attain a given BER would increase. Telecommunication Networks Bit error rate log10(BER)) Electrical signal to noise ratio (dB) FIGURE 6.20 Ideal performance of a long-haul optical link for different values of the ratio between the bilateral optical bandwidth and two times the electrical bandwidth. The equation used to plot the BER curve is the approxima- tion reported in the text and where the approximation is not valid the curves are interrupted. From Figure 6.20 the value of SN when BER = 10-12 and the optical bandwidth is mini- mum (Moe=1) is a bit less than 17 dB. If a simple Gaussian model is used to evaluate the BER, but the noise variance is cor- rectly taken into account like in [2], the required SN to achieve a BER of 10-12 in this condi- tion is almost exactly 17 dB. Although this assumption underestimates a bit (about 0.5 dB) the system performance, the value of 17 dB is often assumed as a design reference and we will do the same in the examples of this chapter. Sometimes, in order to express penalties due to different transmission impairments, the so-called Q factor is used, not to be confused with the Q function. The Q factor is defined as 2=Q-1(BER) (6.66) This definition comes from Equation 6.14 and, if the BER would be given by the relation (Equation 6.14), there would be a direct relationship between the Q factor and the SNo. In our case Equation 6.14 does not hold, and the Q factor has to be evaluated via its definition and the correct expression of the error probability. If Equations 6.65a and 6.65b can be used, the relationship between the squared Q factor and the optical SN ratio is shown in Figure 6.21 for = 2. Up to now, we have assumed that all the amplifiers that are deployed along the line are equal, meaning that all the spans are equal. In real system installations this is not always true. Several times, DWDM systems are installed along the route of old systems where the points of presence where amplifiers can be installed are not equally spaced. In the presence of nonuniform spans, Equ