## 4 BER Performance Analysis  
Direct detection for transmission at 10 Gb/s of 32 OOK-NRZ signals spaced at 50 GHz is considered. For BER performance analysis the impulse response used for pulse shaping was chosen with a rise and fall time of 35% the bit duration. As is known, the effect of filtering operations performed by a certain TX-RX pair on the input signal and the resulting distortions can be estimated by means of the eye diagram [15]. In order to evaluate the distortions introduced by optical filtering, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \(\Delta\)_T_ & \(<\)_IL\(>\)_ & \(IL_{m}\) & \(IL_{M}\) & \(B_{m}\) & \(B_{M}\) & \(X_{A}\) & \(X_{NA}\) & \(X_{FL}\) \\
**[\({}^{\circ}\)C]** & **[dB]** & **[dB]** & **[dB]** & **[GHz]** & **[GHz]** & **[dB]** & **[dB]** & **[dB]** \\ \hline
0 & \(-15.8\) & \(-15\) & \(-17.6\) & \(10.4\) & \(20.1\) & \(-14\) & \(-20.8\) & \(-29\) \\ \(\pm 0.5\) & \(-15.9\) & \(-15.3\) & \(-17.8\) & \(11.9\) & \(19.8\) & \(-12.7\) & \(-19.7\) & \(-29\) \\ \(\pm 1.0\) & \(-16.2\) & \(-16\) & \(-18.4\) & \(11.6\) & \(20.1\) & \(-12.2\) & \(-20.4\) & \(-27\) \\ \(\pm 1.5\) & \(-16.5\) & \(-15.3\) & \(-21.6\) & \(10.7\) & \(20.3\) & \(-11.6\) & \(-15.7\) & \(-23\) \\ \hline \end{tabular}
\end{table} 
Table 3: Resonance frequency drifting, 32_@50 GHz. we consider the case where the detected signal is dominated by the photo-detector thermal noise. Under this assumption the \(Q\) factor can be calculated from the eye diagram as:  
\[Q=\frac{\mu_{1}-\mu_{0}}{\sigma_{1}+\sigma_{0}} \tag{1}\]  
where \(\mu_{1}\) and \(\mu_{0}\) are the average voltages associated to the levels 1 and 0 at the eye center, respectively, while \(\sigma_{1}\) and \(\sigma_{0}\) are the effective standard deviations associated to the levels 1 and 0, respectively. The \(Q\) factor allows for estimating the BER associated to the received signal after its conversion into the electrical domain by using the formula:  
\[\mathrm{BER}=\frac{1}{2}\,\mathrm{erfc}\left(\frac{Q}{\sqrt{2}}\right) \tag{2}\]  
Each signal transmitted at a specific wavelength has been filtered by the PSC transfer function and then selected by the corresponding RSC transfer function. The eye diagram has been evaluated for each of the transfer functions resulting from all the TX-RX pair combinations. Figure 8 shows the best, the worse and the average BER performance versus the electrical Signal-to-Noise Ratio (SNR) obtained considering the case of roundtrip loss \(\alpha=0\). The electrical SNR is given by the ratio of the signal power and noise power after electrical filtering with the same bandwidth as that of the RSC. As a reference, in the Figure, the BER performance obtained in the ideal case, _i.e._, without signal distortions, is also reported. From the curves we observe that the SNR loss of the average case with respect to that without (w/o) distortions varies between 6 dB, at \(\mathrm{BER}=10^{-2}\), and 8 dB, at \(\mathrm{BER}=10^{-10}\). In the same range of BERs, the SNR loss of the best channel with respect to that w/o distortions is comprised between 3.5 and 4 dB. The SNR gap between the best and the worse performance associated to channel #10 and channel #7, respectively, varies between 4 dB, at \(\mathrm{BER}=10^{-2}\), and 5 dB, at \(\mathrm{BER}=10^{-10}\). **Figure 8.** BER _vs._ SNR for transmission at 10 Gb/s of NRZ-OOK channels with roundtrip loss \(\alpha=0\). The best performance was obtained for channel #10, the worse for channel #7 and the average considering the mean over the 32 channels. Figure 9 reports the best and the worst performance associated to channel #10 and channel #7, respectivily, for increasing values of the roundtrip loss \(\alpha=0\), 0.2, 0.4, 0.6, 0.8, 1. From the figure we observe that for a given value of \(\alpha\) the SNR gap between the best and the worse channel is approximately always the same. Moreover, an SNR loss of approximately 5 dB can be observed between \(\alpha=0\) and \(a=1\).