performance evaluation of dpsk optical fiber communication systems jin wang april 22, 2004 dpsk:...
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Performance Evaluation of DPSK Optical Performance Evaluation of DPSK Optical Fiber Communication SystemsFiber Communication Systems
Jin Wang
April 22, 2004
DPSK: Differential Phase-Shift Keying, a modulation technique that codes information by using the phase difference between two neighboring symbols.
2
OutlineOutline
1. Introduction
2. Bit Error Analysis in DPSK Systems
3. Transmission Impairments in DPSK Systems
4. Electrical Equalizer in DPSK Systems
5. Nonlinear DPSK Systems
3
1.1. IntroductionIntroduction
4
Typical Long-Hual Optical Communication SystemTypical Long-Hual Optical Communication System
Optical Transmitter
Communication Channel
Optical Receiver
One Span ~ 80 kmfor terrestrial system
Optical Amplifier Optical Fiber
Performance measure: Bit Error Ratio (BER). Required: 10-9 ~ 10-14.
Dominant noise is Amplified-Spontaneous-Emission (ASE) noise from optical amplifiers.
Capacity record (2002): 40 Gb/s/channel, 64 channel, 4000 km, BER < 10 -12. Using DPSK.
OpticalFilter Elec.
Filter
Photodetector
Decoder
Opticalsignal
Bits
Information Bits
Laser
ModulatorOpticalsignalEncoder
Symbols
5
Modulation Formats Modulation Formats
One or more field properties can be modulated to carry information. Example:
On-off keying (OOK): binary amplitude modulation Binary DPSK, Quadrature DPSK : phase modulation Quadrature Amplitude Modulation (QAM): amplitude and phase
modulation
AmplitudePolarization
PhaseFrequency
Electric field of optical carrier: E(t) = êAexp(jt+
6
DPSK in Optical SystemsDPSK in Optical Systems
1. Early Experiments ( ~ 1990) For the improvement of receiver sensitivity (At BER 10-9, 1000 photons/bit for OOK
v.s. < 100 photons/bit for DPSK) Low bit rate: ~ 1 Gb/s
2. Cooling ( 90’s ) After the Advent of Optical Amplifiers High sensitivity OOK receiver (<100 photons/bit) can be realized with the aid of
optical amplifier (Ex. Erbium-Doped Fiber Amplifier) Complicated DPSK transmitter and receiver Stringent requirements on laser linewidth (< 1% of data rate)
3. Recent Revival ( ~ 2002) For the improvement of receiver sensitivity (< 50 photons/bit), reduction of fiber
nonlinearity and increase of spectrum efficiency Interferometric demodulation + direct detection Data rates of 10 Gb/s and 40 Gb/s relaxed linewidth requirements
7
On-Off Keying (OOK)On-Off Keying (OOK)
Symbol constellation for OOK
Im{E}
Re{E}
0 1
Bits E(t) Opticalfilter Electrical
filter
G
)()( tntEs
LaserMod. i
i0 1
Probability density function of i
E(t)
t
t
Non-return-to-zero (NRZ) OOK Signal
Return-to-zero OOK Signal
1 0 1 1 Bit set {0, 1} symbol set {0, 1}.
One symbol transfers one bit information.
Easy to modulate and detect.
2*22)Re(2 nnEEnEi sss
Signal-ASE beat noise isdominant noise
OOK System:
E(t)
Detected Signal:
8
Binary DPSK (2-DPSK)Binary DPSK (2-DPSK)
LaserMod.
DifferentialEncoder
BitsElec.FilterOptical
Filter
Ts
Interferometer
0
0
1 0
Re{E}
Im{E}
1 1i
1
1
E(t)G
NRZ-2-DPSKsignal t
1 0 0 1
t
RZ-2-DPSKsignal
Bit set {0, 1} symbol set {-1, 1} i.e. {ej , ej0}
One symbol transfers one bit information
Bit 0: leave phase alone, bit 1: introduce a phase change
i+
22
2
)()(
2
)()( ssssss TtEtETtEtEi
2-DPSK System:
Es
E(t)
E(t)
Symbol constellation
9
Quadrature DPSK (4-DPSK)Quadrature DPSK (4-DPSK)
1010
1010
01
0101
01 10
11
01
00
1111
11
11
00
00
00
00
EI
EQ
iI
iQ
Bit-pair set {00,01,10,11} symbol set {e± j/4, e± j3/4}
One symbol transfers TWO bits of information. Ts = 2Tb.
Signal bandwidth is only one half of the bit rate.
