Lecture VII
Introduction to Fiber Optic
Communication
Ver 2
COHERENT DETECTION
•
Moshe Nazarathy All Rights Reserved
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1
Coherent detection SNR limits (analog)
I&D IDEAL
PHOTON COUNTER
Analog coherent
Homodyne transmission:
Instantaneous SNR eval
(t-dependence dropped)
id 
  E LO
1
2
 Ed
2
2
  Ed
2
LO
2
  E r  E LO   E r
 2  R e E r E LO e
id  i L O  2
iLO
j (  E r   E LO )
2
  E LO
i r cos   E r   E L O
  E LO
2
 2  Er

set  E r   E L O ( perfect phase trac k ing )
SN R coh  q coh 
sig am p coh
 LO

2
i LO
ir
2 e iLO W

2
2 ir / e
ir
 2  R e E r E LO
*
 E LO cos   E r   E LO 
iLO
iLO   E LO
ir   E r
2
2
W
SNR (sig. pwr / shot-noise var)
at the output of a W Hz
ir
ir / e
sig am p D D
LPF passing the signal
SN R D D  q D D 



2W
So, what’s the Big Deal?
2 e ir W
just 2  better
but…the coherent performance
<<to add “analog” SNR
(a factor of 4
for OADD and heterodyne is practically achievable, DD performance is not !
SYN/ASYN>>
Coh. Det. overcomes receiver thermal noise <<shot-noise in SNR)
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2
Coherent detection – some advantages
Some key advantages of coherent optical
communications:
• Direct access to the received electric field, linearly
accessible by optically coherent downconversion of
the received bandpass optical field.
• Availability of the field enables electronic (digital)
mitigation of channel impairments (CD, PMD, NL)
• Improved sensitivity with the LO power acting as a
gain, in effect boosting the signal prior to electronic
detection (overcome thermal receiver noise).
• Improved frequency selectivity, allowing to use
electrical filters in the RF domain to remove the
noise around the optical carrier and sharply
suppress adjacent optical channels in a DWDM
system.
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3
Coherent detection – some disadvantages
• Needs more coherent lasers – lower
linewidth
• More complex receiver, requiring to
mitigate the phase wander of the optical
source and the fluctuations of optical
polarization
• Disadvantages mitigated by modern
DSP
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The Coherent Receiver Front-End:
A linear Opto-electronic
Downconverter
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Building block for coherent and differential detection:
The Balanced Optical Mixer
Assume signal and LO have same freq. - homodyne
Initially address a single polarization
(scalar treatment)
r ( t )  R ( t )  -port
r (t )
ik  R e r ( t ) R ( t )
*
coupler
R (t )
r (t )  R (t )
Proof:
ik 

2
2

2
2
r (t )  R (t ) 
ik  Im r ( t ) R ( t )
*
90
Proof: Substitute
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(*)
 -port
r (t )  R (t ) 
r (t )
R (t )
“mixing product”
R ( t )  j R ( t ) in (*)
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A pair of BALANCED optical mixers in quadrature
- called 9 0 optical hybrid
implements the complex MIXING PRODUCT
r (t )
*
R e r (t ) R (t )
R (t )
mixing product
*
r (t ) R (t )
r (t )
*
R (t )
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90
Im r ( t ) R ( t )
7
optical hybrid
Coherent Homodyne Receiver Front-End
(e.g. for QPSK)
90
R e r (t ) R
 r (t )e
j r ( t )
 R r ( t ) cos   r ( t )   R 
r (t )
R
 Re
Local
Oscillator (LO)
*
r (t ) R
j R
*
 R r ( t ) sin   r ( t )   R 
Im r ( t ) R
90
r (t ) R
*
 r (t ) R e
j  r ( t )   R 
 r (t )e
*
j r ( t )
Phase
Info
8
Let  R  0 i.e. assume the LO is aligned with the signal phase reference
(real axis of the signal constellation)
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Polarization Diversity 9 0 Hybrid
E s t 
Signal
y
x
x
LO
yxI
i ,1 t 
Single-Polarization
Downconverter I
yxQ
q ,1 t 
Single-Polarization
yyI
i , 2 t 
Downconverter II
PBS y
yyQ
q , 2 t 
Polarization
Beam Splitter
Opto-Electronic DownConverter
E R ( t )  E LO
E R (t )
E LO
coupler
+
_
iI
E R ( t )  E LO
90
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_
E R ( t )  jE LO
+
E R ( t )  jE LO
iQ
Single-Polarization Down-Converter (Optical Demodulator)
9
Putting it all together:
Coherent Receiver block diagram
(homodyne or intradyne)
Intradyne:
Sig. & LO
have nearly
the same freq.
ADC
ADC
DSP
ADC
ADC
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Si PHOTONIC
INTEGRATED
CIRCUIT (PIC)
OL
Y-P
OL
X-P
TUNABLE
LASER
g N
de TIO
90 RIZA OR
LA TAT
PO RO
(90 deg
ROTATED)
Y-POL
COHFE
90
OPTICAL
Rx
FRONT-ENDS
DS Rx
Coherent
Receiver
with
Integrated
Optical
Front-end
PBS
X-P
OL
SOA
X-POL
COHFE
90
°
Q
I
°
Q
I
ADCs
ADCs
X-POL COH
FRONT-END
DSP
Y-POL COH
FRONT-END
DSP
DS RX - DSP
DATA OUT
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11
Homo/Hetero-dyne detection with balanced Optical
Mixer
SIGNAL & LO at same frequency (homodyne)
r (t )  L
r (t )
“mixing product”
 -port
ik  R e r ( t ) L
*
coupler
L
r (t )  L
ik  r ( t ) e
j c t
 Le
 -port
j L t
2
 r (t )e
j c t
 Le
Now let SIGNAL & LO be at different frequencies (heterodyne)
r (t )e
Le
j L t
j c t
ik  R e  r ( t ) e
j L t
j c t
2
  Le
j L t

