1 Moshe Nazarathy Copyright Lecture V II Introduction to Fiber Optic Communication COHERENT...
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Transcript of 1 Moshe Nazarathy Copyright Lecture V II Introduction to Fiber Optic Communication COHERENT...
1Moshe Nazarathy Copyright
Lecture VIIIntroduction to Fiber Optic Communication
COHERENT DETECTION•
Moshe Nazarathy All Rights Reserved
Ver 2
2Moshe Nazarathy Copyright
LO
I&D IDEAL PHOTON COUNTER
2 2 *2 ReLr rO LOE EE E
2
2
O O
r r
L Li E
i E
coh
2 2 /sigamp
2coh coh
L
LO
OO
r r
L
eSNR q
We
i i
W
i
i
SNR (sig. pwr / shot-noise var)at the output of a W HzLPF passing the signalSo, what’s the Big Deal?
but…the coherent performanceis practically achievable, DD performance is not ! Coh. Det. overcomes receiver thermal noise <<shot-noise
Analog coherentHomodyne transmission:Instantaneous SNR eval (t-dependence dropped)
<<to add “analog” SNR for OADD and heterodyne SYN/ASYN>>
just better(a factor of 4 in SNR)
2
LOiri
2 ( )2 Re r LOELO O
Er L
jE EE e
2 2 212 Ld d d Ori E E EE
2 cosd LO L LOO rri i i i EE
22 cos r LOLO LOr E EE EE
/sigamp
22DD
Dr
DDr
D
r
eSNR q
We i W
i i
( )Lr Oset perfect phase tracE kE ing
Coherent detection SNR limits (analog)
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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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• 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
Coherent detection – some disadvantages
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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
( )R t
( )r t
-port
-port
*Re )) ((k r t R ti
“mixing product”
2 2
2 2( ()() () )ki r t r tR t R t
Proof:
( )r t( )R t
*Im )) ((k r t R ti
90
(( ) )r t R t
(( ) )r t R t
Initially address a single polarization(scalar treatment)
coupler(*)
Proof: Substitute in (*)( ) ( )jR t R t
Assume signal and LO have same freq. - homodyne
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A pair of BALANCED optical mixers in quadrature- called optical hybrid
implements the complex MIXING PRODUCT
( )R t
( )r t
( )R t
( )r t
*( )e ( )R Rr tt
*( )m ( )I Rr tt
*( ) ( )t R tr
90
mixing product
90
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8
Coherent Homodyne Receiver Front-End (e.g. for QPSK)
R
( )r t
*)Re (r t R
*)Im (r t R
*( )Rr t
Local Oscillator (LO)
*( )Rr t
( )( ) Rr tjeRr t
PhaseInfo
90
optical hybrid90
( )( ) j r ter t
RjRe
cos( ) (R )r t Rt r
sin( ) (R )r t Rt r
( )( ) j r ter t
Let i.e. assume the LO is aligned with the signal phase reference (real axis of the signal constellation)
0R
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Polarization Diversity Hybrid
Single-Polarization Downconverter II
tyi 1,
tyq 1,
LO
Signal Single-Polarization Downconverter I
tyi 2,
tyq 2,
tsE
PBS
+_
LOE
+
_
90
coupler
( )RE t
LO( )RE t E
LO( )RE t E
LO( )RE t jE
LO( )RE t jE
Single-Polarization Down-Converter (Optical Demodulator)
Ii
Qi
90
Opto-Electronic DownConverter
Polarization Beam Splitter
xy
x
y
xIxQ
yQyI
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Putting it all together:Coherent Receiver block diagram
(homodyne or intradyne)
ADC
ADC
ADC
ADC
DS
P
Intradyne:Sig. & LOhave nearlythe same freq.
