re complex model of Appendix D. Coherently, with this design approach we will consider the penalty, due to the various noise terms, that we are neglecting in a first time as penalties in the penalty analysis. Following the approach of Chapter 4, the gain of the Raman pumped DCF is given by (6.77) The parameters' meanings are as follows (see Equation 4.86): AD is the DCF attenuation. LD is the DCF length. P10 and P20 are the powers of the Raman pumps. 81 and g2 are the corresponding normalized spectral gains. LeD is the DCF effective length. The optimization consists in substituting in Equation 6.77 the expressions of the Raman local gain that depends on the wavelengths and power of the pumps and on the wave- length of the signal and evaluating the average and the standard deviation of the gain over the bandwidth occupied by the DWDM comb. In these two expressions, the power and the wavelengths of the pumps are considered variables, and the optimization is carried out by minimizing the gain standard deviation with the condition to maintain the average gain constant and equal to the value that is dictated from the system design. This optimization can be carried out both by numerical means and by the Lagrange mul- tipliers if an approximated analytical expression is found for the local Raman gain curve (see references in Chapter 4 for several papers on pumps optimization). The parameters we will use for the numeric optimization and for the following system performance evaluation are reported in Table 6.7, the parameters specific of Raman ampli- fiers are those reported in Table 4.11. Transmission Systems Architectures and Performances TABLE 6.7 Parameters of the Hybrid Amplified 10 Gbit/s Ultra-Long- Haul System General Channel speed 10 Gbit/s Optical bandwidth of the DWDM Extended C band Modulation RZ-25% duty cycle Number of channels Channel spacing 100 GHz Span length Transmitting Chain Source laser emitted power 16 dBm Mach Zehnder lithium niobate modulator loss Multiplexer (multistage AWG X 80) loss Patchcords,