*
c  L
i k  Re r ( t ) L e
*
j IF t
 r ( t ) L cos   IF t   r ( t )   L 
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Balanced coherent receiver
with electrical quadrature demodulation
and electrical/optical PLL
r ( t ) L cos   IF t   r ( t )   L 
r ( t ) L c os   r ( t )   L 
cos  IF t
 sin  IF t
r ( t ) L sin   r ( t )   L 
“Optical Voltage-Tuned-Oscillator”
Tunable laser
VTO
FIXED
Optical PLL
Actually
decision-directed
PLL
Note: Single-lane scalar version
Assume that a polarization controller rotated the input polarization signal to be
parallel to that of the LO. Alternatively, this is one of the two polarization lanes
of a polarization diversity scheme
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Putting it all together
“Classic” coherent heterodyne receiver
Each polarization lane feeds an electrically coherent
receiver extracting the IQ components by electrical downconversion
with cos/sin subcarriers
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Coherent Homodyne BPSK Receiver
*
Re r ( t ) L
r (t )
L
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In this case the 2nd quadrature
is not necessary
as the noiseless part of r ( t )
does not contain an imaginary part.
Assume that L was tuned to be
real-valued (i.e. in phase or in anti-phase
with the possible values of r ( t )
15
Binary Differential Phase Shift Keying (BDPSK)
0 or 180
The optical mixer
becomes a key
building block
in optical DPSK
realization
rk  1 rk
Extract PD
Differentially Coherent Detection
 rk   rk 1   rk rk 1
*
Re r (t )r (t  T )
*
r (t )
sgn( )
T
DELAY
INTERFEROMETER
(DI) FRONT-END
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r (t  T )
*
k k 1
Re r r
 1

 rk rk 1 cos   rk   rk 1 

 rk rk 1  rk   rk 1
 

  rk rk 1  rk   rk 1  
16
Differential
vs. Coherent
Detection
Previous symbol
DPSK reference
Current symbol
rk  4 rk  3 rk  2 rk  1 rk
(a)
DPSK DETECTION
rk  4 rk  3 rk  2 rk  1 rk
*
COHERENT DETECTION
LO
LIGHT
SOURCE
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*
(b)
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QDPSK receiver front-end

I-port
r (t ) r (t  T ) e
*
r (t )
T

 90
T
Q-port
The bias effects a rotation of the constellation: Typically 
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j
18

45
18
QDPSK receiver front-end
r (t )r (t  T )e
*
 45
r (t )
I-port
T


j / 4
45
sgn( )


sgn( )