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PBS
SOA
I Q
Si PHOTONIC INTEGRATED CIRCUIT (PIC)
X-P
OLY
-PO
L
X-P
OL
X-POLCOHFE
TUNABLELASER
90° 90°
X-POL COH FRONT-END
DSP
ADCs ADCs
Y-POL COH FRONT-END
DSP
DS RX - DSP
DATA OUT
OPTICAL Rx
FRONT-ENDS
DS
Rx
Y-POLCOHFE
(90 degROTATED)
90 deg
POLARIZATION
ROTATOR
I Q
CoherentReceiverwithIntegratedOpticalFront-end
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Homo/Hetero-dyne detection with balanced Optical Mixer
*( )Re Lj t j t
kcri t e Le
L
( )r t
-port
-port
*( )Rek ri t L
“mixing product”( ) Lr t
( ) Lr t
coupler
ki
Lc ( ) j tcer t
Lj tLe
*( )Re IFj tLr et
Now let SIGNAL & LO be at different frequencies (heterodyne)
2 2( ) ( )j t j tj t j t
kc cL Li r t r tL Le e e e
( ) ( )cos IFtr t r tL L
SIGNAL & LO at same frequency (homodyne)
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VTO
“Optical Voltage-Tuned-Oscillator”Tunable laser
FIXED
Balanced coherent receiverwith electrical quadrature demodulation
and electrical/optical PLL
Note: Single-lane scalar versionAssume that a polarization controller rotated the input polarization signal to beparallel to that of the LO. Alternatively, this is one of the two polarization lanes of a polarization diversity scheme
Optical PLL
( ) ( )cos IFtLr t r t L
cos IFt
sin IFt
cos( ) ( )L Lr t r t
sin( ) ( )L Lr t r t
Actuallydecision-directedPLL
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Putting it all together“Classic” coherent heterodyne receiver
Each polarization lane feeds an electrically coherentreceiver extracting the IQ components by electrical downconversion
with cos/sin subcarriers
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Coherent Homodyne BPSK Receiver
L
( )r t
*)Re (r t L
In this case the 2nd quadrature is not necessaryas the noiseless part ofdoes not contain an imaginary part.Assume that was tuned to bereal-valued (i.e. in phase or in anti-phasewith the possible values of
( )r t
L
( )r t
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Binary Differential Phase Shift Keying (BDPSK)
( )r t
*( )R ( )e rr Tt t
kr1kr Extract PD 1k krr
T *1Re k kr r
1 1cosk kk kr rr r
1
sgn( )
( )r t T
0 180or
DELAYINTERFEROMETER(DI) FRONT-END
The optical mixerbecomes a keybuilding blockin optical DPSK realization
*1k kr r
1 1
1 1
k k
k k
k k
k k
r r
r r
r r
r r
Differentially Coherent Detection
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kr1kr 2kr 3kr 4kr )a(
Current symbolPrevious symbolDPSK reference
DPSK DETECTION
kr1kr 2kr 3kr 4kr
LOLIGHT
SOURCE
(b)COHERENT DETECTION
*
*
Differentialvs. CoherentDetection
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18
QDPSK receiver front-end
( )r t
*(( )) jr tr t eT T
T
90
I-port
Q-port
The bias effects a rotation of the constellation: Typically 45
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19
QDPSK receiver front-end
( )r t
* /4( ) ( ) jr tr Tt e
T
T
45
45
I-port
Q-port
45
1
sgn( )
1
sgn( )
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Homodyne/Intradyne Coherent Receiver Technology considerations
X-pol.
Y-pol.
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Coherent Transmitter block diagramTechnology considerations
Alternative View
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100G Coherent Polarization-Muxed QPSK (PM-QPSK) is the next step
112Gb/s 2 polarizations 56 Gb/s each, QPSK (2 bits/sym), 28Gsym/sec
Two phase DOFs and two polarization DOFs: 28 Gbaud operationParallel transmission of 28Gb/sec on each quadrature of each polarization: 4 parallel lanes
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A formulation of COHERENT DETECTION
MODELING and error probability performance
- suited for communication engineers
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2 22 cos LOIF rLO LOr r Et EE EE E
2
2ddL
dd
O
r
LO
ri
i
E
E
2 cosddLO
ddr r rF LILO Od i Ei ti g E E
( )2 Re r LOIF Edd
r rj t Edd
LO LO ei i Eg
*2 Re IFddddr rL
j td LO Oii ei Eg
2 2 ( )2 Re L IO Frj j tEr r
ELO LOE EE E e e
22 2 2 *2 Rec LOj tj t j t
LO Lc L
r Ord Or LO
di E EE e eE E E E e
ddLOi
dd ddLO LO LOLO LOEg E i i
ddLO LOi E
LOLO LO
Ejg eg
IFLO
I&D IDEAL PHOTON COUNTER
Coherent detection model (HOM/HET)
0IF
Just setin the HET result
Homodyne: *2 ReddLOd
ddrLOri i g Ei
HOM:
HET:
2 Re IFLOLO
d EddL
tdO
jr r
jei eEgi
Coherent Gain(LO boosting) factor
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Full optical demodulator - 90 deg balanced hybrid – heterodyne
cj trE e
+_
coupler
12
c LOjr
t j tLOEE e e
Single-Polarization Single-Quadrature Down-Converter (Optical Demodulator)
2 2
2*
2 2 Rec LO c LO IFj t j t j tr r rLLO L O
j t jIO
td E E Ei e ge e eE E e
LOEdd
LO LOjeig
*2 Re IFjLO
trE eg
12
c LOjr
t j tLOEE e e
LOjLO
teE
Noise fromthe two PDsadds upincoherentlydoublingin noisepower
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 doubledHowever, setting same # of photons at the PD in both cases, the SNR is double (due to the coh. sig. add.)