Elec.LPF
Ts
Ts
90o
Elec.LPF
iI
iQ
LaserMod.
DifferentialEncoder
Bits Optical BPF
E(t)G
4-DPSK System:
10
Transmission Impairments - ITransmission Impairments - I
Chromatic Dispersion (CD)
Origin: The refractive index of fiber is frequency dependent. Analogy:
Linear effect. Baseband TF of fiber: Phenomenon: pulse broadening intersymbol interference (ISI).
2 2.5 3 3.5 4 4.5 5 5.5 6
x 10-10
0
0.5
1
1.5
2
2.5
3
x 10-3
inte
ns
ity
time1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
x 10-10
0
0.5
1
1.5
2
2.5
3
3.5x 10
-3
inte
ns
ity
time 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
x 10-10
0
0.5
1
1.5
2
2.5
3
3.5
x 10-3
inte
ns
ity
time
40 kmD=17 ps/km/nm
1 1 0 1
40 kmD =17 ps/km/nm
)exp()( 22
DLfc
jfH
CD Parameter, 3 ~ 17 ps/km/nm
Fiber length
10 Gb/s signal
11
Transmission Impairments - IITransmission Impairments - IIFiber Nonlinearity (FNL)
Origin: The refractive index of fiber is power dependent. Nonlinear Schrödinger equation (wave equation in fiber):
Effects: Self-phase modulation (SPM) spectrum broadening. Cross-phase modulation (XPM) spectrum broadening. Four-wave mixing (FWM) noise amplification. interchannel crosstalk.
Spectrum broadening + CD intersymbol interference .
EEjEt
Ej
z
E 2
2
2
2 22
CD Fiber Loss
FNL
No analytic solutions for general input, numerical approach necessary (split-step FFT)
12
Transmission Impairments - IIITransmission Impairments - IIIPolarization Mode Dispersion (PMD)
Origin:
Principal states model
Linear effect in optical domain. Baseband TF of fiber with PMD:
PMD stochastic. PMD causes ISI. Impact .
ideal fiber real fiber slow axis
fast axis
bb fjfH ˆ]2exp[1ˆ)(
Input fieldE0(t)
bbout
aain
tEtEE
tEE
ˆ1)(ˆ)(
)ˆ1ˆ)((
0000
0
: power splitting ratio.
: differential group delay.
13
Challenges for Optical Communication SystemsChallenges for Optical Communication Systems
Challenges Solutions
Transmission at ultra high bit rate requires extremely low CD.
Reduce signal bandwidth by transmitting multi-bits with one symbol. (4-DPSK)
Long transmission distance causes significant FNL.
Reduce FNL by decreasing signal power and its variation. (2-DPSK and 4-DPSK)
Ultra short bit period implies high sensitivity to PMD.
Increase symbol period transmitting multi-bits with one symbol. (4-DPSK)
Fixed channel bandwidth, increasing bit rate.
Improve spectrum efficiency by transmitting multi-bits with one symbol. (4-DPSK)
14
DPSK vs. OOK (ASE dominated)DPSK vs. OOK (ASE dominated)
2-DPSK vs. OOK: Power FNL , Power variation FNL 4-DPSK vs. OOK: Spectrum efficiency , CD , PMD , FNL .
0 3 6 91
2
3
4
Relative Required Light Power (dB) to Achieve 10-9 BER in Ideal System
12 15 18-3
2
4
2
8
16
DPSK
PAM (Pulse Amplitude Modulation)OOK is 2-PAM
16
8
4
Spe
ctra
l Eff
icie
ncy
(bit
s / s
ymbo
l)4
1
3
1
1
Rel
ativ
e B
andw
idth
(H
z)
2
1
15
How Robust is DPSK?How Robust is DPSK?
CD
PMD Impacts on DPSK not quantified before.
FNL
Reasons for the dearth of impact analysis:
The BER of DPSK systems has been difficult to calculate, because of the squaring effect of photodetector.
The interaction of CD and FNL in fiber increases the difficulty of modeling optical noise in fiber.
