ETM 7172 OPTICAL COMMUNICATION SYSTEMS Multimedia University Hairul Azhar Abdul Rashid, 2006 1 Coherent Lightwave Systems.
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ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
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;
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ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
CONTENTS
• Demodulation schemes : – synchronous and – asynchronous demodulation;
• Bit error rate performance analysis;
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ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
CONTENTS
• Performance degradation due to:– laser phase noise, – group velocity dispersion, – self phase modulation, – polarization mode dispersion, – relative intensity noise, – effect of timing jitter;
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ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
CONTENTS
• System design considerations: – power budget, – rise time budget, – power penalty.
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ETM 7172 OPTICAL COMMUNICATION 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
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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
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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
hf
PN
hf
)t(P)t(Np
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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
hf
Edt)t(P
hfm
T
0
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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
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Hairul Azhar Abdul Rashid, 2006
• 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.
!N
e)m(]ONE/photonsN[Pr
mN
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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
2
eBER
N
• It indicates a minimum signal power required by an OOK receiver to achieve a given BER
2
e]ONE/photons0[Pr
2
1BER
m
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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/photons102
m
• 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
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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
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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
R
Tk4df)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
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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
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ETM 7172 OPTICAL COMMUNICATION 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 )
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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
2n
2meann
2n
n 2
)ii(exp
2
1)i(p
• where imean=0 is the mean value of in.
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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
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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
2
1)i(p
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ETM 7172 OPTICAL COMMUNICATION SYSTEMS
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Hairul Azhar Abdul Rashid, 2006
Hence
1
th11
i
21
211
21
i
11th1
2
iIerfc
2
1di
2
)Ii(exp
2
1
)i(d)i(p)iiPr()1/0Pr(
th
th
0
0th0
i20
200
20
i
00th0
2
Iierfc
2
1di
2
)Ii(exp
2
1
)i(d)i(p)iiPr()0/1Pr(
th
th
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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
2
Q
2
iI
2
Ii
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
2
IIi 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 II
2
1erfc
2
1
2
Qerfc
2
1)0/1Pr(
2
1)1/0Pr(
2
1BER
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The output SNR (= signal power to noise power ratio) for a PIN-receiver is given by
NBh2
P
R/FkTB4B)IRP(e2
)RP(SNR
e
in
Lneedin
2in
where Be=Br/2. In terms of number of photons per bit N, the BER can be expressed as
2
Qerfc
2
1BER
where
SNRIII
Q1
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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2
Nerfc
2
1BER
NQ hence
2
Nerfc
2
1
2
Qerfc
2
1BERand
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Principle of Coherent Detection
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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
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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
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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
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ASK, PSK, DPSK, and FSK modulation Formats
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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
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Homodyne Detection
The detector current: )(2)( tPPRtI SLOp
Heterodyne Detection
The detector current:
)cos()(2)( LOsIFLOSp tPtPtI
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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.
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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
2
d
B)IRP(e2
PPR2iSNRIF
e
s
e
s
esLO
LOs2
2
2
d
Bh
P
eB
RP
B)IRP(e2
PPR2iSNRIF
Or
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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/[2
1
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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[2
1P
2
1P 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.
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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,i
The variance are given by:
(Gaussian random variables with zero mean)
scn iji)t(i
2s
2c
2
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After synchronous (coherent) demodulation and LPF
2
icos)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 icosI2
1icos)t(PPR)t(I Or
The analysis is analogous to that for direct detection receiver and the BER is given by
2
Qerfc
2
1BER
where SNR2
1
2
IIIQ
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
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Using the relation SNR=2Np we get
.Det.ASK.Het.Syn]4/N[erfc2
1BER
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The detector current:
its mean square is :
The thermal noise and shot noise variances :
)(2)( tPPRtI SLOp
LOsd PPRti 224)(
2thermal
2shot
2
eLOseLOs2shot B)RPRP(e2B)II(e2
where
Lne2thermal R/FkTB4
Homodyne Synchronous ASK
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IF- Signal to noise ratio (IF-SNR) :
2thermalesLO
LOs2
2
2
d
B)IRP(e2
PPR4iSNRIF
e
s
e
s
esLO
LOs2
2
2
d
Bh
P2
eB
RP2
B)IRP(e2
PPR4iSNRIF
where R=e/h
Or
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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/[2
1
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 performance
Heterodyne 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[2
1cpdiII
"0"bit
"1"bit0
where
"0"bitiI2
1I
"1"bitiI2
1I
cp0
cp1
SNR2
I2IIQ
1
1
01
01
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Using SNR=2N for heterodyne case
PSKSynHetNerfcBER p .][2
1
And using SNR=4N for homodyne case
PSKSynHomNerfcBER ..]2[2
1
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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
LOsdd
NBh
P
eB
PR
BIPRe
PPRiSNR
4
22
)(2
4 2
2
2
The BER is then given by
sSynchronouHeterodyneFSKNerfcBER p ]2/[2
1
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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 Output
Local Optical
Oscillator
Photo-Detector
BPF
Beam Combiner
Envelop Detector
LPF
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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,i
The 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:
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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
2
p02
2p
2
2p
III
2
IIexp
I)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(P2
1)0/1(P)0(p)1/0(P)1(pBER
thi
0
1 dI)I,I(p)1/0(P
thi
0 dI)I,I(p)0/1(P
th0th1 i
,I
Qi
,I
Q12
1BER
and
8
SNRexp
2
1
8
Iexp
2
1BER
2
21
Using SNR=2N for heterodyne detection, BER can be expressed as
4/Nexp2
1BER
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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 Output
Local Optical
Oscillator
Photo-Detector
BPF
Beam Combiner
Frequency discriminator
-------Envelop Detector
LPF
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ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
• 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
63
ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
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.
64
ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
Bit-error rate curves for various modulation formats
Synchronous
Asynchronous
65
ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
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%.
66
ETM 7172 OPTICAL COMMUNICATION SYSTEMS
Multimedia University
Hairul Azhar Abdul Rashid, 2006
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?
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