4 CONTENTS Performance degradation due to: laser phase noise, group velocity dispersion,self phase modulation,polarization mode dispersion,relative intensity noise,effect of timing jitter;
5 CONTENTS System design considerations: power budget, rise time budget, power penalty.
6 Modulation Modulation process: Switching or keying the amplitude, frequency, or phase of the carrier in accordance with the information binary bits.The modulation can be either:Direct modulationLight is directly modulated inside a light sourceExternal modulationUsing external modulator
7 IM-DD system Optical detection Applied in the first generation (1970’s) intensity modulation directdetection is still the most used for optical communicationsInformation is carried only by the intensitynot frequency or phaseOptical detectionThe received signal is applied directly to photodetectorPhoto-detection of light represents the key operation in the optical receiver.Converting the collected field onto a current or voltage.
8 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 lightWhere the Plank constant h = W s2
9 Let P the optical power of a light beam, then the number of photons per second is: For modulated optical signal with power P(t), the instantaneous photon intensity (photon flux) varies with time:photons/s
10 For a PIN-diode photodetector, the average number of electron-hole pairs generated in a time interval of T is given byWhere is the quantum efficiency of the device and E is the energy received in a time interval T.
11 The ideal receiverConsider an ideal OOK transmission system over an ideal channelThe transmitter sends light for a oneNo light for a zeroThe receiver counts N, the number of photons it receives in a bit interval of T seconds, and zero otherwise
12 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 mFor a ONE, the probability of receiving N photons in T seconds is given by by the Poisson distribution.
13 Quantum limitIt is possible that no photons arrive when a ONE is transmitted. This leads to a probability of error or a Bit-error-ratio (BER), ofThis leads to an important lower bound on the BER called the quantum limitIt indicates a minimum signal power required by an OOK receiver to achieve a given BER
14 Example: 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: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.
15 Practical receiver Receiver configuration IM-DD system can only be used for OOK modulation format
16 is a stationary random process with Poisson statistics Shot noiseShot noise (from O-E counting process in PIN):is the averagephotocurrentis a stationary random process with Poisson statisticsis(t) can be approximated by the Gaussian statisticswith its variance given by:
17 current fluctuation induced by thermal noise Including thermal noise (from carrier moving in any conductor):current fluctuation induced by thermal noiseiT(t) can be modeled as a stationary Gaussian random processwith its variance given by:Its spectral density (“white noise”) is given by:.Boltzmann constant,the absolute temperature,and the load resistor
18 Total receiver noiseConsidering the dark current from PIN and the enhancementto thermal noise from the components other than the loadresistor in the linear channel, the total noise variance is:the PIN dark currentand the amplifier noise figure
19 Receiver signal to noise ratio PIN receiver:APD receiver:Wherethe APD gain and the APD excess noise factoris the ionization-coefficient ratio.
21 BER Analysis for IM/Direct Detection The bit error rate can be computed as:wherePr(0/1) is the probability that a "0" is receivedwhen a "1" is transmitted.Pr(1/0) is the probability that a "1" is receivedwhen a "0" is transmittedThe values of Pr(0/1) and Pr(1/0) depends on the statisticalnature of the output signal in the presence of noise.
22 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 byWhere in is the noise current due to shot and thermal noise.The probability density function of in is given bywhere imean=0 is the mean value of in.
23 Bit Error RateThe bit error rate can be computed as:
24 Since in is Gaussian with zero mean and variance n2 , the probability density function (pdf) of the receiveroutput corresponding to bit "1" and bit "0" are alsoGaussian with mean I1 and I0 respectively and given bywhere 12 and 02 are the noise variances corresponding tobit "1" and bit "0" respectively.
26 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 asThe optimum threshold is then given byUnder the assumption that the noise current is same for bit "0" and bit "1",1=0, then the optimum threshold is given byThe 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.
27 The value of the parameter Q at the receiver output under optimum threshold condition is expressed asand the corresponding BER for optimum threshold is given by
28 Where we assumed that I0=0 and 0= 0 which is valid when the The output SNR (= signal power to noise power ratio) for a PIN-receiveris given bywhere Be=Br/2. In terms of number of photons per bit N, the BER can be expressed aswhereWhere we assumed that I0=0 and 0= 0 which is valid when thereceiver is dominated by shot noise.
31 Coherent DetectionCoherent detection receiver adds light to the receivedsignal as part of the detection processLocalOpticalOscillatorPhoto-DetectorElectronicCircuitsOptical Signal InputElectrical Signal OutputBeamCombinerCoherent receiver model
32 Detection Schemes 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 modulationHeterodyne detectionNeither optical phase locking nor frequency matching is ofthe local oscillator is required ( c LO).