16
2.2. Bit Error Analysis in DPSK SystemsBit Error Analysis in DPSK Systems
17
BER Calculation using Eigenfunction ExpansionBER Calculation using Eigenfunction Expansion
'])'(2exp[)'()',()(*)( dfdftffjfEffKfEti
Bits
e(t)
OpticalBPF Electrical
LPF
GLaserMod. i
| .|2)( fHo
i(t))( fH e
Square in time domain Convolution in frequency domain
')'()',()( dffffKf mmm
The 2nd kind of homogeneous Fredholm integral equation:
Eigenfunction expansion:
m
mmmftj fnsefE )()()( 2
mmmm nsti
2)(
2 distribution
Neglect fiber nonlinearity
K(f, f’) Hermitian
{m(f)} is a complete orthornormal function set
Signal Noise
18
BER calculation in DPSK system – IIBER calculation in DPSK system – II
Moment generating function (MGF) of i(t) is (s), i.e.,
(s)= E[esi] = Laplace transform of PDF of i(t)
)(s L-1PDF of i(t) BER (CDF of i(t))
We use saddle point integration method to calculate the integral of MGF.
One more step to obtain BER:
di
One Integral
19
Saddle Point IntegrationSaddle Point Integration
Also called stationary phase method, especially in physics.
Basic idea: For the calculation of line integral :
If amplitude f(u) changes slowly compared to phase q(u), the main contribution
to the integral comes from very near u0 where the phase is stationary, i.e,
duufeH ujq )()( )(
0)(' 0 uq
0near
)( )()(u
uqj duufeH u
q(u)
u0
20
Accuracy of BER calculation methodAccuracy of BER calculation method 10 Gb/s system, with Gaussian optical filter and 5th-order Bessel electrical filter.
8 10 12 1410
-6
10-5
10-4
10-3
10-2
OSNR (dB)
BE
R
NRZ-DPSK
BER calculationMonte Carlo
8 10 12 1410
-6
10-5
10-4
10-3
10-2
OSNR (dB)
BE
R
RZ-DPSK
BER calculationMonte Carlo
2-DPSK
4-DPSK
2-DPSK
4-DPSK
OSNR is optical signal-to-noise ratio
21
3.3. Transmission Impairments in DPSK Transmission Impairments in DPSK SystemsSystems
22
Power penalty of CDPower penalty of CD
Power Penalty: To account for the transmission impairments, the increase in the optical power to maintain a fixed BER such as 10-9 .
D: CD parameter, R: Bit rate, L: fiber length
0 5 10 150
1
2
3
4
5
6
DB2L [104 (GHz)2ps/nm]
Pow
er P
enal
ty (
dB)Super-Gaussian Optical Filter
NRZ-OOKRZ-OOKNRZ-2-DPSKRZ-2-DPSKNRZ-4-DPSKRZ-4-DPSK
4-DPSK
R: Bit rate, D: CD parameter, L: fiber lengthR2DL
NRZ-2-DPSK
RZ-OOK
RZ-2-D
PSK
NRZ-OOK
23
Power Penalty of PMDPower Penalty of PMD
: Differential group delay, Tb: Bit period.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
1
2
3
4
5
6
/Tb
Pow
er P
enal
ty (
dB)
Super-Gaussian Optical Filter
NRZ-OOKRZ-OOKNRZ-2-DPSKRZ-2-DPSKNRZ-4-DPSKRZ-4-DPSK
RZ-4-DPSK
NRZ-4-DPSK
RZ-OOK andRZ-2-DPSK
NRZ-OOK andNRZ-2-DPSK
24
Link Distance Limitation due to PMDLink Distance Limitation due to PMD
10-8
10-7
10-6
10-5
10-4
10-3
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
10 G
b/s
Syst
em
Outage Probability
NRZ-OOKRZ-OOKNRZ-2-DPSKRZ-2-DPSKNRZ-4-DPSKRZ-4-DPSK
40 G
b/s
Syst
em
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
(km) (km)
Fiber PMD parameter 0.25 ps/ km
NRZ-4-DPSK
RZ-4-DPSK
25
Power Penalty of Interferometer Phase ErrorPower Penalty of Interferometer Phase Error
Ts
m path error 15º phase error
0 5 10 15 20 25 30 35 40 45 500
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Phase Error (deg)
Pow
er P
enal
ty (
dB)
Super-Guassian Optical Filter
NRZ-2-DPSKRZ-2-DPSKNRZ-4-DPSKRZ-4-DPSK
4-DPSK
2-DPSK
26
4.4. Electrical Equalizer in DPSK SystemsElectrical Equalizer in DPSK Systems
27
Electrical Equalizer in Optical SystemsElectrical Equalizer in Optical Systems
Td Td Td
c1 c2 cM
From electrical low-pass filter
Feed-forward equalizer (FFE)
Ts Ts
d1 d2 Data-feedback equalizer (DFE)
Ts
dN
…
…
Decided bits
Electrical equalizer is used to reduce ISI caused by CD, PMD, etc.
