
.
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 12/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Impairment Coefficients
ISI
ρISIk,k
= exp
[−(k − k)2T 2
s
2T 2f
].
Intrachannel
ρintraf ,k,l ,m,n = iγE intra
l ,m,n
∫ L
0exp(−αz)J intra
l ,m,ndz .
intra = SPM, IXPM, IFWM
Interchannel
ρinterf ,k,u,v ,w = iγE inter
u,v ,w
∫ L
0exp(−αz)J inter
u,v ,wdz .
inter = XPM,FWM
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 13/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Intrachannel Example
Table: Index Triplets [lmn] for a Triple Pulse Case
Nonlinearity Time Location l −m + n-2 -1 0 1 2 3 4
SPM 000 111 222
IXPM 011 001 002022 221 112110 100 200220 122 211
IFWM 020 010 121 012 101 102 202021 210 201120 212
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 14/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Intrachannel Coefficients Example
Table: Intrachannel Coefficients for a Triple Pulse Case
NL Time Location l −m + n-2 -1 0 1 2 3 4
SPM 0.0212 0.0212 0.0212
IXPM 0.0096 0.0096 0.00520.0052 0.0096 0.00960.0096 0.0096 0.00520.0052 0.0096 0.0096
IFWM 0.0003 0.0028 0.0028 0.0028 0.0028 0.0012 0.00030.0012 0.0028 0.00120.0012 0.0028
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 15/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Interchannel Example
Table: Index Triplets [uvw] for a Triple Channel Case
Nonlinearity Frequency Location u − v + w-2 -1 0 1 2 3 4
XPM 011 001 002022 221 112110 100 200220 122 211
FWM 020 010 121 012 101 102 202021 210 201120 212
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 16/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Interchannel Coefficients Example
Table: Interchannel Coefficients for a Triple Channel Case
NL Frequency Location u − v + w-2 -1 0 1 2 3 4
XPM 0.0207 0.0207 0.01910.0191 0.0207 0.02070.0207 0.0207 0.01910.0191 0.0207 0.0207
FWM 0.0187 0.0206 0.0206 0.0197 0.0206 0.0194 0.01870.0194 0.0197 0.01940.0194 0.0206
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 17/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
2D Discrete-time Model:
rf (kTs) = afkAf e(if ∆kTs +iΦfk ) +
K−1∑k=0;k 6=k
af kAf e(if ∆kTs +iΦf k )ρISI
k,k
+ Na3fkA
3f T
3f e
(if ∆kTs +iΦfk )ρSPM
+ NK−1∑
l ,m,n=0
aflafmafnA3f T
3f e
(if ∆kTs )
× e [i(Φfl−Φfm+Φfn)][ρIXPM
f ,k,l ,m,n + ρIFWMf ,k,l ,m,n
]+ N
F−1∑u,v ,w=0
aukavkawkAuAvAw TuTv Twe(if ∆kTs )
× e [i(Φuk−Φvk +Φwk )][ρXPM
f ,k,u,v ,w + ρFWMf ,k,u,v ,w
]+
F−1∑f =0;f 6=f
K−1∑k=0
af kAf e(if ∆kTs +iΦf k )e
[− (k−k)2T 2
s2T 2
f
]
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 18/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Advantages
Mapping: binary input matrix ⇒ sampled output matrix
Greatly reduced computational complexity
Arbitrarily isolate any individual physical impairment
Strong analytic capacity
Effects of system parameters: F ,∆,T , L,NEffects of pulse parameters: K ,Af ,T0f ,Cf ,Φfk
Effects of fiber parameters: α, β2, γ
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 19/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Range of Influence (RoI) Definitions
Definition: the number of adjacent symbols/channels causing asignificant effect (smaller than some tolerance)
D ISI (k) =∑k+k
k=k+1
∣∣∣ρISIk,k
∣∣∣D IXPM(IFWM)(k) =
∑k+kl ,m,n=k+1
∣∣∣ρIXPM(IFWM)f ,k,l ,m,n
∣∣∣DXPM(FWM)(f ) =
∑f +fu,v ,w=f +1
∣∣∣ρXPM(FWM)f ,k,u,v ,w
∣∣∣
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 20/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Range of Influence (RoI) of ISI
0 1 2 3 4 5 6 7 8 9 1010
−3
10−2
10−1
100
Number of Symbols
Cum
ulat
ive
ISI D
egra
datio
n
Rs=40 Gs/s
Rs=100 Gs/s
RoI(40)=RoI(100)=1
Figure: Computation of cumulative degradation due to ISI for SMF fiberoperating at 1.55 µm for various symbol rates
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 21/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Range of Influence (RoI) of IXPM
0 20 40 60 80 100 120 140 160 180 20010
−3
10−2
10−1
100
Number of Symbols
Cum
ulat
ive
IXP
M D
egra
datio
n (m
W−1
ps−3
)
Rs=40 Gs/s
Rs=100 Gs/s
RoI(100)=185
RoI(40)=19
Figure: Computation of cumulative degradation due to IXPM for SMFfiber operating at 1.55 µm for various symbol rates
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 22/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Range of Influence (RoI) of IFWM
0 50 100 150 200 250 300 350 40010
−3
10−2
10−1
100
101
Number of Symbols
Cum
ulat
ive
IFW
M D
egra
datio
n (m
W− 1p
s− 3)
Rs=40 Gs/s
Rs=100 Gs/sRoI(40)=65
RoI(100)=300
Figure: Computation of cumulative degradation due to IFWM for SMFfiber operating at 1.55 µm for various symbol rates
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 23/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Range of Influence (RoI) of XPM
0 2 4 6 8 10 12 14 16 18 2010
−4
10−3
10−2
Number of Channels
Cum
ulat
ive
XP
M D
egra
datio
n (m
W−1
ps−3
)
∆=50 GHz
∆=100 GHz
RoI(50)=3
RoI(100)=2
Figure: Computation of cumulative degradation due to XPM for SMFfiber operating at 1.55 µm for various channel spacings
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 24/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Range of Influence (RoI) of FWM
0 2 4 6 8 10 12 14 16 18 2010
−5
10−4
10−3
10−2
Number of Channels
Cum
ulat
ive
FW
M D
egra
datio
n (m
W−1
ps−3
)
∆=50 GHz
∆=100 GHz
RoI(50)=4
RoI(100)=3
Figure: Computation of cumulative degradation due to FWM for SMFfiber operating at 1.55 µm for various channel spacings
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 25/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Conclusion
Development of a 2D discrete-time model of physicalimpairments in long-haul WDM systems
Determination of Range of Influence (RoI) of physicalimpairments
Potential foundation of signal processing for opticalcommunications
multichannel signal processing for intersymbol and interchannelinterference mitigationmultiuser coding, multichannel detection and path-diversity forall-optical networksconstrained coding for WDM systems
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 26/27
Outline Introduction 2D Discrete-Time Model Range of Influence Conclusion
Thank You
RoI of Physical Impairments in WDM Systems: Houbing Song and Maıte Brandt-Pearce, UVA 27/27