pli- fied SO that only the terms in the first and the last instants of the interval remain. (9.76) where B is the lock loop bandwidth It derives a general result: better performances of the LO lock loop are achieved if it is possible to find a loop bandwidth sufficiently large to efficiently follow the lasers param- eters fluctuations but much smaller than the symbol rate. Next Generation Transmission Systems In the low penalty limit, we will assume that the error probability expression versus the SN does not change, thus the penalty can be evaluated evaluating the SN . We can always rotate the reference system in the quadrature space SO that the e1 axis is along the segment joining the two first neighbors we are considering. In this way, it is e2 e4 = e3 = 0 and the decision variable C, at the first order in the phase noise, has the fol- lowing form: (9.77) To evaluate the electrical SN we will neglect the additive noise with respect to the ASE contribution and all the terms of second order in the noise. Moreover we note that (9.78) due to the fact that Sw and PT-QL - are not uncorrelated and their product cannot be set to zero. Finally (9.79) The behavior of the SN in the presence of Phase noise for M-4QAM is plotted in Figure 9.46. Electrical signal to noise ratio (dB) 0.0012% 0.012% FIGURE 9.46 SN penalty due to phase noise for M-4QAM Decision distance (Pd2, dBm) in the approximation of small impairment. Telecommunication Networks The most striking feature of the curves representing the SN behavior is the presence of a clear plateau due to phase noise. When the plateau is reached, increasing the power does not change the SN due to the fact that the phase noise term also depends on the power. 9.3.5.2 Depolarization Penalty for Coherent Quadrature Receiver The working of the coherent quadrature system is based on the assumption that the evolu- tion of the signal polarization is linear SO that a linear estimate of the channel can com- pletely compensate the polarization rotation. If a nonlinear polarization evol