Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 10

Recall from Eq. (7.13) that the bit-error rate (BER) can be given in terms of a Q factor, where, from Eq. (7.14),
When thermal noise is dominant, we have . However, for an EDFA the existence of signal-ASE beat noise produces the condition . In this case, from Eq. (11.30),
and
Noting that the receiver sensitivity P R is half the signal power of a transmitted 1 bit for a uniform distribution of ones and zeros (i.e., P s = 2 P R ), show that in terms of the Q factor the receiver sensitivity is
where F is the noise figure given by Eq. (11.35).