1
1
 45
T
Q-port
19
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Homodyne/Intradyne Coherent Receiver
Technology considerations
X-pol.
Y-pol.
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Coherent Transmitter block diagram
Technology considerations
Alternative
View
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100G Coherent Polarization-Muxed QPSK
(PM-QPSK) is the next step
Two phase DOFs and two polarization DOFs: 28 Gbaud operation
Parallel transmission of 28Gb/sec on each quadrature of each polarization: 4 parallel lanes
112Gb/s  2 polarizations 56 Gb/s each, QPSK (2 bits/sym), 28Gsym/sec
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A formulation of
COHERENT DETECTION
MODELING
and error probability performance
- suited for communication
engineers
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Coherent detection model (HOM/HET)
iLO   E LO
dd
I&D IDEAL
PHOTON COUNTER

id   E d
  Er
  Er
2
2
  E re
j c t
 E LO e
 IF
j LO t
2
  Er
2
  E LO
 j (  E r   E LO )
dd
ir
 2  R e E r E LO e
*
 2  R e E LO E r e
  E LO
2
 2  E LO E r cos   IF t   E r   E LO 

e
dd
ir
j
 c   L O  t
j I F t
2
 E LO 
(LO boosting) factor

2
  E LO
Coherent Gain g L O   E L O 
id 
2
 E LO

dd
iLO
LO
2
2
  Er
dd
ir

dd
iLO
 iLO

dd
dd
iL O
 i LO  2 g LO E r cos   I F t   E r   E L O 
dd
 i LO  2 R e g LO E r e
dd
g LO  g LO e
j (  IF t   E r   E LO )
j  E LO
Homodyne: Just set  IF  0
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
HET: i d 
HOM:
 i L O  2 R e g LO e
dd
dd
ir
id 
 j  E LO
E re
j IF t
 i LO  2 R e g L O E r e
dd
dd
ir
dd
ir
*
j IF t
 i LO  2 R e g LO E r
dd
*
25
Full optical demodulator - 90 deg balanced hybrid – heterodyne
i 
I
d

E re
2
j c t
 E LO e
j LO t
2


Ere
2
j c t
 E LO e
Ere
E LO e
1

1
1 

 1
1
2
2
 2 R e g LO E r e
g LO 
Coupling matrix
1
2
j LO t
in field 
1
2
 E re

j c t
 E LO e
j LO t


j LO t
dd
+
_
1
2
 E re

j c t
 E LO e
j LO t


Single-Polarization Single-Quadrature Down-Converter
(Optical Demodulator)
Relative to a single-ended detector,
the SNR at the balanced detector differential output is halved
(assuming same # of signal photons at input)
as sig. gain did not change, while noise doubled
However, setting same # of photons at the PD in both cases,
the SNR is double (due to the coh. sig. add.)
j IF t
j E LO
Signal is atten.
thru the coupler
but sig. currents
add-up
in amplitude
*
coupler
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 iLO e
in current ; but 2  balanced P D gain
j c t
1
2
*
2 R e g LO E r e
j IF t
Same factor of 2
as in the single-ended
Noise from
the two PDs
adds up
incoherently
doubling
in noise
power
26
Full optical demodulator - 90 deg balanced hybrid –
homodyne

i 
I
d
i

Q
d
E r  E LO
2
E r  jE LO
2
4

4




E r  E LO
4
2
E r  jE LO
4
Half the
single-ended case
(and the DD terms
cancel out)
 R e g LO E r
*
2
 Im g L O E r
*
 g L O   E L O  0 means phase error –
received constellation tilt
g LO 
 iLO e
dd
j E LO
We shall assume that the carrier-recovery system effected  g LO  0
id  j id  E r
I
E R (t )
E LO
1
2
 E R ( t )  E LO 
1
2
 E R ( t )  E LO 
coupler
+
_
Re g
*
LO
Er
i
I
d
*
g LO E r
90
1
2
 E R (t ) 
 E R (t ) 
j E LO 
j E LO 
i
_
splitting
factor
1
2
+
1
2
Im g LO E r
Q
d
*
Single-Polarization Down-Converter (Optical Demodulator)
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Q
Lost a
factor of 2
in ampl.
due to input
splitting
27
Full optical demodulator - 90 deg balanced hybrid –
serodyne (for heterodyne just use upper branch)
i 
I
d
i
Q
d