Electrical equalizer is compact, flexbile, low-cost.
High speed electrical equalizers operate at 10 Gb/s and 40 Gb/s.
Tap weights can be adapted using Least-Mean-Square (LMS), Q-factor maximization
and BER minimization schemes.
Td may be symbol duration or a
fraction of it.
28
-5 0 5-1.5
-1
-0.5
0
0.5
1
1.5x 10
-7
Time
Am
plitu
de
Eye Diagram
Equalizer based on LMS algorithmEqualizer based on LMS algorithm
T
+_
T…
c0 c1 cM
ek
v(t)
+++
kT
T T…
d1dN
DFE
FFE
++ yk Ik
)()()1( kk
kk VeCC
],,,,,,[ 110 NM ddcccC
],,,,,,[ 1)1(1)(
NkkMkkkk IIvvvV
)sgn()sgn( )()()1( kk
kk VeCC
or
0
1 ek
<ek2> is minimized
29
Performance of Electrical EqualizerPerformance of Electrical Equalizer
0 5 10 150
2
4
6OOK
CD
Pen
alty
(dB
)
R2DL [104 (Gb/s)2ps/nm]0 0.2 0.4 0.6
0
2
4
6OOK
PMD
pen
alty
(dB
)
/Tb
0 5 10 150
2
4
6
CD
Pen
alty
(dB
)
R2DL [104 (Gb/s)
2ps/nm]
2-DPSK
0 0.2 0.4 0.60
2
4
62-DPSK
/Tb
PMD
pen
alty
(dB
)
W/O EQFFEFFE+DFE
DPSK - CD
OOK - PMDOOK - CD
DPSK - PMD
30
5.5. Nonlinear DPSK SystemsNonlinear DPSK Systems
31
Nonlinear 2-DPSK and OOK SystemsNonlinear 2-DPSK and OOK Systems
TransmitterBits
E(t)
G
10080 km, LEAF fiberDL = 280 ps/nm
DCF fiberDL = 258 ps/nmPulses: Chirped RZ
(phase varies with power)
NF: 4.5 dB
Total link distance 8000 km.
CD of green fiber + CD of blue fiber + CD of Pre, Post-Compensators 0
( Local high dispersion, global low dispersion )
Pre-Compensator spreads pulses quickly, realizing quasi-linear transmission.
Light loss in fiber: 0.2 dB/kmNonlinear parameter : 1.5 /W/km
noise
Pre-Compensator
Post-Compensator Receiver
DL = 1176 ps/nm DL = 1176 ps/nm
32
BER Calculation in Nonlinear DPSK SystemBER Calculation in Nonlinear DPSK System
No noise model for general nonlinear DPSK or OOK system.
No BER calculation method for general nonlinear DPSK or OOK
system.
Q-factor is not a reliable performance measure, especially for DPSK
system (2~3 dB OSNR error).
In CRZ-DPSK or CRZ-OOK system, noise can be modeled as additive
non-white Gaussian noise because of low fiber nonlinearity.
Non-white Gaussian noise model + eigenfunction expansion method
yields accurate BER.
33
-5 0 5-1.5
-1
-0.5
0
0.5
1
1.5x 10
-7
Time
Am
plitu
de
Eye Diagram
Performance of Nonlinear OOK and DPSKPerformance of Nonlinear OOK and DPSK
1 2 310
-10
10-5
CRZ-OOKB
ER
1 2 3 4 510
-10
10-5
2 4 6 810
-10
10-5
2 4 6 810
-10
10-5
Decision threshold (a.u.)
-1 0 110
-10
10-5
CRZ-DPSK
-2 0 210
-10
10-5
-4 -2 0 2 410
-10
10-5
-5 0 510
-10
10-5
Decision threshold (a.u.)
BE
R 1/6 mW 1/3 mW 1/2 mW 2/3 mW
There exists an optimum optical power for both OOK and DPSK systems. DPSK has lower BERs than OOK because of lower FNL.
CRZ-OOK
CRZ-DPSK
Threshold
34
Current WorkCurrent Work
4-DPSK long-haul transmission experiment
Fiber
Fiber
TX / MUX
Coupler
DMUX / RX
5.6 dB 3 dB
4-10 dB
SW 2
Raman DCF
+21 dBmCoupler
VOA
100 km
100 km
BERT
Preamp
Raman Pol ScrDCF
+21 dBmCoupler
VOA
SW 1
EDFA
EDFA
• Recirculating Loop
Fiber
Fiber