coherent lightwave systems

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1 ETM 7172 OPTICAL COMMUNICATION SYSTEMS ultimedia University Hairul Azhar Abdul Rashid, 2006 Coherent Lightwave Systems

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Coherent Lightwave Systems. CONTENTS. Principles of coherent and non-coherent detection : heterodyne and homodyne detection; Modulation formats: ASK,PSK,FSK,PPM,DPSK; . CONTENTS. Demodulation schemes : synchronous and asynchronous demodulation; - PowerPoint PPT Presentation

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Page 1: Coherent Lightwave Systems

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ETM 7172 OPTICAL COMMUNICATION SYSTEMS

Multimedia University

Hairul Azhar Abdul Rashid, 2006

Coherent Lightwave Systems

Page 2: Coherent Lightwave Systems

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ETM 7172 OPTICAL COMMUNICATION SYSTEMS

Multimedia University

Hairul Azhar Abdul Rashid, 2006

CONTENTS

• Principles of coherent and non-coherent detection : – heterodyne and – homodyne detection;

• Modulation formats:– ASK,PSK,FSK,PPM,DPSK;

Page 3: Coherent Lightwave Systems

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ETM 7172 OPTICAL COMMUNICATION SYSTEMS

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Hairul Azhar Abdul Rashid, 2006

CONTENTS

• Demodulation schemes : – synchronous and – asynchronous demodulation;

• Bit error rate performance analysis;

Page 4: Coherent Lightwave Systems

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CONTENTS

• Performance degradation due to:– laser phase noise, – group velocity dispersion, – self phase modulation, – polarization mode dispersion, – relative intensity noise, – effect of timing jitter;

Page 5: Coherent Lightwave Systems

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CONTENTS

• System design considerations: – power budget, – rise time budget, – power penalty.

Page 6: Coherent Lightwave Systems

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Modulation

The modulation can be either:– Direct modulation

• Light is directly modulated inside a light source– External modulation

• Using external modulator

Modulation process: Switching or keying the amplitude, frequency, or phase of

the carrier in accordance with the information binary bits.

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• Applied in the first generation (1970’s) intensity modulation direct detection is still the most used for optical communications • Information is carried only by the intensity

• not frequency or phase

• The received signal is applied directly to photodetector• Photo-detection of light represents the key operation in

the optical receiver. • Converting the collected field onto a current or voltage.

Optical detection

IM-DD system

Page 8: Coherent Lightwave Systems

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• Light is described as a stream of photons (quanta)• The theory of quantum states that the energy of a photon is

proportional to the frequency of light

fhE

Where the Plank constant h = 6.6261 10-34 W s2

Page 9: Coherent Lightwave Systems

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For modulated optical signal with power P(t), the instantaneous photon intensity (photon flux) varies with time:

• Let P the optical power of a light beam, then the number of photons per second is:

photons/s

hfPN

hf)t(P)t(Np

Page 10: Coherent Lightwave Systems

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Where is the quantum efficiency of the device and E is the energy received in a time interval T.

• For a PIN-diode photodetector, the average number of electron-hole pairs generated in a time interval of T is given by

hfEdt)t(P

hfm

T

0

Page 11: Coherent Lightwave Systems

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The ideal receiver• Consider an ideal OOK transmission system over an ideal

channel• The transmitter sends light for a one • No light for a zero• The receiver counts N, the number of photons it receives in a bit

interval of T seconds, and zero otherwise

Page 12: Coherent Lightwave Systems

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• If a zero is transmitted, then there is a zero probability of receiving zero photons.

• If a one is transmitted, then the photons arrive according to a Poisson process with mean m

• For a ONE, the probability of receiving N photons in T seconds is given by by the Poisson distribution.

!Ne)m(]ONE/photonsN[Pr

mN

Page 13: Coherent Lightwave Systems

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Quantum limit• It is possible that no photons arrive when a ONE is transmitted.

