Performance Evaluation of DPSK Optical Fiber Communication Systems

1
Performance Evaluation of DPSK Optical Fiber
Communication Systems
DPSK Differential Phase-Shift Keying, a
modulation technique that codes information by
using the phase difference between two
neighboring symbols.

• Jin Wang
• April 22, 2004

2
Outline

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
Introduction
4
Typical Long-Hual Optical Communication System

• 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 lt 10-12. Using DPSK.

5
Modulation Formats
Electric field of optical carrier E(t)
êAexp(jwtf)
Amplitude
Polarization
Phase
Frequency

• 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

6
DPSK in Optical Systems

• Early Experiments ( 1990)
• For the improvement of receiver sensitivity (At
  BER 10-9, 1000 photons/bit for OOK v.s. lt 100
  photons/bit for DPSK)
• Low bit rate 1 Gb/s
• Cooling ( 90s ) After the Advent of Optical
  Amplifiers
• High sensitivity OOK receiver (lt100 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 (lt 1
  of data rate)
• Recent Revival ( 2002)
• For the improvement of receiver sensitivity (lt 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)
OOK System
Bits
E(t)
G
i
Electricalfilter
1 0 1 1
E(t)

• Bit set 0, 1 ? symbol set 0, 1.
• One symbol transfers one bit information.
• Easy to modulate and detect.

Non-return-to-zero (NRZ) OOK Signal
t
E(t)
Return-to-zero OOK Signal
t
Detected Signal
Symbol constellation for OOK
Signal-ASE beat noise is dominant noise
ImE
Probability density function of i
ReE
0
1
8
Binary DPSK (2-DPSK)
2-DPSK System
i
Ts
Elec.Filter
E(t)
Bits
Differential Encoder
Optical Filter
Laser Mod.
G
Es
Interferometer
1 0 0 1
E(t)

• 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 p-
  phase change

NRZ-2-DPSK signal
t
E(t)
RZ-2-DPSK signal
t
Symbol constellation
9
Quadrature DPSK (4-DPSK)

• 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.

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Transmission 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).

CD Parameter, 3 17 ps/km/nm
Fiber length
1
1
1
0
40 km D17 ps/km/nm
40 km D 17 ps/km/nm
10 Gb/s signal
11
Transmission Impairments - II

• Fiber 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 .

? No analytic solutions for general input,
numerical approach necessary (split-step FFT)
12
Transmission Impairments - III

• Polarization Mode Dispersion (PMD)
• Origin
• Principal states model
• Linear effect in optical domain. Baseband TF of
  fiber with PMD
• PMD stochastic. PMD causes ISI. Impact ? D?.

Input field E0(t)
D?
? power splitting ratio. D? differential group
delay.
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Challenges 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)
4
16
16
8
8
3
DPSK
Relative Bandwidth (Hz)
Spectral Efficiency (bits / symbol)
PAM (Pulse Amplitude Modulation) OOK is 2-PAM
4
4
2
2
2
1
1
0
3
6
9
12
15
18
-3
Relative Required Light Power (dB) to Achieve
10-9 BER in Ideal System

• 2-DPSK vs. OOK Power ? ? FNL ?, Power variation
  ? ? FNL ?
• 4-DPSK vs. OOK Spectrum efficiency ?, CD ? , PMD
  ? , FNL ?.

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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
Bit Error Analysis in DPSK Systems
17
BER Calculation using Eigenfunction Expansion
Bits
G
i
ElectricalLPF

• Neglect fiber nonlinearity

e(t)
i(t)
.2

• Square in time domain ? Convolution in
  frequency domain

K(f, f) Hermitian

• The 2nd kind of homogeneous Fredholm integral
  equation

?m(f) is a complete orthornormal function set

• Eigenfunction expansion

?2 distribution
Noise
Signal
18
BER calculation in DPSK system II
One more step to obtain BER
Moment generating function (MGF) of i(t) is ?
(s), i.e., ? (s)
Eesi Laplace transform of PDF of i(t)
? di
L-1
PDF of i(t)
BER (CDF of i(t))
One Integral
We use saddle point integration method to
calculate the integral of MGF.
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Saddle 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,

q(u)
u
u0
20
Accuracy of BER calculation method

• 10 Gb/s system, with Gaussian optical filter
  and 5th-order Bessel electrical filter.

4-DPSK
4-DPSK
2-DPSK
2-DPSK
OSNR is optical signal-to-noise ratio
21

1. Transmission Impairments in DPSK Systems

22
Power 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 .
RZ-2-DPSK
NRZ-OOK
RZ-OOK
NRZ-2-DPSK
4-DPSK
D CD parameter, R Bit rate, L fiber length
R Bit rate, D CD parameter, L fiber length
R2DL
23
Power Penalty of PMD
NRZ-OOK and NRZ-2-DPSK
RZ-OOK and RZ-2-DPSK
NRZ-4-DPSK
RZ-4-DPSK
D? Differential group delay, Tb Bit period.
24
Link Distance Limitation due to PMD
RZ-4-DPSK
NRZ-4-DPSK
Fiber PMD parameter 0.25 ps/
25
Power Penalty of Interferometer Phase Error
Ts
0.1 mm path error ? 15º phase error
4-DPSK
2-DPSK
26

1. Electrical Equalizer in DPSK Systems

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Electrical Equalizer in Optical Systems
Feed-forward equalizer (FFE)

Td
Td
Td
From electrical low-pass filter
c1
c2
cM
?
Decided bits
d1
d2
dN
Data-feedback equalizer (DFE)

Ts
Ts
Ts
Td may be symbol duration or a fraction of it.

• 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.

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Equalizer based on LMS algorithm
FFE
ek
1
v(t)
?

T
T
ek
c0
_
c1
cM




0
?
yk


kT
Ik
dN
d1

T
T
ltek2gt is minimized
DFE
or
29
Performance of Electrical Equalizer
OOK - CD
OOK - PMD
DPSK - PMD
DPSK - CD
30
Nonlinear DPSK Systems
31
Nonlinear 2-DPSK and OOK Systems
E(t)
Bits
Post-Compensator
Receiver
Pre-Compensator
Transmitter
DL ?1176 ps/nm
DL ?1176 ps/nm
DCF fiber DL ?258 ps/nm
Pulses Chirped RZ (phase varies with power)
noise
G
Light loss in fiber 0.2 dB/km Nonlinear
parameter ? 1.5 /W/km
80 km, LEAF fiber DL 280 ps/nm
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.

32
BER 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 (23 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
Performance of Nonlinear OOK and DPSK
CRZ-OOK
CRZ-DPSK
Threshold

• There exists an optimum optical power for both
  OOK and DPSK systems.
• DPSK has lower BERs than OOK because of lower
  FNL.

34
Current Work

• 4-DPSK long-haul transmission experiment

EDFA
21 dBm
Coupler
VOA
100 km
Raman
Pol Scr
DCF
EDFA
Fiber
21 dBm
Coupler
Fiber
VOA
100 km
DCF
Raman
4-10 dB
5.6 dB
3 dB
Coupler
SW 2
Preamp

• Recirculating Loop

DMUX / RX
SW 1
TX / MUX
BERT