12
1 1
1 1
Coupling matrix
Signal is atten.thru the couplerbut sig. currentsadd-up in amplitude
Same factor of 2as in the single-ended
1 122
; 2in field in current but balanced PD gain
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Full optical demodulator - 90 deg balanced hybrid – homodyne
( )RE t
+_
LOE
+
_
90
coupler
12 LO( )RE t E
Single-Polarization Down-Converter (Optical Demodulator)
2 2
4 4*Re LLOr r rOL
IOd E E EgE Ei
Idi
Qdi
Half the single-ended case(and the DD terms cancel out)
2 2
4 4*Im LLOr r rO
Qd LOE EE Ei j Ej g
LOEdd
LO LOjeig
*rLOEg
0LO LOg E
means phase error – received constellation tilt
We shall assume that the carrier-recovery system effected 0LOg
jI Qd d ri i E
*Re LO rg E
*Im LO rg E
12 LO( )RE t E
12 LO( )R t jE E
1
2 LO( )R t jE E
12
splittingfactor
Lost afactor of 2 in ampl.due to inputsplitting
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Full optical demodulator - 90 deg balanced hybrid – serodyne (for heterodyne just use upper branch)
( )RE t
+_
LOE
+
_
90
coupler
12
c LOjr
t j tLOEE e e
12
c LOjr
t j tLOEE e e
12
c LOjr
t j tLOEeE j e
12
c LOjr
t j tLOEeE j e
Single-Polarization Down-Converter (Optical Demodulator)
2 2
4*
4 Rec LO c LO IFj t j t j t jLOr r r
t j tId LO LO gi e e e eEE EE E e
Idi
Qdi
2 2
4*
4 Imc LO c LO IFj t j t j t j tr rL
j tQrLO LO Odi e j e e j e gE E eE EE
LOddLO LO
Ejeig
* IFr
jLO
tg eE
*Re IFLO
j trE eg
*Im IFLO
j trE eg
2 IFj te
drop IF carrierfor homodyne
( )rE t
I Id d Qi i ji
( )shi t
*LOgEquivalent
system:
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Full optical demodulator - 90 deg balanced hybrid – intradyne(for heterodyne just use upper branch)
( )RE t
+_
LOE
+
_
90
coupler
Single-Polarization Down-Converter (Optical Demodulator)
Idi
Qdi
*2 IFLO r
j tE eg
*Re2 IFrLO
j tg E e
*Im 2 IFrLO
j tg E e
/ 4 / 2LOL
dLOO LOdEj ig ge
2 IFj te
drop IF carrierfor homodyne
( )rE t
/I Qdi
( )shi t
Re/ Im
*LOg
0 2 42 /dd ddLO LOPD
ie eN i
0PSD=2N
Noise power summationin balanced PD pair
2 / 42 dd ddLO LOe i e i
* IFr
tLO
jE eg
Pwr SNR3 dB worsethan single-ended
Noise pwr3 dB lowerthan single-ended
12
c LOjr
t j tLOEE e e
12
c LOjr
t j tLOEE e e
12
c LOjr
t j tLOEeE j e
12
c LOjr
t j tLOEeE j e
32Moshe Nazarathy Copyright
LO SHOT-NOISE limited ANALYSIS
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The total photocurrent in each quadrature branch is then expressed as
(( ) )) (( ( ) ) shdddd
s Os Lr i t i ti i tt it 2,( ) ( )dd
s si t E t
( )
Re
cos
2
2 )( (
( ) ( )
( ) )
IFHET jj t
IF
LO
LO
s
s
s
s
i t E t e
t
g
t t
e
g E
02
0/ /( )s si t NdtN
2
0
2( )4 s
LO
h
E dtn
tN
g
2( ) ( )dd
LO LOi t E t
Symbol SNR evaluation (single-ended det. , counting sig. photons right at PD)
SYMBOL SNR EVALUATION
HET
HOM
2
1hn
0
22 ( )
2 2 2LO
LO
LOi
eiN h
g
e
2( )
2s
h
E t dtn e
(2
)dd
hsi t dt
n e
0
HOM
HET
2 ,
,ss
s
K
KN
( ) / /dds s dtK i e qt e
2s
hnK# of PHOTO-ELECTONS
(22 ) 222 2 cos (( ) )( )( ) ( )4 2IF ss LO LO ss t tt gdg E ti t Edt tt d
HET:
( )
2 2
2
Re
cos
( ) ( ) ( )
( ) ( )( ) 2
LO LO
LO
HOMs s s
s LOs s
i t E t E t
E
g g
g gt t E t
Assume real-valued1-D HOM constellation: specifically BPSK
222 ( )) 4(sLs O E dtg tdi t t
HOM:HOM twice as large !No squared-cosaveraging
35Moshe Nazarathy Copyright
( )( )2 Re (( ) )IFj tc shs
xr E it et ti g
( )f t
( )shi tkr
2 IFj te
( )sE t
RX backend: SYN / ASYN
RX front-end equivalent circuitAWGN module
2 LOgRe
Effective TXsignal
0 2 LON eiOne-sided PSD:
0
HOM
HET
2 ,
,ss
s
K
KN
2
( ) kk kjkr T e nr A
Equivalent electrical circuit for optically coherent detection
(absent forlocked HOM)
2 Re ()) )( (xsr h
jc se E tti g it
HOM
HET
( )xri t
je
random phase picked up by the signal over thechannel, minus the phase of the LO
2 ( )s si t dt
( )si t
( )si t
photodiode effective input
below
36Moshe Nazarathy Copyright
Equivalent electrical circuit for optically coherent detection
HOM / HET SYN ASYN
PSK / OOK / M-ASK / DB
M-ary PSK, BPSK and QPSK in particular
and passband
37Moshe Nazarathy Copyright
Comparing OADD and COH detection
for the
Essentially the same substitutionfor an Optical Amplifier with Direct Detection (OADD ) with
OADD and HET ASYNwill be seen to be equivalent !!