This leads to a probability of error or a Bit-error-ratio (BER), of

• This leads to an important lower bound on the BER called the quantum limit

2eBER

N

• It indicates a minimum signal power required by an OOK receiver to achieve a given BER

2e]ONE/photons0[Pr

21BER

m

Page 14: Coherent Lightwave Systems

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• Letting BER= 10-9 gives m = 20.03.• Hence, to achieve a BER of 10-9, the pulse must have an optical

energy corresponding to an average of 20 photons.• On average, half the signal intervals contain optical pulses, and

the average number per transmitted bit is:

Example:

bit/photons102m

• This quantity of of 10 photons/bit is called the quantum limit for optical detection.

• It represents a lower limit on the received power necessary in a direct detection.

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Practical receiver

Receiver configuration

IM-DD system can only be used for OOK modulation format

Page 16: Coherent Lightwave Systems

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Shot noise

Shot noise (from O-E counting process in PIN):

)t(iRP)t(iI)t(I sinsp

is the average photocurrent

is a stationary random process with Poisson statistics

is(t) can be approximated by the Gaussian statistics with its variance given by:

eps

2s

2s BqI2df)f(S)t(i

Page 17: Coherent Lightwave Systems

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Thermal noiseIncluding thermal noise (from carrier moving in any conductor):

current fluctuation induced by thermal noise iT(t) can be modeled as a stationary Gaussian random process with its variance given by:

)t(i)t(iI)t(I Tsp

e

L

BT

2T

2T B

RTk4df)f(S)t(i

Its spectral density (“white noise”) is given by:.

LBT R/Tk2)f(S :R,T,k LBBoltzmann constant,the absolute temperature, and the load resistor

Page 18: Coherent Lightwave Systems

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Total receiver noise

Considering the dark current from PIN and the enhancementto thermal noise from the components other than the load resistor in the linear channel, the total noise variance is:

enL

Bdarkp

2T

2s

2 B]FR

Tk4)II(q2[

:F,I ndthe PIN dark current and the amplifier noise figure

Page 19: Coherent Lightwave Systems

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Receiver signal to noise ratio

PIN receiver:en

L

Bdin

2in

2

B]FR

Tk4)IRP(q2[

PRSNR

APD receiver:en

L

BdinA

2

2in

22

B]FR

Tk4)IRP(FqM2[

PRMSNR

Where

:F,M A the APD gain and the APD excess noise factor

)M/12)(k1(MkF AAA

:kAis the ionization-coefficient ratio.

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PIN and APD Noise limitations

P I N A P DS h o t n o i s e

l i m i t e d inPSNR ~ Ain FPSNR /~( w o r s e )

T h e r m a ln o i s e

l i m i t e d

2~ inPSNR( l a r g e l o a d i m p e d a n c e

r e q u i r e d )

22~ inPMSNR( b e t t e r )

Page 21: Coherent Lightwave Systems

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BER Analysis for IM/Direct Detection

The bit error rate can be computed as:

)0/1(P)0(p)1/0(P)1(pBER

• Pr(0/1) is the probability that a "0" is received when a "1" is transmitted.

• Pr(1/0) is the probability that a "1" is received when a "0" is transmitted

where

• The values of Pr(0/1) and Pr(1/0) depends on the statistical nature of the output signal in the presence of noise.

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• For a binary symmetric channel, p(0)=p(1)=1/2 which indicates equal probability of occurrence for a "1" and a "0" bit.

The output signal current is given by

"0"bitiIi"1"bitiIi

n00

n11

Where in is the noise current due to shot and thermal noise. The probability density function of in is given by

2

n

2meann

2n

n 2)ii(exp

21)i(p

• where imean=0 is the mean value of in.

