Transcript LO - Technion moodle

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)
2
LO
*
id  12  Ed   Ed   Er  ELO   Er   ELO  2  Re Er ELO
2
2
  ELO  2  Re Er ELO e j ( Er ELO )
2
2
  ELO  2  Er
2
id  iLO  2 iLO ir cos  Er   ELO
set Er  ELO ( perfect phasetracking )
SNRcoh  qcoh 
sig ampcoh
 LO

2
2

iLO
iLO   ELO
2
2 ir / e
ir   Er

W
W
SNR (sig. pwr / shot-noise var)
2
iLO ir
2e iLO
ir
 ELO cos  Er  ELO 
at the output of a W Hz
LPF passing the signal
SNRDD  qDD 



2e ir W
So, what’s the Big Deal?
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)
sig amp DD
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ir
ir / e
2W
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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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  Re r (t ) R (t )
*
coupler
R (t )
Proof:
ik 
r (t )  R (t )

2

2
r (t )  R (t ) 
2
ik  Im r (t ) R (t )
*
90
Proof: Substitute
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(*)
 -port
r (t )  R (t ) 
2
r (t )
R (t )
“mixing product”
R(t )  jR(t )
in (*)
6
A pair of BALANCED optical mixers in quadrature
- called 90 optical hybrid
implements the complex MIXING PRODUCT
r (t )
*
Re 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
Re r (t ) R*
 R r(t ) cos r(t )  R 
 r (t )e jr ( t )
r (t )
R
r (t )R
 Re jR
*
 R r(t ) sin r(t )  R
Local
Oscillator (LO)
Im r (t ) R*
90
r (t )R
*
 r (t ) Re
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 90 Hybrid
E s t 
Signal
y
x
x
LO
Single-Polarization
Downconverter I
Single-Polarization
Downconverter II
PBS y
yxI
i ,1 t 
yxQ
q,1 t 
yyI
i , 2 t 
yyQ
q,2 t 
Polarization
Beam Splitter
Opto-Electronic DownConverter
ER (t )  ELO
E R (t )
ELO
coupler
+
_
ER (t )  ELO
90
+
ER (t )  jELO
_
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ER (t )  jELO
iI
iQ
Single-Polarization Down-Converter (Optical Demodulator)
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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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Homo/Hetero-dyne detection with balanced Optical
Mixer
SIGNAL & LO at same frequency (homodyne)
r (t )  L
r (t )
 -port
“mixing product”
ik  Re r (t ) L
*
coupler
L
r (t )  L
ik  r(t )e
jct
 Le
 -port
jLt 2
 r (t )e
jct
 Le
Now let SIGNAL & LO be at different frequencies (heterodyne)
r (t )e
Le
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jLt
jct
ik  Re  r (t )e
jLt 2
jc t
  Le 
jLt *
c  L
ik  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 cos  r(t )  L
cos IF t
 sin IF t
“Optical Voltage-Tuned-Oscillator”
Tunable laser
VTO
FIXED
Optical PLL
r(t ) L sin  r(t )  L
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 )
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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
1


Re r r
 rk rk 1 cos rk  rk 1 
 rk rk 1 rk  rk 1

  rk rk 1 rk  rk 1  
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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
*
T
r (t )
j
 90
T

The bias
Q-port
effects a rotation of the constellation: Typically 
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 45
18
18
QDPSK receiver front-end
r(t )r* (t  T )e j /4
45
r (t )
I-port
T

