# Nonlinear Effect and MAI Impact on SAC-OCDMA System Based on 2D Multi-Diagonal Code and Laser Array
## 5 Results and Discussion
### Second Scenario: With Considering MAI Effect
As a conclusion, the raising of the bit rate and the increasing of the number of users (i.e., increasing the MAI) and the nonlinear effects (by decreasing the fiber mode effective area) are the most important causes of 2D-MD SAC-OCDMA system performance degradation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Linear Effects**} & \multicolumn{2}{c}{**Nonlinear Effects**} & \multirow{2}{*}{**Linear Effects**} \\  & **(A\({}_{\text{eff}}\) = 93 \(\upmu\)m\({}^{2}\))** & **(A\({}_{\text{eff}}\) = 23 \(\upmu\)m\({}^{2}\))** & **(A\({}_{\text{eff}}\) = 23 \(\upmu\)m\({}^{2}\))** \\ \hline User 1 & 31.3 & 29.9 & 31.7 \\ User 2 & 26.7 & 26.5 & 27.6 \\ User 3 & 21.1 & 20.8 & 21.4 \\ User 4 & 17.2 & 16.9 & 17.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Q-factor (dB) for the four users. Figure 7: Received electrical eye diagrams: (a) for user 1; (b) for user 2; (c) for user 3; (d) for user 4. The bit rate is 5 Gb/s per user and the transmission is over 50 km of SMF. To show the maximum number of allowed users permitted by the system as function of the bit rate, Figure 8 represents the variation of the bit rate per user versus the number of users. According to Figure 8, the maximum number of the allowed users is equal to 16, 8 and 4 at a BER value equal to \(10^{-9}\) and operating at 1.25 Gb/s, 2.5 Gb/s and 5 Gb/s per user, respectively. Furthermore, a trade-off is observed between the raising of the bit rate and the decreasing of the number of the allowed users. In order to show the add value of our proposed system compared to the literature, Table 6 makes a fair comparison of the different SAC-OCDMA systems in PON configuration in terms of coding scheme, cardinality (i.e., number of users supported in the system setup), performance measured metrics, supported bit rate per user and transmission reach. As shown from Table 6, various OCDMA coding schemes are proposed by researchers for SAC-OCDMA based on coherent sources such as 1D random diagonal (1D-RD) codes [18], 1D-BIBD codes [19] and 1D-MD codes [20; 21]. As depicted in Table 6, the proposed 2D-MD SAC-OCDMA system for LR-PON outperforms alternate proposals in literature in terms of the aggregate bit rate (i.e., 20 Gb/s) and transmission reach up to 50 km over SMF link, while maintaining a high-performance measured metrics via a Q-factor greater than 15.5 dB. As a conclusion, our proposed 2D-MD SAC-OCDMA system is well suited for LR-PON and can be a potential candidate for granting access network with high system performance and high security. In addition, it is known \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**System**} & **Coding** & **Cardinality for** & **Performance** & **Aggregate Bit** \\  & **Scheme** & **System Setup** & **Measured Metrics** & **Rate** \\ \hline
1D-RD with multi-laser source [18] & 1D-RD & 2 & BER \(<10^{-9}\) & 10 Gb/s \\
1D-BIBD with multi-laser source [19] & 1D-BIBD & 12 & BER \(\leq 10^{-12}\) & 1.25 Gb/s \\ SAC-OCDMA with 1D-MD codes [20] & 1D-MD & 5 & BER \(<10^{-9}\) & 10 Gb/s \\
1D-MD with multi-array laser [21] & 1D-MD & 7 & BER \(<10^{-9}\) & 12 Gb/s \\
**2D-MD SAC-OCDMA for LR-PON 1** & **2D-MD** & **4/8/16** & **Q-factor \(\geq\)15.5 dB** & **20 Gb/s** \\ \hline \hline \end{tabular}  
* Our proposed system.  
\end{table} 
Table 6: Comparison of SAC-OCDMA systems based on coherent source. Figure 8: Bit rate versus the number of simultaneous users. that SAC-OCDMA system provides the integrity security component inherited from the OCDMA features. In fact, without knowing the 2D-MD coding scheme it is impossible for any eavesdropper to decode the user's signal and make any unauthorized change.