33 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
37 Heterodyne Synchronous Coherent Receiver Optical Signal InputBaseband Signal OutputLocal Optical OscillatorPhoto-DetectorBPFBeam CombinerDelayCarrier RecoveryLPFIn 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.
38 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.
39 Heterodyne Synchronous ASK The detector current:its mean square is :The thermal noise and shot noise variances :where
41 If the bit rate is Br=1/T, then average signal power Let Be=Br/2, then SNR can be expressedThe corresponding BER for heterodyne ASK receiver is
42 Receiver sensitivityReceiver 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=144or 21.6 dB.Average received power Pr can be obtained asFor an ideal photodetector =1 and the number of photons per bit required for BER=10-9 is 72 for ASK heterodyne.
43 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:)The noise at the output of the filter can be expressed interms of its in-phase and quadrature components as :where(Gaussian random variables with zero mean)The variance are given by:
44 With noise included after BPF: After synchronous (coherent) demodulation and LPFIt shows that only the in-phase noise component affects the performance of synchronous heterodyne receivers.
45 The analysis is analogous to that for direct detection receiver whereThe analysis is analogous to that for direct detection receiverand the BER is given bywhereWhere we assumed that I0=0 and 0= 1 which is valid when thereceiver is dominated by shot noise at higher values of PLO.
47 Homodyne Synchronous ASK The detector current:its mean square is :The thermal noise and shot noise variances :where
48 IF- Signal to noise ratio (IF-SNR) : Orwhere R=e/h
49 If the bit rate is Br=1/T, then average signal power Let Be=Br/2, then SNR can be expressedThe corresponding BER for homodyne ASK receiver isFor an ideal photodetector =1 and the number of photons per bit required for BER=10-9 is 36 for Homodyne Syn. ASK.
50 Heterodyne Detection versus IM/DD Homodyne Syn. ASK Versus Heterodyne Syn. ASKASK homodyne receiver requires 3 dB less power and is therefore 3-dB more sensitive than ASK heterodyne receiver.Heterodyne Detection versus IM/DDSensitivity Improvement of 10 dB to 20 dBFrequency selectivityIF domain signal processing provides better performanceHeterodyne DetectionReceiver is more sensitive to the phase noise of lasersAdditional signal power is required for the same reliability of operation which is called power penalty
51 Synchronous PSK Detection in the presence of noise The detector current at the receiver output is given bywhereso that the output current is positive or negative depending on the bit transmitted as:and
52 Using SNR=2N for heterodyne case And using SNR=4N for homodyne case
53 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.
55 Heterodyne Asynchronous receiver Optical Signal InputBaseband Signal OutputLocal Optical OscillatorPhoto-DetectorBPFBeam CombinerEnvelop DetectorLPFAsynchronous demodulation does not require recovery of the microwave carrier at the intermediate frequencyThe 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.
56 Heterodyne Asynchronous Detection in the presence of noise The current after heterodyne photo-detectionThe noise at the output of the filter can be expressed interms of its in-phase and quadrature components as :where(Gaussian random variables with zero mean)The variance are given by:
57 With noise included after BPF, envelope detector and LPF: 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.
58 because the output of an envelop detector is square of its input. In case of asynchronous demodulation, the noise at the output of the envelop detector is no longer Gaussianbecause 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 ispresent corresponding to bit "1" is given by
59 The probability density function (pdf) of the output current I is given by a Rice distribution aswhere 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" isand 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).
60 The bit error rate (BER) is then obtained as andThe final form of the BER is given byThe minimum BER corresponding to optimum threshold can be obtainednumerically. If I0=0 and I1>>, ith=I1/2. Under such conditions, BER is given byUsing SNR=2N for heterodyne detection, BER can be expressed as
61 Heterodyne Asynchronous FSK- Single filter Receiver Optical Signal InputBaseband Signal OutputLocal Optical OscillatorPhoto-DetectorBPFBeam CombinerFrequency discriminatorEnvelop DetectorLPFThe 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)
62 Heterodyne Asynchronous 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 data decision is then made by comparing the output samples with a threshold of zero value.
63 Heterodyne Asynchronous DPSK Delay-Demodulation ReceiverIn 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 Bit-error rate curves for various modulation formats SynchronousAsynchronous
65 TutorialConsider a 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 TutorialCalculate 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?