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