ability at least when only the dominant ASE noise is present. Assuming that no pattern effect is present and that thermal noise at the receiver is neg- ligible with respect to the ASE noise, the error probability expression (6.64) relative to an intensity modulated systems with in line amplifiers simplifies as (6.65a) [1+X(SN,)]2Moo X(SNo) = (6.65b) where The value of the threshold in terms of a fraction of the signal to noise ratio at the optical level is given by Cth=ySN,/Moer is the ratio between the optical and the electrical bandwidth Moreover, the saddle point approximation has been further simplified assuming a high SN ratio situation and SN,>>Moe (such a simplified approximation is also called Chernov bound). This approximation is quite accurate for low values of approximately up to M = 5 if we look below a BER of X 10-4 and up to 3 if we look to a BER below 10-12. Often in practical systems the target pre-FEC BER is on the order of 10-4 and the value of is below 3; thus, this is a good approximation. Out of these intervals, in particular for systems with a large value of and a strong FEC SO that the BER pre-FEC is very low, the complete saddle point approximation has to be used, that is much more accurate but produces an optimization equation whose solu- tion has to be found numerically. Naturally, to evaluate the BER, for each value of SNo, the decision threshold (thus y) has to be optimized. The BER curves obtained by Equations 6.65a and 6.65b are plotted for reference in Figure 6.20 versus SN If a plot versus SN, is deduced, it can be noted that increasing Moer the BER seems to be better and better, against intuition. In reality this is not true, since it is not to forget that increasing a certain value of the optical SN ratio is more and more difficult to attain due to the increase of the optical bandwidth. If this effect is evaluated it is discovered that it largely overcomes the slight decrease of the BER with Moer SO that if a plot versus the received power is done, increasing the power needed to 