1 Moshe Nazarathy Copyright Lecture V II Introduction to Fiber Optic Communication COHERENT DETECTION Moshe Nazarathy All Rights Reserved Ver 2

1Moshe Nazarathy Copyright

Lecture VIIIntroduction to Fiber Optic Communication

COHERENT DETECTION•

Moshe Nazarathy All Rights Reserved

Ver 2


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)


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.


• 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


The Coherent Receiver Front-End:A linear Opto-electronic

Downconverter


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


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


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


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


Putting it all together:Coherent Receiver block diagram

(homodyne or intradyne)

ADC

ADC

ADC

ADC

DS

P

Intradyne:Sig. & LOhave nearlythe same freq.


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


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)


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


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


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


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


kr1kr 2kr 3kr 4kr )a(

Current symbolPrevious symbolDPSK reference

DPSK DETECTION

kr1kr 2kr 3kr 4kr

LOLIGHT

SOURCE

(b)COHERENT DETECTION

*

*

Differentialvs. CoherentDetection


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


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( )


Homodyne/Intradyne Coherent Receiver Technology considerations

X-pol.

Y-pol.


Coherent Transmitter block diagramTechnology considerations

Alternative View


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


A formulation of COHERENT DETECTION

MODELING and error probability performance

- suited for communication engineers


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


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


Full optical demodulator - 90 deg balanced hybrid – homodyne

( )RE t

+_

LOE

+

_

90

coupler

12 LO( )RE t E


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


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


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:


Full optical demodulator - 90 deg balanced hybrid – intradyne(for heterodyne just use upper branch)

( )RE t

+_

LOE

+

_

90

coupler


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


LO SHOT-NOISE limited ANALYSIS


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


( )( )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


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


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)


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


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


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


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


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


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


IT’S OVER...GOOD LUCK!

Documents

1 Moshe Nazarathy Copyright Lecture V II Introduction to Fiber Optic Communication COHERENT DETECTION Moshe Nazarathy All Rights Reserved Ver 2