Chapter 4 Modulation and Demodulation

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Chapter 4 Modulation and Demodulation
Modulation/Demodulation schemes, Receiver design,
Signal-to-noise ratio (SNR), Bit error rate (BER)
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4.1 Modulation

• Intensity modulation/ Direct detection
• i. digital (on- off keying, OOK)
• ii. analog
• Coherent modulation

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4.1.1 Signal format (digital)

• Unipolar return-to-zero (RZ, x)
• Unipolar non-return-to-zero (NRE)
• need good DC balance
• For time recover circuits, transitions are
  needed. (line coding or scrambling) (8,10) or
  (4,5) coding needs extra bandwidth
• The NRE format is very popular for high speed
  communication systems (e.g. 10Gb/s)

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4.2 Subcarrier Modulation (SCM) and Multiplexing

• Data first modulate the microwave carrier
  (10MHz10GHz). Then we use the modulated
  microwave carrier to modulate the optical carrier.

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• CATV

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4.2.1 Clipping and Intermodulation products

• The main issues
• a. power efficiency
• b. signal fidelity
• Source of signal distortion
• a. clipping

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b. nonlinearity
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• Provided a number M of simultaneously present
  sinusoids lying between ,the
  second-order terms at frequencies
  appear.

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• In general a1gtgt a2gtgt a3
• gt It seems the second-order terms are more
  harmful than the third terms.
• If we make
• will lie completely outside the
  band
• For the following two reasons, may
  not be satisfied
• Waste about half the available bandwidth
• Because is higher, a laser which can be
  modulated at high frequency is needed.

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• two-tone third-order terms (because there are
  only two distinct frequencies)
• triple-beat (CTB)
• Define Composite second order (CSO) distortion
• Composite triple-beat (CTB)
  distortion
• In general CTB distortion is larger than CSO
  distortion.

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4.2.2 Applications of SCM

• Transmitting multiple analog video signal using a
  single optical transmitter. (CATV, Hybrid
  fiber-coax HFC)
• Carrying control data along with the actual data
  steam. For example, the pilot tone in WDM
  systems.

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4.3 Optical Duobinary Modulation (controlled ISI)
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4.3.2 Optical Single sideband Modulation
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4.3.3 Multilevel Modulation (M-level)

• M2R
• R bits
• TTb log2M
• T band duration
• Tb bit duration

4.3.4 Capacity Limits of Optical Fiber
Shanons Theorem CB log2(1S/N) B bandwidth, C
capacity S/N signal-to-noise ratio

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4.4 Demodulation

• BER 10-9 or 10-12

3R Regeneration, reshaping and retiming
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4.4.1 An Ideal Receiver

• It can be viewed as photon counting.
• Direct detection is used with the following
  assumptions
• When any light is seen, the receiver makes in
  favor of symbol 1, otherwise it makes in favor
  of symbol o
• Photons will generate electron-hole pairs
  randomly as a Poisson random process.
• When o was sent, there is no light. For an
  ideal receiver, it is error free.
• When 1 was sent, because of Poisson random
  process, if no electron-holes are generated the
  receiver will make in favor of o gt error occurs

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• The photon arriving rate for a light pulse with
  power P is P/hf
• h plancks constant
• 6.63 x 10-34 J-sec
• hf the energy of a single photon
• Let B denote the bit rate,
• the T 1/B is the bit duration
• Recall for Poisson process
• P(?) exp(-?T) (?T)n /n!
• where ? P / hf (photon arriving rate)
• The probability that n electron-hole pairs are
  generated during T 1/B seconds
• P(?) exp(-P/hfB) (P/hfB)n /n!

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• If n?1 we decide that the bit is 1 otherwise it
  is o bit.
• The probability the a light pulse does not
  generate any electron-hole pair is
• P(?) exp(-P/hfB)
• Assuming that 1 and o are transmitted with
  equal probability,
• BER ½ exp (-P/hfB) ½ x 0

0
1
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• Let M be the number of photons for 1 bit in T
  seconds (M P/hfB)
• BER ½ e-M
• which is called the quantum limit
• BER 10-12 M 27
• BER 10-9 M 21 (BER 7.6 x
  10-10)
• Practically the receiver has noise, more light
  power is needed to achieve the same BER.

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4.4.2 A Practical Direct Detection Receiver
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• The noise sources
• a. thermal noise
• b. shot noise
• The thermal noise current in a resistor R at
  temperate T can be modeled as Additive White
  Gaussian Noise (AWGN) with zero mean and variance
  4KBT/R
• KB Boltzmanns constance
• 1.38 x 10-23 J/Ko
• Let Be be the signal bandwidth
• The variance of the thermal noise is

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• It is the current standard deviation in
• where Tbit duration, Beelectrical bandwidth
• Let B0 be the optical bandwidth (passband)
• B0 ? 2 Be (Haykin P.49)

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• For a receiver using PIN diode, the photocurrent
  is given by
• where e the electronic charge
• e h(t-tk) the current impulse due to a
  photon arriving at tk
• Let p(t) be the optical power and p(t)/hfc be the
  photon arrival rate, fc be the optical frequency.
• The rate of generation of electrons is Poisson
  process with rate