 45
sgn()
1


sgn()
1


45
T
Q-port
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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)

id   Ed   Er e
2
jc t
 ELO e
2
iLddO   ELO
I&D IDEAL
PHOTON COUNTER
LO
irdd   Er
2
dd
iLO
  ELO
 IF
jLO t 2
2
2
j  
t
  Er   ELO  2 Re Er EL*O e  c LO 
  Er   ELO  2  Re ELO Er e  j ( Er ELO )e jIF t
2
2
  Er   ELO  2  ELO Er cos IF t  Er  ELO 
2
2
Coherent Gain g LO   ELO    ELO  
(LO boosting) factor
dd
dd
iLO
  iLO
dd
iLO
dd
id  irdd  iLO
 2 g LO Er cos IF t  Er  ELO 
 jE
dd
dd
dd
Er e j
 irdd  iLO
 2 Re g LO Er e j (IF t Er ELO )  ir  iLO  2 Re g LO e
LO
g LO  g LO e
jELO
Homodyne: Just set  IF  0
Moshe Nazarathy Copyright in the HET result
HET:
HOM:
IF t
dd
id  irdd  iLO
 2 Re g L*O Er e jIF t
dd
*
id  irdd  iLO
 2 Re g LO
Er
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Full optical demodulator - 90 deg balanced hybrid – heterodyne
i 
I
d

2
Er e
jc t
 ELO e
jLO t 2


2
Er e
jc t
 ELO e
jLO t 2
 2 Re g L*O Er e jIF t
dd
g LO   iLO
e jELO
Coupling matrix
1 1 
Signal is atten.
1
1
1
in
field

in
current
;
but
2

balanced
PD
gain
2
2

2 
thru the coupler
1 1
but sig. currents
jc t
Er e
add-up
jc t
jLO t
1
+
 E e  ELO e

2  r
in amplitude
_
E LO e jLO t
coupler
1
2
 Er e jct  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.)
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*
2 Re g LO
Er 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
2
2


I
Half the
id  4 Er  ELO  4 Er  ELO  Re gL*O Er
single-ended case
i 
Q
d

4
Er  jELO 
2
g LO  ELO  0

4
dd
g LO   iLO
e jELO
means phase error –
received constellation tilt
We shall assume that the carrier-recovery system effected
E R (t )
ELO
(and the DD terms
cancel out)
Er  jELO  Im gL*O Er
2
1
2
 ER (t )  ELO 
1
2
 ER (t )  ELO 
coupler
+
_
g LO  0
idI  jidQ  Er
*
LO
Re g Er
i
I
d
*
g LO
Er
90
1
2
 ER (t )  jELO 
 ER (t )  jELO 
_
splitting
factor
1
2
+
1
2
Q
d
i
*
Im g LO
Er
Single-Polarization Down-Converter (Optical Demodulator)
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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
Er e
Er e
 ELO e
jLO t 2
 jELO e
jLO t 2
jc t
jc t




4
4
Er e
 ELO e
jct
Er e
Er (t )
2e jIF t
drop IF carrier
for homodyne
1
2
ELO
coupler
1
2
ish (t )
+
_
 Er e
 jELO e

_
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 Er e jct  jELO e jLOt 
+
1
2
 Im g L*O Er e jIF t
I
Q
dd
g LO   iLO
e jELO
 Er e jct  ELO e jLOt 
jLO t
jLO t 2
id  i  ji
 Er e jct  ELO e jLOt 
jc t
*
 Re g LO
Er e jIF t
I
d
90
1
2
jLO t 2
 jELO e
*
g LO
Equivalent
system:
E R (t )
jct
*
Re g LO
Er e jIF t
idI
idQ
*
g LO
Er e jIF t
*
Im g LO
Er 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)
dd
gLO  e jELO  iLO
/ 4  g LO / 2
*
g LO
I /Q N  2e i dd
0
LO PD  2e
d Noise power summation
i
Re/ Im
Er (t )
2e jIF t
drop IF carrier
for homodyne
ish (t )
1
2
E R (t )
ELO
coupler
1
2
in balanced PD pair
dd
dd
/ 4  e iLO
PSD=2N 0  2  2e iLO
 Er e jct  ELO e jLOt 
+
_
 Er e jct  ELO e jLOt 
90
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 Er e
jc t
 jELO e
jLO t
 jELO e
jLO t


_
1
2
 Er e
jc t
+
1
2
dd
iLO
/4
Noise pwr
3 dB lower
than single-ended
*
Re 2 g LO
Er e jIF t
idI
idQ
Pwr SNR
3 dB worse
than single-ended
*
2 g LO
Er e jIF t
*
 g LO
Er e jIF t
*
Im 2 g LO
Er e 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
isdd (t )   Es (t ) , iLO
dd
dd
(t )   ELO (t )
ir (t )  is (t )  is (t )  iLO (t )  ish (t )
HET
s
i
(t )  2 g LO Re Es (t )e
jIF t
e
j