Page 23: Coherent Lightwave Systems

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Bit Error Rate The bit error rate can be computed as: )0/1(P)0(p)1/0(P)1(pBER

Page 24: Coherent Lightwave Systems

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• Since in is Gaussian with zero mean and variance n2 ,

the probability density function (pdf) of the receiver output corresponding to bit "1" and bit "0" are also Gaussian with mean I1 and I0 respectively and given by

where 12 and 0

2 are the noise variances corresponding to bit "1" and bit "0" respectively.

21

211

21

1 2)Ii(exp

2

1)i(p

20

200

20

0 2)Ii(exp

21)i(p

Page 25: Coherent Lightwave Systems

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Hence

1

th11

i

21

211

21

i

11th1

2iIerfc

21di

2)Ii(exp

2

1

)i(d)i(p)iiPr()1/0Pr(

th

th

0

0th0

i20

200

20

i00th0

2Iierfc

21di

2)Ii(exp

21

)i(d)i(p)iiPr()0/1Pr(

th

th

Page 26: Coherent Lightwave Systems

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Minimum BER occurs when Pr(0/1)=Pr(1/0) which corresponds to an optimum value of the threshold current ith and can be determined as

2Q

2iI

2Ii

1

th1

0

0th

The optimum threshold is then given by

01

0110th

IIi

Under the assumption that the noise current is same for bit "0" and bit "1", 1=0, then the optimum threshold is given by

2IIi 01

optth

The above optimum threshold is applicable in absence of laser phase noise. In the presence of laser phase noise, the optimum threshold is to be determined numerically because 1 does not equal 0.

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The value of the parameter Q at the receiver output under optimum threshold condition is expressed as

01

01 IIQ

and the corresponding BER for optimum threshold is given by

01

01 II2

1erfc21

2Qerfc

21)0/1Pr(

21)1/0Pr(

21BER

Page 28: Coherent Lightwave Systems

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The output SNR (= signal power to noise power ratio) for a PIN-receiver is given by

NBh2

PR/FkTB4B)IRP(e2

)RP(SNRe

in

Lneedin

2in

where Be=Br/2. In terms of number of photons per bit N, the BER can be expressed as

2Qerfc

21BER

where

SNRIIIQ1

1

01

01

Where we assumed that I0=0 and 0= 0 which is valid when the receiver is dominated by shot noise.

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2Nerfc

21BER

NQ hence

2Nerfc

21

2Qerfc

21BERand

Page 30: Coherent Lightwave Systems

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Principle of Coherent Detection

Page 31: Coherent Lightwave Systems

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Coherent Detection

Coherent receiver model

LocalOptical

Oscillator

Photo-Detector

ElectronicCircuits

Optical Signal Input Electrical Signal OutputBeam Combiner

Coherent detection receiver adds light to the received signal as part of the detection process

Page 32: Coherent Lightwave Systems

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• Homodyne detection– The optical signal is demodulated directly to the baseband.

– It requires a local oscillator whose frequency match the carrier signal and whose phase is locked to the incoming signal ( c= LO).

– Information can be transmitted through amplitude, phase, or frequency modulation

• Heterodyne detection– Neither optical phase locking nor frequency matching is of

the local oscillator is required ( c LO).

– Information can be transmitted through amplitude, phase, or frequency modulation

Detection Schemes

Page 33: Coherent Lightwave Systems

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Demodulation schemes in coherent detection

• There are two basic types of demodulation in coherent detection of optical signals :

(a) Synchronous demodulation(is essential for homodyne detection)

(b) Asynchronous demodulation

Page 34: Coherent Lightwave Systems

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ASK, PSK, DPSK, and FSK modulation Formats

Page 35: Coherent Lightwave Systems

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Modulated signal: )]t(jexp[AE ScSS

Local oscillator signal:

)]t(jexp[AE LOLOLOLO

The output power of the photodetector

)cos(2)( tPPPPtP IFLOSLOS

LOSLOcIF

2LO

LO

2S

S ,,2

AP,2

AP

where

Optical Detection

Page 36: Coherent Lightwave Systems

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Homodyne Detection

The detector current: )(2)( tPPRtI SLOp

Heterodyne Detection

The detector current:

)cos()(2)( LOsIFLOSp tPtPtI

Page 37: Coherent Lightwave Systems

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Heterodyne Synchronous Coherent Receiver

Optical Signal Input

Baseband Signal OutputLocal

Optical Oscillator

Photo-Detector

BPF

Beam Combiner

Delay

Carrier Recovery

LPF

• In which the IF modulated signal is mixed with an IF carrier recovered from the IF signal. At the output of the mixer the baseband signal is received which is filtered by a low pass filter and fed to the decision circuit.

