rmances H(t) is the pulse response of the electrical front end following the photodiode * represents convolution In the absence of any optical amplification, the noise is fully due to the sum of two terms: the shot noise and the receiver thermal noise [3]. However, in practical systems without amplifiers, the signal arrives on the photodiode with a great attenuation due to fiber prop- agation; thus, the shot noise is generally negligible with respect to the thermal noise. Assuming to have a photodiode based on a internal depletion zone (PIN), in Chapter 4 we have seen that, if the filter H(t) eliminates the low frequency 1/f noise contribution, ne(t) is a band-limited white Gaussian noise whose variance can be indicated with on At this point, a small part of the signal is baseband filtered SO to insulate only the carrier contribution and is sent to a phase lock loop (PLL) that maintains the sampler synchro- nized with the received signal. The sampler extracts a sample of the signal (6.10) at the center of the bit interval and compares it with a threshold. If the sample is higher than the threshold, the received bit is assumed to be a one, otherwise a zero. Calling Cth the threshold, two possible receivers do exist: fixed and adaptive threshold receivers. In the case of fixed threshold, Cth is set at the beginning of operation to an optimum value, while in adaptive one it is adapted over times much longer than the bit time to fol- low slow random fluctuations in the power of the received signals. If the received signal has a constant average power, the two receivers have the same per- formances, while this is not true in the presence of intensity noise. In any case, the BER of our much simplified system is BER=P(1/0)po+P(0/1)p = (6.11) where Po and P1 are the probabilities that a zero or a one is transmitted P(a/a') is the probability that a is detected when a' is transmitted Let us define the Q function as (6.12) where the asymptotic approximation holds for high values of X. The error probability can be expressed