se of the required optical filter bandwidth. Next Generation Transmission Systems The SN, is inversely proportional to the optical bandwidth, thus it can seem that the impact of increasing the bit-rate by a factor 10 with respect to 10 Gbit/s reflects in the need of an SN0 10 dB greater. Even if this is a good first approximation, two effects could reduce the needed SN0 increase. First, the signal statistical distribution is not Gaussian. Second, and potentially more important, while in practice it is very difficult in a 10 Gbit/s system to maintain the optical bandwidth equal to the bit rate, it is much easier at 100 Gbit/s. Thus the extra optical noise power is greater at 10 Gbit/s. In order to verify the impact of the bit-rate increase on the needed SNo, let us use the cor- rect error probability model introduced for amplified systems in Chapter 6. Assuming that no pattern effect is present and that thermal noise at the receiver is neg- ligible with respect to the Amplified Spontaneous Emission (ASE) noise, the error prob- ability expression (6.65) relative to an intensity modulated system with in-line amplifiers simplifies as (9.1a) (9.1b) (compare Equations 6.65a and b) where Cth = YSN./Moe is the threshold value in terms of a fraction of the signal to noise ratio at the optical level is the ratio between the unilateral optical bandwidth and the electrical bandwidth (often approximated with the bit rate R) Moreover, the saddle point approximation has been further simplified assuming SN,>>Moe Naturally, for each value of SN the decision threshold (thus y) has to be optimized. To reflect the practical difficulty in implementing stable optical filters with a very small bandwidth, we will assume that at 10 Gbit/s, a filter with 60 GHz bandwidth (Moe = 6) is used, corresponding in wavelength to a bandwidth of about 0.5nm at 1.55 um. The filter band- width is increased at 120 GHz (1 nm) for the 40 (M  = 3 ) = and to 200 GHz at 100 Gbit/s (Moe = 2). Passing from = 6 to M = 3 to = 2 implies that the SNo correspondin