4

4
E re
E re
j c t
j c t
 E LO e
j LO t
 jE LO e
j LO t
2
2




4
4
j c t
E re
 E LO e
j c t
E re
j LO t
 j E LO e
2
j LO t
 R e g LO E r e
*
2
j IF t
 Im g L O E r e
*
j IF t
*
g LO
Equivalent
system:
E r (t )
2e
j IF t
drop IF carrier
for homodyne
id  i d  jiQ
I
i sh ( t )
I
g LO 
*
1
2
E R (t )
E LO
coupler
1
2
 E re

 E re

j c t
j c t
 E LO e
 E LO e
j LO t
+
_


j LO t
Re g LO E r e
dd
j IF t
I


*
g LO E r e
Q
j c t
 E re

j c t
 j E LO e
j LO t
 j E LO e
j LO t




_
1
2
 E re

+
1
2
j E L O
id
90
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 iLO e
j IF t
id
*
Im g LO E r e
j IF t
Single-Polarization Down-Converter (Optical Demodulator)
28
Full optical demodulator - 90 deg balanced hybrid –
intradyne(for heterodyne just use upper branch)
g L O  e
j E L O
 iLO / 4  g LO / 2
dd
*
g LO
I /Q
N 0  2 e iLO

PD
d
Noise power summation
dd
i
R e/ Im
E r (t )
2e
j IF t
drop IF carrier
for homodyne
i sh ( t )
1
2
E R (t )
E LO
coupler
1
2
 E re

 E re

in balanced PD pair
j c t
 E LO e
 E LO e
j LO t
+
_


j LO t
j t
*
Re 2 g LO E r e IF
Pwr SNR
3 dB worse
than single-ended
I
id


2 g LO E r e
*
Q
90
 E re

j c t
 j E LO e
j LO t
 j E LO e
j LO t




_
1
2
 E re

j c t
+
1
2
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Noise pwr
3 dB lower
than single-ended
dd
dd
PSD =2N 0  2  2 e i LO / 4  e i LO
j c t
dd
2 e iLO / 4
id
 g LO E r e
*
Im 2 g LO E r e
*
j IF t
j IF t
j IF t
Single-Polarization Down-Converter (Optical Demodulator)
29
LO SHOT-NOISE limited ANALYSIS
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32
Symbol SNR evaluation (single-ended det. , counting sig. photons right at PD)
The total photocurrent in each quadrature branch is then expressed as
2
2
dd
dd
dd
dd
is ( t )   E s ( t ) , i L O ( t )   E L O ( t )
ir ( t )  i s ( t )  i s ( t )  i L O ( t )  i sh ( t )
i
HET
s
( t )  2 g LO R e E s ( t ) e
j IF t
e
( )
 2 g LO E s ( t ) cos (  IF t   s
HOM
is
j

HET:

i ( t ) dt  4
( )
s / N0 

Ks 

i
i
2
s

dd
s
( t ) dt / N 0  4
E s ( t ) cos (  IF t   s


i (t )dt  4
2
s
2
g LO

2
g LO
N 0nh

2

E s (t ) dt

2
E s ( t ) dt 

averaging
2
nhe

2
g LO

N0

(  iLO )

2

2 e iLO

2e

2 h
2

E s ( t ) dt


2
nhe
i
dd
s
2
(t )dt 
nh

2
nh  
1
s
N0
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2
HOM twice as large !
2
E s ( t ) dt No squared-cos

Assume real-valued1-D HOM
constellation: specifically BPSK

(t )   )dt
2
g LO

( t ) dt / e  q / e # of PHOTO-ELECTONS

( )
2

HOM:
( t )   2 g LO E s ( t )
SYMBOL SNR
EVALUATION


2

( t )  2 g LO R e E s ( t )  2 g LO E s ( t )
 2 g LO E s ( t ) cos  s
2
g LO

(t )   )


2
s
Ks
HET
HOM
2K s ,

 Ks,
HOM
HET
33
Equivalent electrical circuit for optically coherent detection
below
HOM
is ( t )
HET
x
i (t )  2 g c R e E s (t )e
x
r
j (  IF t   )
 i sh ( t )
j
ir ( t )  2 g c R e e E s ( t )  ish ( t )
random phase picked up by the signal over the
channel, minus the phase of the LO
E s (t )
2 g LO i
(t )
s
x
ir ( t )
e
2e
j
j IF t (absent for
locked HOM)
i sh ( t )
Effective TX
signal
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photodiode
effective input
One-sided PSD:
N 0  2 ei LO
RX front-end
equivalent circuit
AWGN module
2
f (t )
Re
rk
RX backend: SYN / ASYN
rk  r ( k T )  Ak e
s
N0
2K s ,