Page 38: Coherent Lightwave Systems

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• Heterodyne detection needs neither frequency matching nor phase locking.

• The detected electrical signal is carried by the intermediate frequency and must be demodulated again to the baseband.

• This demodulation scheme can be used for ASK, FSK or PSK modulation formats.

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Heterodyne Synchronous ASK

The detector current:

its mean square is :

The thermal noise and shot noise variances :

LOs22

d PPR2)t(i

2thermal

2shot

2

eLOseLOs2shot B)RPRP(e2B)II(e2

where

Lne2thermal R/FkTB4

)cos(2)( tPPRtI IFLOSp

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IF- Signal to noise ratio (IF-SNR) :

2thermalesLO

LOs2

2

2d

B)IRP(e2PPR2i

SNRIF

e

s

e

s

esLO

LOs2

2

2d

BhP

eBRP

B)IRP(e2PPR2i

SNRIF

Or

Page 41: Coherent Lightwave Systems

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If the bit rate is Br=1/T, then average signal power

rs BNhT

NhP

Let Be=Br/2, then SNR can be expressed

N2SNR

The corresponding BER for heterodyne ASK receiver is

ASKHetSynNerfcBER ..]4/[21

Page 42: Coherent Lightwave Systems

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Receiver sensitivity can be defined as the minimum required received optical power to attain a BER of 10-9

which corresponds to Q=6 or when SNR=144 or 21.6 dB.

Receiver sensitivity

Average received power Pr can be obtained as

/Bh72/BhQ2]/BhQ4[21P

21P ee

2e

2sr

For an ideal photodetector =1 and the number of photons per bit required for BER=10-9 is 72 for ASK heterodyne.

Page 43: Coherent Lightwave Systems

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Heterodyne Synchronous ASK in the presence of noise

The current after photo-detection(the output of the photodiode is passed through a BPF centered at the IF frequency and the filter out put can be written as:)

)]tsin(sin)tcos([cos)t(PPR2

)tcos()t(PPR2)t(I

IFIFSLO

IFSLOf

The noise at the output of the filter can be expressed in terms of its in-phase and quadrature components as :

where sc i,iThe variance are given by:

(Gaussian random variables with zero mean)

scn iji)t(i

2s

2c

2

Page 44: Coherent Lightwave Systems

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After synchronous (coherent) demodulation and LPF

2icos)t(PPR

)t(cos]icos)t(PPR2[

)tcos()tsin(]isin)t(PPR2[

)tcos(]icos)t(PPR2[)t(I

cSLO

IF2

cSLO

IFIFsSLO

IFcSLOd

It shows that only the in-phase noise component affects the performance of synchronous heterodyne receivers.

With noise included after BPF:

)tsin(]isin)t(PPR2[

)tcos(]icos)t(PPR2[)t(I

IFsSLO

IFcSLOf

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cpcSLOd icosI21icos)t(PPR)t(I Or

The analysis is analogous to that for direct detection receiver and the BER is given by

2Qerfc

21BER

where SNR21

2IIIQ

1

1

01

01

Where we assumed that I0=0 and 0= 1 which is valid when the receiver is dominated by shot noise at higher values of PLO.