HOM 3 dB betterthan HET SYN
HET
HOM
SYN ASYN
/ins s spK K n
Further to the symbol SNRs, we must also consider the equivalent block diagrams.We shall see that the following two properties hold:
sK is the number of photo-electronsgenerated by the signal pulse inan equiv. DD system (the current system with the LO turned off)
Here is the number of photonsin the signal pulse at the OA input, normalized by spn
sK
also OADD (ASYN)
38Moshe Nazarathy Copyright
OADD ASYN HET analogy
Photonsper pulse
( )sE t
LO
( )resi t
sKPhotonsper pulse
( )n t
( )sjE t e
2 IFj te
2 LOg
Re
LO shot-noise
G
+
( )aseE t
( )outsE t OF
( )f tsK
0A( )sE t
G
( )f tkr
RX backend
2
AWGNEff. ch.
LLOddOig
LO Mixinggain
OA gainSIG. GEN. MODELASE noise
ElectricalIF Filter
ElectricalENV. DET
Optical Filter (OF)
PHOTO-DET
The receiver block diagrams are identical!received SNRs Es/Noas functions of Ks are also identical!
( )shi t
41Moshe Nazarathy Copyright
BER OF PAM WITH OADD AND COH DETECTION
0
HOM
HET
2 ,
,ss
s
K
KN
38 ph/bit taking into account more sophisticated OA statistics
†,ˆ
2 sf h
sq Kd
K
2 2
0ˆ 2/ 20 / 2
a ad
aa
†,ˆ 2
f h s sK Kq d
2 2
0ˆ 2/ 20 / 2
a ad
aa
42Moshe Nazarathy Copyright
BER OF PAM WITH OADD AND COH DETECTION
0
HOM
HET
2 ,
,ss
s
K
KN
†,ˆ 2
f h s sK Kq d
( )ˆ 2a a
da
Note: this pertains to an idealized configuration
whereby the loss entailed in combining the sig and LOis ignored
43Moshe Nazarathy Copyright
DD ASK
PHOTONCOUNTER
SLICER0 ”0”
1,2,3…”1”
( ) 0r pE E
1( ) 2
r p pN E m E 0( )
0rN
1( )
ASK-DD
2
1
2
1 1
2 2
p
r r
E
e
N N
mP e
e e
9ASK 10eP
ˆ 1\ 0
Requires negligible receiver thermal noise!!! unattainable ideal!!!
20 10
( )
A
1
SK20rN
ASK10rN
9@10 BERpeak
avg
However, with either coherent or optical amplified detectionwe may get the receiver thermal noise out of the way!!
Coherent: we are left with the shot-noise of the LOOA: we are left with the ASE
Self-study
44Moshe Nazarathy Copyright
Comparison of receiver sensitivities for several modulation formats
HOM HET HET OADD
BPSK 9 18 - -BDPSK 10 - 20 20
DB 15 30 31 31
OOK 18 36 38 38
QPSK 18 36 - -
SYN ASYN
45Moshe Nazarathy Copyright
Summary: comparative ideal performancePSK HET ASK HET DPSK
HOMPSK HOM ASK
HOM
Photons/bit
72ASYN ASK HET
40
QDPSK-BAL
37.3
SYN ASK HET
36
20
4PSK-BAL 18.7PSK HET COH
DPSK-BAL ASK-BAL 18
DD-ASK 10
PSK-BAL 9Super-Quantum-Limit PSK 5
DB
SYN HOM 15
SYN HET 30
ASYN HET 31
46Moshe Nazarathy Copyright
IT’S OVER...GOOD LUCK!