## 3 Simulation Results
29.1 dBm, 31.0 dBm, and 31.7 dBm can be reached for _NL memory_ = 5 samples, 10 samples, 15 samples and 20 samples, respectively; when SQRT + VNLE is applied, the maximum ODN loss of about 26.6 dBm, 30.0 dBm, 31.7 dBm, and 32.0 dBm can be reached for _NL memory_ = 5 samples, 10 samples, 15 samples and 20 samples, respectively. The VNLE can provide up to 3 dB improvement for every five samples additional NL memory, while the SQRT can provide about 0.5-1.0 dB improvement compared to the VNLE only option. However, the complexity of the VNLE is much higher than that of the SQRT (the complexity will be discussed and analyzed in detail in the following section). It is a trade-off between the system performance and the complexity of RX DSP options. In addition to the modulation nonlinear effect and the fiber Kerr nonlinear effect, the nonlinear effect in the electrical domain caused by chromatic dispersion after the modulus square operation of DD (DD is inherently nonlinear due to the square-law detection) can be mitigated by using the SQRT as shown in [30]. By comparing Figures 2-5, we can also notice that the optimum normalized amplitude \(V_{PP,I}/V_{\pi}\) of the option SQRT + VNLE is slightly larger than that of the VNLE method (with the same NL memory). Therefore, a higher OMI can be set using VNLE with high NL memory combined with the SQRT, which allows to compensate for stronger nonlinear distortion. Figure 6 shows the maximum ODN loss as a function of TX and RX bandwidth and of the VNLE NL memory at the optimum normalized amplitude \(V_{PP,I}/V_{\pi}\), for 20 km SMF. On the x-axis, the VNLE _NL memory_ equal to 0 corresponds to the SQRT + FFE + DFE technique used in the receiver DSP. This option, which does not include the VNLE, is used as the lowest complexity reference case. Note that, in all cases, the transmitted optical power, the normalized amplitude \(V_{PP,I}/V_{\pi}\) and the pre-compensated length \(L_{\text{C}}\) are optimized. The optimum _TOP_ is 11 dBm and 15 dBm for the SQRT + FFE + DFE and VNLE techniques, respectively. We limit our analysis to TOP = 15 dBm as higher transmitted power levels are unrealistic in PON applications. The optimum \(L_{\text{C}}\) is 19 km for SQRT + FFE + DFE (with 11 dBm TOP) and 18 km for the VNLE (with 15 dBm TOP). The optimum \(L_{\text{C}}\) decreases as TOP increases. This is related to the fact that a higher transmitted optical power results in a higher fiber nonlinear interference [33], which partially counteracts CD due to interaction between the CD and the Kerr effect [15; 31]. At the very demanding 200 Gbps rate, the system performance is very poor (maximum ODN loss <23 dB) when strong TX and RX bandwidth limitations are present (i.e., \(\leq\)25 GHz) even when using the most complex DSP approach (VNLE + SQRT with _NL memory_ = 20 samples). For SQRT + FFE + DFE (i.e., _NL memory_ = 0), the largest maximum ODN loss is only about 25 dB even if using very high 70 GHz TX and RX bandwidth. Therefore, this simple DSP solution is not enough to meet the ODN loss requirement with PAM-8 200 Gbps transmission. By using the VNLE, both alone and in combination with the SQRT, a considerable gain can be obtained when we increase the NL memory. As shown in Figures 2-6, about 3 dB, 5 dB and 6 dB maximum ODN loss increase can be obtained when the NL memory is increased from 5 samples to 10 samples, 15 samples and 20 samples, respectively. The trend shows that the improvement would be very limited by further increasing the NL memory above 20 samples. This means that almost all the fiber nonlinear interference is compensated for by the VNLE. About a 3 dB gain in terms of maximum ODN loss can be obtained by relaxing the TX and RX bandwidth limitation from 30 GHz to 50 GHz, with the same NL memory. As shown in Figure 6, for a fixed NL memory value, the improvement is more evident when increasing the TX and RX bandwidth from 30 to 40 GHz. When the TX and RX bandwidth are above 50 GHz, only very limited improvement can be obtained when TX and RX bandwidth are increased.