1. Coherent Lightwave Systems

2. CONTENTS Principles of coherent and non-coherent detection :
heterodyne and
homodyne detection;
Modulation formats:
ASK,PSK,FSK,PPM,DPSK;

3. CONTENTS Demodulation schemes : Bit error rate performance analysis;
synchronous and
asynchronous demodulation;
Bit error rate performance analysis;

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 modulation
Light is directly modulated inside a light source
External modulation
Using external modulator

7. IM-DD system Optical detection
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
Optical detection
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.

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

11. 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

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

13. 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
It 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 noise
Shot noise (from O-E counting process in PIN):
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:

17. current fluctuation induced by thermal noise
Including 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:
Its spectral density (“white noise”) is given by:.
Boltzmann constant,
the absolute temperature,
and the load resistor

18. Total receiver noise
Considering the dark current from PIN and the enhancement
to thermal noise from the components other than the load
resistor in the linear channel, the total noise variance is:
the PIN dark current
and the amplifier noise figure

19. Receiver signal to noise ratio
PIN receiver:
APD receiver:
Where
the APD gain and the APD excess noise factor
is the ionization-coefficient ratio.

20. PIN and APD Noise limitations

21. BER Analysis for IM/Direct Detection
The bit error rate can be computed as:
where
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
The values of Pr(0/1) and Pr(1/0) depends on the statistical
nature 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 by
Where in is the noise current due to shot and thermal noise.
The probability density function of in is given by
where imean=0 is the mean value of in.

23. Bit Error Rate
The 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 receiver
output corresponding to bit "1" and bit "0" are also
Gaussian with mean I1 and I0 respectively and given by
where 12 and 02 are the noise variances corresponding to
bit "1" and bit "0" respectively.

25. Hence

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

27. The value of the parameter Q at the receiver output under optimum
threshold condition is expressed as
and 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-receiver
is given by
where Be=Br/2. In terms of number of photons per bit N, the BER can be expressed as
where
Where we assumed that I0=0 and 0= 0 which is valid when the
receiver is dominated by shot noise.

29. hence
and

30. Principle of Coherent Detection

31. Coherent Detection
Coherent detection receiver adds light to the received
signal as part of the detection process
Local
Optical
Oscillator
Photo-
Detector
Electronic
Circuits
Optical Signal Input
Electrical Signal Output
Beam
Combiner
Coherent 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 modulation
Heterodyne detection
Neither optical phase locking nor frequency matching is of
the 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

34. ASK, PSK, DPSK, and FSK modulation Formats

35. Optical Detection Modulated signal: Local oscillator signal:
The output power of the photodetector
where

36. Homodyne Detection Heterodyne Detection
The detector current:
Heterodyne Detection
The detector current:

37. Heterodyne Synchronous Coherent Receiver
Optical Signal Input
Baseband Signal Output
Local 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.

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

40. IF- Signal to noise ratio (IF-SNR) :Or

41. If the bit rate is Br=1/T, then average signal power
Let Be=Br/2, then SNR can be expressed
The corresponding BER for heterodyne ASK receiver is

42. Receiver sensitivity
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.
Average received power Pr can be obtained as
For 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 in
terms 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 LPF
It 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
where
The analysis is analogous to that for direct detection receiver
and the BER is given by
where
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.

46. Using the relation SNR=2Np we get

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) :Or
where R=e/h

49. If the bit rate is Br=1/T, then average signal power
Let Be=Br/2, then SNR can be expressed
The corresponding BER for homodyne ASK receiver is
For 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. 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

51. Synchronous PSK Detection in the presence of noise
The detector current at the receiver output is given by
where
so that the output current is positive or negative depending on the bit transmitted as:
and

52. Using SNR=2N for heterodyne case
And using SNR=4N 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.

54. The BER is then given by

55. Heterodyne Asynchronous receiver
Optical Signal Input
Baseband Signal Output
Local Optical Oscillator
Photo-
Detector
BPF
Beam Combiner
Envelop Detector
LPF
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.

56. Heterodyne Asynchronous Detection in the presence of noise
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
(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 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

59. The probability density function (pdf) of the output current I
is given by a Rice distribution as
where I0 is the Bessel function of the first kind and 2 is
the noise variance .
The output of the envelop detector corresponding to a bit "0" is
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).

60. The bit error rate (BER) is then obtained as
and
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
Using SNR=2N for heterodyne detection, BER can be expressed as

61. Heterodyne Asynchronous FSK- Single filter Receiver
Optical Signal Input
Baseband Signal Output
Local Optical Oscillator
Photo-
Detector
BPF
Beam Combiner
Frequency discriminator
Envelop Detector
LPF
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)

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
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. Bit-error rate curves for various modulation formats
Synchronous
Asynchronous

65. Tutorial
Consider 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. 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?