Subject : Optical Fiber Communication
FSK Heterodyne Detection
Introduction:
FSK transmission systems are more promising than ASK or PSK. Optical FSK transmission and heterodyne detection experiments at 560-Mbit/s and 1-Gbit/s are conducted at a wavelength of 1497 nm. Receiver sensitivities of -39 dBm at 560 Mbit/s and -37 dBm at 1 Gbit/s are obtained.
Heterodyne Detection for FSK:
- By considering FSK heterodyne synchronous detection in the shot or quantum noise limit.
- The two angular frequencies for the transmitted 1 and 0 bits are assumed to be ω_{1 }and ω_{2} so that
…1
Where I_{SH} is defined as
...2
- And φ, which is a function of time, represents the phase noise associated with the semiconductor laser.
- This is neglected because we are concerned with shot-noise-limited detection
- It is assumed that the signal I_{S}(t) is received using two receivers tuned to ω_{1} and ω_{2} and that the output voltages from receivers 1 and 2 are V_{1 }and V_{2} respectively.
- It is assumed that the two receivers exhibit ideal frequency selectivity such that there is no crosstalk between ω_{1 }and ω_{2 }and therefore any additional voltages are generated by shot noise effects only.
- It is possible to just consider the time slot when a 1 bit (ω_{1}) is transmitted without losing generality.
…3
- We assume the local oscillator output power to be much higher than that of the incoming signal so that the total noise current is approximately equal.
- The noise output from receiver 2 can therefore be written as:
…4
- As an error occurs when V_{2} > V_{1}, then the probability of error P (e) is equivalent to the probability that V_{1 }− V_{2} < 0. Hence:
…5
- Changing the limits of the integration gives
…6
- Comparison with the definition for the complementary error function allows Eq. (6) to be written as
…7