LOsp PPR2I

where

Page 46: Coherent Lightwave Systems

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Using the relation SNR=2Np we get

.Det.ASK.Het.Syn]4/N[erfc21BER

Page 47: Coherent Lightwave Systems

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The detector current:

its mean square is :

The thermal noise and shot noise variances :

)(2)( tPPRtI SLOp

LOsd PPRti 22 4)(

2thermal

2shot

2

eLOseLOs2shot B)RPRP(e2B)II(e2

where

Lne2thermal R/FkTB4

Homodyne Synchronous ASK

Page 48: Coherent Lightwave Systems

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IF- Signal to noise ratio (IF-SNR) :

2thermalesLO

LOs2

2

2d

B)IRP(e2PPR4i

SNRIF

e

s

e

s

esLO

LOs2

2

2d

BhP2

eBRP2

B)IRP(e2PPR4i

SNRIF

where R=e/h

Or

Page 49: Coherent Lightwave Systems

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If the bit rate is Br=1/T, then average signal power

rs BNhT

NhP

Let Be=Br/2, then SNR can be expressed

N4SNR

The corresponding BER for homodyne ASK receiver is

ASKHomSynNerfcBER ..]2/[21

For an ideal photodetector =1 and the number of photons per bit required for BER=10-9 is 36 for Homodyne Syn. ASK.

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Homodyne Syn. ASK Versus Heterodyne Syn. ASK

– ASK homodyne receiver requires 3 dB less power and is therefore 3-dB more sensitive than ASK heterodyne receiver.

Heterodyne Detection versus IM/DD– Sensitivity Improvement of

10 dB to 20 dB– Frequency selectivity– IF domain signal processing

provides better performanceHeterodyne Detection– Receiver is more sensitive

to the phase noise of lasers– Additional signal power is

required for the same reliability of operation which is called power penalty

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Synchronous PSK Detection in the presence of noise

The detector current at the receiver output is given by

so that the output current is positive or negative depending on the bit transmitted as:

and

]cos[21

cpd iII

"0"bit"1"bit0

where

"0"bitiI21I

"1"bitiI21I

cp0

cp1

SNR2

I2IIQ1

1

01

01

Page 52: Coherent Lightwave Systems

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Using SNR=2N for heterodyne case

PSKSynHetNerfcBER p .][21

And using SNR=4N for homodyne case

PSKSynHomNerfcBER ..]2[21

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Heterodyne Synchronous Dual-Filter FSK Receiver

• FSK synchronous receiver is equivalent to two ASK asynchronous heterodyne receivers operating in parallel. The signal is received during both binary bits, the SNR is 3-dB higher than that for ASK heterodyne receiver.

• In dual filter FSK receiver, two band-pass filters are used to pass the mark and space frequencies separately. • The BPF are centered at (IF+) and (IF-) corresponding to "mark" and "space" frequencies. • The output of the BPF are passed through envelope detectors and low-pass filters. The differential signal at the

output of the low-pass filter is then obtained by subtracting the one from the other. The data decision is then made by comparing the output samples with a threshold of zero value.

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pe

s

e

sd

esLOd

LOsddN

BhP

eBPR

BIPRePPRi

SNR

422

)(24 2

2

2

The BER is then given by

sSynchronouHeterodyneFSKNerfcBER p ]2/[21

Page 55: Coherent Lightwave Systems

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Heterodyne Asynchronous receiver

• Asynchronous demodulation does not require recovery of the microwave carrier at the intermediate frequency

• The output of the IF filter is passed through an envelope detector and is low-pass filtered.

• The output of the LPF is sampled and compared with a threshold of optimum value to make bit decisions.

• This demodulation scheme can be used for ASK and FSK.

Optical Signal Input

Baseband Signal OutputLocal

Optical Oscillator

Photo-Detector

BPF

Beam Combiner

Envelop Detector

LPF

Page 56: Coherent Lightwave Systems

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The current after heterodyne photo-detection

The noise at the output of the filter can be expressed in terms of its in-phase and quadrature components as :

where

)]tsin(sin)tcos([cos)t(PPR2

)tcos()t(PPR2)t(I

IFIFSLO

IFSLOd

sc i,iThe variance are given by:

2T

2s

2 (Gaussian random variables with zero mean)

scn iji)t(i

Heterodyne Asynchronous Detection in the presence of noise

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• It shows that both the in-phase and out-of-phase noise components affects the performance of asynchronous (incoherent) heterodyne receivers.

