D), besides the thermal noise contri- bution (Equation 6.28), the APD introduces a so-called excess noise due to the intrinsic random nature of the avalanche gain (see Chapter 5). The excess noise is generally represented as a sort of shot noise amplification, SO that Equation 6.27 can be modified as follows: (6.29) where Gm is the avalanche gain FA is the excess noise factor, that is a function of the ionization ratio ri (see Chapter 5) and can be written as Telecommunication Networks (6.30) Besides multiplication noise, when using an APD, one has to take into account that also the dark current noise is amplified by the avalanche mechanism. In order to give a correct expression of the amplified dark current noise, one has to take into account that dark current can be divided into two components, depending on the physical phenomenon generating it. There is a bulk dark current and a surface leakage dark current; the first is really ampli- fied by the APD, the second does not undergo amplification due to the fact that it is a surface phenomenon. Thus, indicating with Sbd and Ssd the spectral densities of the two components, the final APD dark current power in the detector bandwidth will be (6.31) 6.2.3.5 Performance Evaluation of an Unrepeated IM-DD System At this point, we have all the elements to evaluate the BER for an IM-DD system, at least in the hypothesis that the receiver signal processing (i.e., baseband filtering and clock recov- ery) can be assumed perfect. Since dispersion involves nearby bits, we need to start from the consideration of the eight pattern of 3 bits that we have called Pk (k = 1, 2, ... 8). The current corresponding to a certain pattern after detection and front-end amplifica- tion can be written as (6.32) where ny(t) collects all the receiver related noise terms: thermal noise, excess thermal noise, and dark current noise and the diode gain Gm has to be set to 1 for a PIN. Due to the presence of the shot noise term, the statistical distribution of the photocurrent now is not Gaussian. Ho