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• To evaluate (I.1), we break up the time axis into
  small interval dt.
• The current is given by
• Nk are Poisson random variables with rate

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• Assume that
• The mean value of the photocurrent is

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Shot noise
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• The photocurrent is given by
• is the shot current with zero mean and
  variance

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• Let the local resistance be RL
• The total current in the resistor is
• Where is the thermal current with variance
• Assume and are independent, the total
  current has mean and variance
• Note that is proportional to
• there is a trade-off between SNR and
• For IM/DD receivers

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4.4.3 Front end amplifier noise

• Define Noise Figure (Fn) of the amplifier
• (SNR)in / (SNR)out
• typically Fn 35dB
• The thermal noise contribution is
• Similary

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4.4.3 APD Noise
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• Gm(t) Gm
• Avalanche multiplication gain
• will be amplified
• Let RAPDresponsivity of APD
• The average APD photocurrent is
• The variance of shot noise is
• FA(Gm) the excess noise factor
• FA(Gm) KAGm (1 - KA)(2 -1 / Gm)
• KA ionization coefficient ratio
• For silicon KAltlt1
• For InGaAs KA0.7
• Note if Gm1, FA1 (4.4) is the variance of
  shot noise of PIN

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4.4.5 Optical Amplifiers

• The Amplified Spontaneous Emission (ASE) noise is
  the main noise source of optical amplifiers.
• The ASE noise power for each polarization is
• Where nsp the spontaneous emission factor
• G the amplifier gain
• Bo the optical bandwidth
• nsp depends of level of population inversion,
  With complete inversion nsp 1
• typically nsp 25

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• There are two independent polarizations in a
  single mode fiber
• The total ASE noise power
• P2PN
• Define
• If the standard PIN is used
• IRGP (4.6)
• R responsivity
• P received power

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• Photocurrent I is proportional to the optical
  power P which is proportional to the square of
  the electrical field. Thus the noise field beats
  against the signal and against itself. Thus
  signal-spontaneous beat noise and
  spontaneous-spontaneous beat noise are produced.
• For Appendix I, we have

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• It is the received thermal noise current
• If G is large (e.g gt 10dB)
• If Bo is small 2Be
• Pn nsphfc ltlt P
• is dominant, which can be modeled as
  a Gaussian process.

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• Recall (4.2)
• At the amplifier input
• At the amplifier output, using (4.6) and (4.9) we
  have

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• The noise figure of the amplifier is
• In the above derivation, we assume no coupling
  losses. The input coupling loss will degrade Fn

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4.4.6 Bit Error Rates (BER)

• BER is a very important measure for digital
  communication systems.
• Other measures are SNR, CNR, error free second,
  packet loss
• Consider a PIN receiver without optical
  amplifiers
• P1 optical power of bit 1
• P0 optical power of bit 0
• Assume that thermal noise dominates and is
  Gaussian.

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• For bit 1, the mean photocurrent is
• The variance is
• RL load resistant
• For bit 0, the variance is
• For ideal case P00 I00

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• Assume the decision threshold current is Ith
• If I gt Ith decision is made in favor of 1
• If I lt Ith decision is made in favor of 0

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• Assume that bits 1 and 0 are transmitted
  equally likely
• Problem 4.7
• The threshold current is

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• If 1 and 0 are transmitted equally likely

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• We may specify BER then calculate the received
  power (BER10-12)
• Define The receiver sensitivity as
• Psens The minimum average optical power for
  given BER (e.g 10-12 )
• It is also expressed as the number of photons per
  bit.
• Recall page252

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(KA0.7, Gm10)
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• For a system with optical amplifier

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• If systems with cascades of optical amplifiers,
  optical signal consists of a lot of optical
  noise, and can be ignored.
  The received optical noise power PASE dominates.
• Define
• Optical signal-to-noise ratio (OSNR)
• Based on above equation, (4.6), (4.9), (4.10) and
  (4.14)
• We have

For 2.5Gb/s system, Be2 GHz, Bo 36GHz, r7
gt OSNR 4.37 6.14 dB A rule of thumb used by
designers OSNR 20dB because of dispersion and
nonlinearity
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4.4.7 Coherent Detection (ASK)

• Assume that phase and polarization of two waves
  are matched ?0
• The optical power at the receiver.

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• At BER10-12 r 7 M 49
• Recall for the optical amplified system (p.262)
• at BER10-12 M98,
• coherent PSK has sensitivity about 45dB better
  than optical amplified ook.
• Disadvantages
• 1. receivers are very complicated
• 2. phase noises must be very small
• 3. high frequency stability is needed
• 4. optical phase locked loop is needed
• 5. polarization must be matched
• Advantages
• 1. very good performance
• 2. less effect by nonlinearity and dispersion
• 3. DPSK does not need OPLL

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4.4.8 Timing Recovery

• Timing circuit produces timing clock for the
  decision circuit.
• Inband timing
• Outband timing
• Reference Alain Blancharal Phase-Locked Loops
  John Wiley and Sons., 1976 Chapter3

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Sinusoidal
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• Let F(iw) be the loop filter transfer function
  and f(t) be its impulse response

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4.4.9 Equalization

• The equalizer is used to reduce the effect of
  intersymble interference (ISI) due to pulse
  spreading caused by dispersion.