• The equalizer signal is compared with a threshold level to determine the presence of a The comparison is done on time slot basis.

Probability of Error


  • Bit error rate (BER) is defined as the ratio of number of errors occurring over a time interval to the number of pulses transmitted during the


                                                                                                                    … (5.5.1)

                                                                                                                    … (5.5.2)



Ne is number of errors occurring during the interval. Nt is number of pulses transmitted during the interval.

B is bit rate          or pulse transmission rate.


  • BER for optical fiber communication system is ranging between 10-9 to 10-12. BER of receiver depends on S/N ratio. To compute the BER at receiver probability distribution of output signal is considered.
  • Condiitonal PDF : P(y/x) is the probability that the output voltage is y when x was The functions p (y/1) and p (y/0) are conditional PDF as shown in Fig. 5.5.1.
  • The probability distributions are given as –


It is the probability that output voltage is less than threshold when logic ‘1’ is sent.


It is the probability that output voltage exceeds threshold voltage when a logic ‘0’ is sent. The error probability is expressed as

                                                                                         … (5.5.3)




a and b are probabilities that either 1 or 0 occurs.

                           … (5.5.4)




V is the pulse amplitude.


σ is standard deviation (measure of width of probability distribution)


Quantum Limit


  • For an ideal photodetector having quantum efficiency η = 1 and has zero dark current (i.e. no output when light is absent) then the minimum received power for a specific bit – error rate is known as Quantum
  • Let an optical pulse of energy E is incident on photoetector in time interval τ. Then the probability of emitting zero electrons during the interval is


                                           … (5.5.5)



XXXX is average number of electron – hole pairs.

Example 5.5.1 : A digital fiber link operating at 850 nm requires a BER of 10-9. Calculate the quantum limit in terms of quantum efficiency.

Solutions :                   λ = 850 nm = 850 x 10-9 m BER = 10-9

Probability of error



No. of electron – hole paid generated (XXXX), quantum efficiency (η), photo energy (hv) and energy received (E) are related by,

Comparison of Receiver Performance



PIN Detecor

APD Detector

Preamplifier noise level (A2)

10-15 to 10-18

10-15 to 10-18

Digital receiver sensitivity (dBm)

-34.21 to -49.21

-51.00 to -51.65

Analog receiver S/N (dBm)

13.00 to 37.78

34.36 to 38.27


Review Questions


  1. In an optical receiver explain the sources of errors.
  2. Deduce the expression for mean output current from
  3. For a digital optical receiver find the expression of probability of
  4. Find the expression for mean square noise voltage for optical University Questions