HET:
 2 g LO Es (t ) cos(IF t  s( ) (t )   )
 i (t )dt  4
2
s

2
g LO

Es (t ) cos (IF t  s (t )   )dt  2
( )
2
2
g LO

2
Es (t ) dt



HOM:
isHOM (t )  2 g LO Re Es (t )  2 g LO Es (t )


2

 i (t )dt  4  E (t )
2
s
2
g LO

s

 2 g LO Es (t ) cos s( ) (t )  2 g LO Es (t )
Assume real-valued1-D HOM
constellation: specifically BPSK
SYMBOL SNR
EVALUATION



2
HOM twice as large !
dt No squared-cos
averaging
2
(  iLO )2 
g LO




N0
2eiLO
2e 2h
2
2
 Es (t ) dt  n e  Es (t ) dt

h 


dd
2
dd
K s   is (t )dt / e  q / e # of PHOTO-ELECTONS  2
Ks
is (t )dt 


nh e 
nh
 2 HET
nh  
1 HOM
2
g LO
2
 s / N 0  is (t )dt / N 0 4
N 0nh

2
s
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2 K s ,

N0  K s ,
HOM
HET
33
Equivalent electrical circuit for optically coherent detection
below
HOM
is (t )
HET
i (t )  2 g c Re Es (t )e j (IF t  )  ish (t )
x
r
irx (t )  2 g c Re e j Es (t )  ish (t )
random phase picked up by the signal over the
channel, minus the phase of the LO
Es (t )
Re
e j
2e
jIF t (absent for
locked HOM)
Effective TX
signal
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2 g LO is (t ) irx (t )
ish (t )
f (t )
photodiode
effective input
RX front-end
equivalent circuit
AWGN module
rk
RX backend: SYN / ASYN
rk  r (kT )  Ak e j  nk
One-sided PSD:
N 0  2eiLO
2
s
2 K s ,

N0  K s ,
HOM
HET
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
the number of photo-electrons
K s isgenerated
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 nsp
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   i
dd
LO
re
s
i (t )
Ks
Photons LO
per pulse
LO Mixing LO shot-noise
gain
Es (t )e j
2 g LO
Re
AWGN
Eff. ch.
Electrical
IF Filter
RX
backend
f (t )
G ish (t ) n(t )
2e jIF t
SIG. GEN. MODEL
OA gain
Optical
ASE noise Filter (OF)
G out
The receiver block
E
(
t
)
E s (t )
s
diagrams
+
are identical!
received SNRs Es/No K s
Ease (t )
as functions of Ks
Photons
are Nazarathy
also identical!
Moshe
Copyright
per pulse
OF
Electrical
ENV. DET
2
rk
PHOTO-DET
Â0
f (t)
38
BER OF PAM WITH OADD AND COH DETECTION
s
2 K s ,

N0  K s ,
q
 f ,h dˆ
dˆ  
q
dˆ  
†
Ks
a0
a
2
 02  / 2
 f ,h dˆ 
Ks
†
a0
a
2

2
 02  / 2

HOM
HET
 2
Ks
a
 2
a/ 2

Ks
a
 2
a/ 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
2 K s ,

N0  K s ,
q
 f ,h dˆ
†
Ks
2
a  (a )
dˆ  
2
a
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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
( )
r
E
 Ep  0
(1)
Nr
Nr
ASK
ASK
  E p  m  E p 
(0)
0
Nr
ˆ  1\ 0
 20 peak
 10
2
(1)
Nr
PHOTON
COUNTER
Self-study
@109 BER
SLICER
0
”0”
1,2,3…”1”
avg
Requires negligible receiver thermal noise !!!
unattainable ideal !!!
However, with either coherent or optical amplified detection
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
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1
Pe  ASK-DD   e
 m  E p 

2
(1)
1
 e
2
 Nr
20
1
2 N r
2
10
 e
Pe  ASK  10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