- 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 (A^{2}) |
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
- In an optical receiver explain the sources of errors.
- Deduce the expression for mean output current from
- For a digital optical receiver find the expression of probability of
- Find the expression for mean square noise voltage for optical University Questions