er quadratic detection, all the channel spectra superimpose in the electrical baseband. Indicating with Ho(t) the optical pulse response of the optical filter, the electrical field relative to channel k=0 after demul- tiplexing and, if needed, further optical filtering is given by (6.40) where Gk(t,c) represents the signal conveyed by the kth channel, whose expression can be easily deduced from Equation 6.33, in a first approximation the filtering effect of Ho(t) on the selected channel is neglected and Generally, for a well designed WDM system, only adjacent channels generate relevant linear interference; thus, the index k in Equation 6.40 can assume only the values -1 and 1. From Equation 6.40, the current after detection can be derived obtaining in the jth time slot: (6.41) where n(t) represents the global noise term, and a PIN receiver is assumed. From Figure 6.15 it is clear that the part of the spectrum of an adjacent channel entering the selection filter has to be small. In this condition, the 0-j beat term is quite bigger with respect to the j-j SO that this last term can be neglected. Optical spectrum (AU) Channel Channel Channel Optical filter FIGURE 6.15 Linear interference due to the overlap between adjacent chan- Angular frequency (AU) nel optical spectra. Telecommunication Networks Even with this simplification, the analysis of the linear interference impact is difficult due to the random nature of this effect. As a matter of fact, both the scalar product of the polarization vectors and the relative delay are slowly varying random variables. However, due to the slow variation, calculating their distribution and the related average BER can be misleading. As a matter of fact, the random variables related to polarization and delay can assume, for a long time, values near the worst case, thus heavily influencing the transmission of many bits. For these reasons, it makes sense to evaluate the worst case BER penalty. The worst situation is obtained when interfering channels carrying a "one" signal are syn