 in terms of the Q function like (6.13) where c(1) and c(0) are the average currents corresponding to the transmission of the two bits. Equation 6.13 gives the expression of the BER in the very simplified case we have consid- ered up to now, but it is an important reference. The optimum threshold is the value of Cth that minimizes the error probability. Deriving Equation 6.13 with respect to Cth and equating Telecommunication Networks the derivative to zero it is obtained 2cth=c(1)+c(0) and substituting in Equation (6.13) the BER with the optimum threshold becomes (6.14) where On is the standard deviation of the noise term SN indicates the electrical signal to noise ratio In this ideal system, EOP P=c(1)-c(0) = SO that it is clear why a phenomenon affecting EOP causes a BER reduction. A realistic example of a phenomenon reducing EOP is a limited transmitter signal dynamic range. Ideally, for a given peak power, the BER is maximized for c(0) =0. In prac- tice, however, the signal zero level is not exactly zero, due to both the inability of the source laser to switch rapidly between the off and the on status and various phenomena like interference with other channels or pulse broadening during propagation that move energy into the bit periods in which a zero is transmitted. Thus, if the ideal SN = c2(1)/o? in practice, it is SN = [c(1)-c(0)]2/0", with c(0) 0. The corresponding optical penalty due to the reduction of the dynamic range can be obtained by passing in logarithmic units SO that SN (dB) 20log10[c(1)-c(0)]-20log10 (6.15) taking into account that c(1) >> c(0) is needed to assure system working, it can be written SN (dB) = (6.16) Thus, the expression of the logarithmic power penalty due to the reduction of the trans- mitter dynamic range is (6.17) 6.2.3 Analysis of a Realistic Single-Channel IM-DD System The hypotheses that produce Equation 6.14 generally are not fulfilled by a realistic system, due to different reasons. First of all, transmission through the line is not ideal; dispersion and nonlinear effec