## 3 Simulation Results  
In our simulation setup, shown in Figure 1, we varied the transceiver bandwidth up to 70 GHz and the VNLE NL memory from 0 to 20 samples. We started by showing the impact of the normalized peak-to-peak amplitude of the in-phase signal \(V_{PP,J}/V_{\pi}\) by optimizing \(V_{PP,J}\) for options VNLE and SQRT + VNLE. Figures 2-5 shows the system performance when \(L\) = 20 km and _TOP_ = 15 dBm, in terms of the maximum ODN loss as a function of TX  
Figure 1: Simulation setup of the proposed CD-DPC DD link, emulating a PON downstream transmission. Dispersion compensation blocks with different DSP options are indicated. and RX bandwidth and of the normalized amplitude \(V_{PP,J}/V_{\pi}\), for _NL memory_ = 5 samples, 10 samples, 15 samples and 20 samples, respectively. Note that the pre-compensated length \(L_{\text{C}}\) is optimized for each pair of the two parameters. The optimum \(L_{\text{C}}\) is slightly smaller than the fiber length \(L\), and the difference \(\Delta L\) between \(L\) and \(L_{\text{C}}\) increases with TOP. For instance, \(L_{\text{C}}\) is around 18 km when \(L\) = 20 km and \(TOP\) = 15 dBm. This phenomenon is due to the interaction between the fiber Kerr effect and the chromatic dispersion, as explained in [15; 31]. Figure 3: Maximum ODN loss at \(BER_{T}=10^{-2}\) as a function of TX and RX bandwidth and of the normalized peak-to-peak amplitude of the in-phase signal \(V_{PP,J}/V_{\pi}\) with _NL memory_ = 10 samples. The fiber length is \(L\) = 20 km. The transmitted optical power is \(TOP\) = 15 dBm: (**a**) VNLE; and (**b**) SQRT + VNLE. Figure 2: Maximum ODN loss at \(BER_{T}=10^{-2}\) as a function of TX and RX bandwidth and of the normalized peak-to-peak amplitude of the in-phase signal \(V_{PP,J}/V_{\pi}\) with _NL memory_ = 5 samples. The fiber length is \(L\) = 20 km. The transmitted optical power is \(TOP\) = 15 dBm: (**a**) VNLE; and (**b**) SQRT + VNLE. From Figures 2-5, we can observe that the optimum normalized amplitude \(V_{PP,I}/V_{\pi}\) is in the range 0.55-0.60, 0.70-0.90, 0.90-1.00 and 1.00-1.10 for the VNLE NL memory equal to 5 samples, 10 samples, 15 samples and 20 samples, respectively. The optimum normalized amplitude \(V_{PP,I}/V_{\pi}\) increases as the NL memory increases. This can be explained considering the effect of the optical modulation index (OMI) on the nonlinearities generated in the modulation process. The OMI can be used to find the optimum operation point (at which the highest modulation levels can be obtained without introducing additional distortions) [32]. Smaller \(V_{PP,I}/V_{\pi}\) results in lower nonlinearity of the modulation, but also into a lower modulation level. In contrast, larger \(V_{PP,I}/V_{\pi}\) can result in a higher modulation level but also in stronger nonlinear effects of the modulation. Therefore, it is very important to set the optimum driving signal amplitude by optimizing the normalized amplitude \(V_{PP,I}/V_{\pi}\). Without TX and RX bandwidth limitations and at the optimum \(V_{PP,I}/V_{\pi}\), when the VNLE is applied alone, the maximum ODN loss of about 26.1 dBm,  
Figure 4: Maximum ODN loss at \(BER_{T}\) = 10\({}^{-2}\) as a function of TX and RX bandwidth and of the normalized peak-to-peak amplitude of the in-phase signal \(V_{PP,I}/V_{\pi}\) with _NL memory_ = 15 samples. The fiber length is \(L\) = 20 km. The transmitted optical power is \(TOP\) = 15 dBm: (**a**) VNLE; and (**b**) SQRT + VNLE. Figure 5: Maximum ODN loss at \(BER_{T}\) = 10\({}^{-2}\) as a function of TX and RX bandwidth and of the normalized peak-to-peak amplitude of the in-phase signal \(V_{PP,I}/V_{\pi}\) with _NL memory_ = 20 samples. The fiber length is \(L\) = 20 km. The transmitted optical power is \(TOP\) = 15 dBm: (**a**) VNLE; and (**b**) SQRT + VNLE.