• The SNR is thus degraded comparing with that of synchronous (coherent) heterodyne receivers.

2sSLO

2cSLOd ]isin)t(PPR2[]icos)t(PPR2[)t(I

With noise included after BPF, envelope detector and LPF:

Page 58: Coherent Lightwave Systems

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• In case of asynchronous demodulation, the noise at the output of the envelop detector is no longer Gaussian– because the output of an envelop detector is square of its

input. – So, the noise statistics are changed due to envelope

detection and hence the BER calculation becomes complicated.

The current at the output of the envelop detector when a signal pulse is present corresponding to bit "1" is given by

2/12s

2cp i)iI(I

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The probability density function (pdf) of the output current I is given by a Rice distribution as

2p

02

2p

2

2p

III

2II

expI)I,I(p

where I0 is the Bessel function of the first kind and 2 isthe noise variance .

The output of the envelop detector corresponding to a bit "0" is

2/12s

2c iiI

and the pdf of the output is given by a Raleigh distribution which can be obtained by putting Ip=0 in the expression for p(I,Ip).

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The bit error rate (BER) is then obtained as

The final form of the BER is given by

The minimum BER corresponding to optimum threshold can be obtained numerically. If I0=0 and I1>>, ith=I1/2. Under such conditions, BER is given by

)0/1(P)1/0(P21)0/1(P)0(p)1/0(P)1(pBER

thi

01 dI)I,I(p)1/0(P

thi

0 dI)I,I(p)0/1(P

th0th1 i,IQi,IQ1

21BER

and

8

SNRexp21

8Iexp

21BER 2

21

Using SNR=2N for heterodyne detection, BER can be expressed as

4/Nexp21BER

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Heterodyne Asynchronous FSK- Single filter Receiver

• The output of the IF filter is passed through a frequency discriminator followed by an envelope detector and is low-pass filtered.

• The output of the LPF is sampled and compared with a threshold of optimum value to make bit decisions.• The single filter FSK receiver is suitable for narrow deviation FSK (for modulation index, <1)

Optical Signal Input

Baseband Signal OutputLocal

Optical Oscillator

Photo-Detector

BPF

Beam Combiner

Frequency discriminator

-------Envelop Detector

LPF

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• Two band-pass filters are used to pass the mark and space frequencies separately.

• The BPF are centered at (IF+) and (IF-) corresponding to "mark" and "space" frequencies.

• The data decision is then made by comparing the output samples with a threshold of zero value.

Heterodyne Asynchronous Dual-Filter FSK Receiver

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Heterodyne Asynchronous DPSK Delay-Demodulation

Receiver

• In this demodulation scheme, a replica of the IF signal is delayed by a fraction of a bit and then multiplied with the original signal.

• The resulting signal is a phase modulated signal of differential phase, =(t)-(t-) where is delay time.

• The optimum value of is T/2.

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Bit-error rate curves for various modulation formats

Synchronous

Asynchronous

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Tutorial

• Consider a 1.55- μm heterodyne receiver with a p–i–n photodiode of 90% quantum efficiency connected to a 50-Ω load resistance. How much local-oscillator power is needed to operate in the shot-noise limit? Assume that shot-noise limit is achieved when the thermal-noise contribution at room temperature to the noise power is below 1%.

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Tutorial

• Calculate the sensitivity (in dBm units) of a homodyne ASK receiver operating at 1.55 μm in the shot-noise limit. Assume that η= 0.8 and ∆f = 1 GHz. What is the receiver sensitivity when the PSK format is used in place of ASK?