• 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)

Where,

 

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)

 

Where,

 

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

                           … (5.5.4)

 

Where,

 

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)

Where,

 

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

 

Parameter

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