## 4 Back-to-Back and Propagation Results and Discussion  
The results of the proposed LDOTN were evaluated based on analytical calculations as discussed in Section 2, which are elaborated in Figure 7. The proposed LDOTNs model mentioned in Figures 4 and 5 were analyzed in terms of a back-to-back framework and propagation set up to show the initial and secondary outcomes' behavior. Figures 8-10 describe the back-to-back optical transmission network (OTN) performance using NMI and OSNR estimating elements. The results explain that no NLPns sources ever existed in the back-to-back OTN structure. The generated NLPns are fully recovered with the help of the carrier phase estimation (CPE) at the receiver end. The threshold of NMI estimations is declared to be 0.9, presented as the dotted line in Figures 8-10. The DP-64 QAM back-to-back setup penalties are recorded as less than the DP-16 QAM back-to-back framework. The performance calculations of the proposed model using a different transmission reach as a function of input power per channel are depicted in Figure 11. In opposition to a back-to-back structure, NLPns factors have a strong impact on various transmission-covered paths. From \(-10\) to 2 dBm per channel, input powers are applied to the proposed LDOTN with a divergent 100-500 km transmission reach. The results' analysis finds that the proposed technique for deducing NLPns factors yields efficient estimations compared to when not using the NLPns recovery procedure. Figure 12 expresses the graphical analysis of the presented LDOTN in terms of the number of spans and NMI for DP-16 QAM including AWGN, DP-64 QAM involving AWGN and the used procedure for optimizing the NLPns at a 500 km transmission reach. Multiple spans of SMF (G-652.D and G-657.A1) are applied, whose elements are listed in Table 2. The investigations correlate with and without using the NLPns-aware technique with the 5 bit/symbol entropy. The losses in data transmission resulting from NLPns are optimized by installing the proposed soft detecting mechanism. The inputs propagation over long spans is evaluated for conventional 16/64 QAM modulation formats, as shown in Figure 13. Figure 13 contains information based on the AWGN gap in dB against OSNR, which declares that the AWGN gap is high in conventional enabled LDOTNs as related to the proposed LDOTN. In order to review the continuity of proposed soft detecting-enabled LDOTNs, the simulation model is evaluated, using OSNR as a function of NMI, as presented in Figure 14. The DP-16/64 QAM received information is transformed over universal DSP followed by a soft decoding decision block. The decision block comprises the prominent steps (DC blocking, normalizing, optimization, gray coding and differential coding) which modify system consequences against NLPns. Figure 14 clarifies that the information at the reaching side is not justified without applying the soft detecting mechanism. Figure 15 declares the analysis of input and received powers for the AWGN channel and NLPns-aware-based DP-64 QAM channel. This shows that acceptable received power is gained with minimum input power compared to the AWGN-based channel. The experimental analysis of the proposed model are compared between with and without compensation of nonlinearities as presented in Figure 16, which declares that the system performances are reduced by reason of nonlinearities. Figure 16 also depicts the correlation among 25 and 50 GHz channels for different input powers, this explains that the impact of nonlinearities is higher in less channel spacing transmitted optical signals. Figure 17 shows the relation between DP-16 QAM and DP-64 QAM modulation