 Ks,
HOM
HET
j
 nk

s 
i
2
s
( t ) dt

35
Equivalent electrical circuit for optically coherent detection
and passband
PSK / OOK / M-ASK / DB
M-ary PSK, BPSK and QPSK in particular
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HOM / HET
SYN
ASYN
36
Comparing OADD and COH detection
for the
HET
HOM
is the number of photo-electrons
K s generated by the signal pulse in
SYN
ASYN
also OADD (ASYN)
Essentially the same substitution
for an Optical Amplifier with Direct Detection
(OADD ) with K  K in / n
s
an equiv. DD system
(the current system with the LO turned off)
s
sp
Here K s is the number of photons
in the signal pulse at the OA input,
normalized by n sp
Further to the symbol SNRs, we must also consider the equivalent block diagrams.
We shall see that the following two properties hold:
HOM 3 dB better
than HET SYN
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OADD and HET ASYN
will be seen to be equivalent !!
37
OADD  ASYN HET analogy
E s (t )
g LO 
E s (t )e
 i
dd
LO
re
s
i (t )
Ks
Photons LO
per pulse
LO Mixing LO shot-noise
gain
j
2 g LO
AWGN
Eff. ch.
Re
Electrical
IF Filter
RX
backend
f (t )
G i sh ( t ) n ( t )
2e
j  IF t
SIG. GEN. MODEL
OA gain
Optical
ASE noise Filter (OF)
G
The receiver block
out
E
(
t
)
E
(t )
s
s
diagrams
OF
+
are identical!
received SNRs Es/No K s
f (t )
E ase ( t )
as functions of Ks
Photons
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also identical!
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Copyright
per pulse
Electrical
ENV. DET
2
rk
PHOTO-DET
Aˆ
0
38
BER OF PAM WITH OADD AND COH DETECTION
s
N0
q 

f ,h

dˆ 

dˆ
†
Ks
a0

dˆ 
q 
2K s ,

 Ks,
a

f ,h
2
0
2

dˆ
†
2
0
2

/2
a/
Ks

2
Ks
a

2
2
2
a0
a
a
a/
Ks
HET


/2
HOM

2
2
38 ph/bit taking into account more sophisticated OA statistics
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41
BER OF PAM WITH OADD AND COH DETECTION
s
N0
q 

f ,h
†

dˆ
Ks
 2
a  ( a )

dˆ 
2
a
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2K s ,

 Ks,
HOM
HET
Ks
Note: this pertains to an idealized configuration
whereby the loss entailed in combining the sig and LO
is ignored
42
DD ASK
(1 )
Nr
E
( )
r
 Ep  0
PHOTON
COUNTER
(0)
Nr
  Ep
Self-study
2
 m  E p 
0
ˆ  1 \ 0
(1 )
Nr
Nr
 20
peak
ASK
ASK
9
SLICER
0
”0”
1,2,3…”1”
@ 10 BER
 10
avg
Requires negligible receiver thermal noise !!!
unattainable ideal !!!
Pe  A S K -D D  
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e
m E p 



2
(1 )
1
However, with either coherent or optical amplified detection  e
2
we may get the receiver thermal noise out of the way !!
Coherent: we are left with the shot-noise of the LO
OA: we are left with the ASE
1
 Nr
20

1
2
e
2 N r
10
Pe  A S K   1 0
9
43
Comparison of receiver sensitivities for
several modulation formats
HOM HET
SYN
BPSK 9
BDPSK 10
DB
15
OOK 18
QPSK 18
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18
30
36
36
HET
OADD
ASYN
20
31
38
-
20
31
38
-
44
Summary: comparative ideal performance
Photons/b
it
ASK
HOM
PSK HOM
DPSK
HOM
ASK HET
PSK HET
DB
72
ASYN ASK
HET
40
QDPSKBAL
37.3
ASYN
HET 31
SYN ASK
HET
36
SYN
HET
20
30
4PSK-BAL
18.7
18
ASK-BAL
10
DD-ASK
DPSK-BAL
9
PSK-BAL
5
Super-QuantumLimit PSK
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PSK HET
COH
SYN
HOM 15
45
IT’S OVER...
GOOD LUCK!
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46