## 3 Simulation Results
System performance cannot be usually enhanced by relaxing the bandwidth limitations. More powerful RX DSP options are needed. Comparing the VNLE and the SQRT + VNLE, we observe a non-negligible ODN loss gain of about 1 dB, at the cost of slightly increased complexity due to the SQRT. Moreover, in some cases the overall complexity can be reduced by introducing the SQRT. As shown in Figure 6a), in the 35 GHz to 40 GHz TX and RX bandwidth range representing commercially available 50G-O/E [23],the VNLE approach requires NL memory from 12 samples to 13 samples to achieve 29 dB maximum ODN loss, whereas a lower 9 samples to 11 samples NL memory is needed when combining the VNLE and the SQRT (see Figure 6b)). This reduction in NL memory can provide a significant improvement in RX DSP complexity in terms of MPS, which will be discussed later. When _NL memory_ = 20 samples is applied, the 29 dB maximum ODN loss can be reached even with 30 GHz TX and RX bandwidth, at the cost of a very high DSP complexity (which will be discussed later). It is typical in PON architectures that each served ONU is located at a different distance from the OLT. In Figure 7, we present the maximum ODN loss as a function of fiber link lengths \(L\) ranging from 5 km to 20 km, which is the typical reach range in PONs. TX and RX bandwidth is set to 37.5 GHz, a typical value for 50G-O/E devices [23]. In all cases, the normalized amplitude \(V_{PP,J}/V_{\pi}\) and the pre-compensated length \(L_{C}\) are optimized. For \(L\) = 5 km, the optimum \(L_{C}\) is 4 km and 4.5 km for the VNLE and the SQRT + VNLE, respectively. The optimum \(L_{C}\) is 9 km, 14 km, and 18 km for \(L\) equal to 10 km, 15 km, and 20 km, respectively. We select the VNLE _NL memory_ = 5 samples, 10 samples and 20 samples. The maximum ODN loss gain obtained by increasing the NL memory increases as the fiber length \(L\) increases. At very short distance, for example \(L\) = 5 km, the improvement is negligible due to the limited nonlinear distortions introduced by the fiber. To achieve 29 dB ODN loss, only _NL memory_ = 5 samples is required for \(L\) \(\leq\) 14 km, whereas _NL memory_ = 10 samples is required for \(L\) in the 15-20 km range. In PON solutions, the ONU is the most cost-sensitive element. Here we compare the complexity in terms of MPS of different RX DSP options, which are placed at the ONU side in the downstream transmission. The MPS of the SQRT, FFE, and DFE techniques can be calculated as described in [17]. For the VNLE, the MPS can be evaluated by using Equation (5) in [34]. In this paper, the order of VNLE is equal to 3, the linear memory is 121 samples, and the quadratic and cubic memory (NL memory) are equal to 5 samples, 10 samples, 15 samples or 20 samples. The complexity in terms of MPS of the different RX DSP used in the paper is summarized in Table 1. The least complex method that allows us to achieve 29 dB maximum ODN loss with 50G-O/E devices (indicated with an asterisk in Table 1) is the SQRT + VNLE with _NL memory_ = 10 samples, requiring 893 MPS. Small  
Figure 6: Maximum ODN loss at \(BER_{T}\) = 10\({}^{-2}\) as a function of TX/RX bandwidth and nonlinear memory of VLNE. The fiber length is \(L\) = 20 km: (**a**) VNLE; and (**b**) SQRT + VNLE. The light blue area is where ODN loss is above 29 dB, and the light grey area is where commercial 50G-O/E are considered. The VNLE NL memory = 0 is equivalent to RX DSP option SQRT + FFE + DFE. TOP is 11 dBm for SQRT + FFE + DFE and 15 dBm for all other RX DSP options. increments in NL memory (especially in cubic memory) can introduce a significant increase in complexity. Although VNLE is an effective RX DSP option to compensate for linear and nonlinear distortion, its complexity can be extremely high. The SQRT provides a marginal performance improvement but at the cost of a limited complexity enhancement by only 2 MPS. Thus, the SQRT can be used in combination with the VNLE to decrease the NL memory as well as maintain the desired system performance.