nder Demux Booster In line-amp Pre-amp Transmitted Received Optical power distribution along the link FIGURE 9.39 Architecture of the amplified system used to evaluate theoretical performances of the considered modulation formats at 100 Gbit/s. Telecommunication Networks We will not follow in detail all the calculations that are needed to arrive at the error prob- ability for each format/receiver. The methods are all explained in Chapter 6 SO that for the interested reader it should not be difficult to reconstruct the steps to arrive to the results. 9.3.4.1 M-QAM and M-4QAM with Quadrature Receiver First we will analyze the coherent quadrature homodyne receiver. In this case, as evident from Equation 9.35, the dominant noise term is the ASE compo- nent of the photocurrent that results amplified by the local oscillator. This term is linear in the ASE amplitude, thus resulting in a Gaussian white noise at electrical level. Since attenuations due to the receiver are experienced both by the signal and by the ASE noise, these do not appear in the error probability, at least as far as the ASE term is the dominant noise. Thus, the electrical signal to noise ratio SN E is given by (9.58) where the baseband has been assumed equal to the symbol rate. Using the approximation (9.56) with Y equal to the average number of first neighbors for the symbol rate and the bound (9.50), (9.59) is obtained where d is the normalized minimum distance of the constellation. From Equation 9.59 the importance of maximizing the constellation minimum distance is clearly seen. In Figure 9.40, the error probability is plotted for a multilevel M-QAM system using a quadrature receiver. Due to the rapid decrease of the minimum distance with the number of constellation points, the performances get rapidly worse increasing the number of lev- els. On the other hand, for a low number of levels, this is an effective modulation format. Bit error rate (log10(BER)) FIGURE 9.40 Plot of the ideal performance of M-QAM for various values of the number of level