# Nonlinear Effect and MAI Impact on SAC-OCDMA System Based on 2D Multi-Diagonal Code and Laser Array
## 5 Results and Discussion
### First Scenario: Without Considering MAI Effects
#### 5.1.2 Q-Factor versus Effective Area  
Figure 4 presents the SAC-OCDMA system performance versus the effective area (Aeff) in the range of (13-93) \(\upmu\)m\({}^{2}\) while increasing the bit rate and taking into account the second order dispersion (\(\beta\)2), the third order dispersion (\(\beta\)3) and the nonlinear coefficient  
Figure 3: SAC-OCDMA system performance versus bit rate.  
(\(\gamma\)). The optical launch power was fixed to \(-3.4\) dBm per user to facilitate isolating the effect of changing the effective area of the optical fiber. The numerical simulations can tolerate a maximum nonlinear phase shift of 10 mrad prior to updating the step-size of the fiber propagator.  
As depicted in Figure 4, at 30 Gb/s per user, the SAC-OCDMA system based on 2D-MD codes can tolerate the effects of second and third order dispersion and results in a Q-factor above the Q-limit with an average of 7 dB margin across all values of Aeff. However, above 40 Gb/s the second and third order dispersion become dominant leading to a degradation of the system performance while increasing the effective area. From Equation (16), the effective area of the SMF is inversely proportional to the nonlinear coefficient. Since the effective area decreases the nonlinear effect increases leading to the degradation of the system performance. When the effective area is considered and through increasing the bit rate from 30 Gb/s to 40 Gb/s, a degradation of the system performance of 5.3 dB, 5.2 dB and 5.1 dB is observed in terms of Q-factor at 93 \(\upmu\)m\({}^{2}\), 63 \(\upmu\)m\({}^{2}\) and 33 \(\upmu\)m\({}^{2}\), respectively. In addition, while increasing the bit rate from 40 Gb/s to 50 Gb/s a degradation of system performance of 7.2 dB, 7.2 dB and 7.1 dB is observed at 93 \(\upmu\)m\({}^{2}\), 63 \(\upmu\)m\({}^{2}\) and 33 \(\upmu\)m\({}^{2}\), respectively. As a result, the nonlinear effects with a high bit rate above 40 Gb/s led to a marginal performance degradation in the proposed SAC-OCDMA system. Therefore, the nonlinear effects seem to have insignificant effects on the Q-factor values unless the bit rate is relatively low (i.e., 30 Gb/s). This in fact can be explained in terms of the interplay between fiber dispersion and nonlinearity. At higher bit rates, pulse durations are shorter and thus experience the onset of fiber dispersion more rapidly resulting in pulse broadening and overlapping in time. Consequently, the induced nonlinear phase noise is largest when the signal is slow to evolve during propagation in dispersion managed systems. Furthermore, the results in Figure 4, show that the use of Large Effective Area Fibers (LEAF) in dispersion managed systems offer marginal improvement in system performance. It is worth noting that our computer simulator tool utilizes the so called \"total field model\", which merges all channels into a single optical field and propagated it through a single scaler version of Equation (14). Inherently, the effects of four wave mixing (FWM) is also modelled through this approach. The effect of FWM is reduced with the presence of chromatic dispersion as the propagating user channels become decoherent with reduced phase matching. As FWM does not depend on bit rate, the results in Figure 4 illustrate that SPM is indeed the predominant nonlinear distortion.  
Figure 4: SAC-OCDMA system performance versus effective area.