• 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,   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