## 3 Proposed LDOTNs Model  
Dual-polarization 16- and 64-QAM (DP-16/64 QAM) modulation methodologies were developed and applied for treating NLpns using soft decoding-based DSP techniques. The presented framework is expressed in Figure 4, which uses low-dispersion G-652.D and G-657.A1 single-mode fibers (SMF). Long-distance communications with a high data rate, huge bandwidth capacity and multichannel transmission generate strong short autocorrelation NLpns, the impacts of which are investigated using time-domain pulse collision theory [36]. Continuous wave laser is installed as a light source with 1550 nm, 65,536 sequence length, 112 Gb/s data rate, 14 Gsymbol/s and 100 Guard bits. The bits are randomly generated for transmitting and analyzing the suggested scheme. Differential coding is applied before attaining the optical DP = 16/64 QAM waves. After achieving the optical DP-16/64 QAM signals, including a \(-25\) to \(-30\) dBm sensitivity rate, the optical pulses are passed over an optical amplifier (OA) for decreasing the aliasing from transmitting  
Figure 3: Constellation-diagrams: (**a**) CS at 0.35 variance and \(-60\) NLpns; and (**b**) CS at 0.35l, variance and \(-70\) NLpns. Figure 2: The 16-QAM for estimating the probability of CS. data. The noise figure and gain of OA are determined as 4 dB and 16 dB, respectively. The filtered optical signals are then propagated over the international telecommunication union-telecommunication (ITU-T) standard (G-652.D and G-657.A1) SMF with several spans. The rectangular optical filter (ROF) is used at the end of SMF in order to minimize the effects of NLPns from the received optical waves. ROF has attained a successfully rectangular filter shape with precise digital feedback compensation and nonlinearity management. The filter bandwidth could be tuned from 50 MHz to 4 GHz. Compared with the sweeping pump-based method in [37], our approach could more precisely control the filter shape by controlling the amplitude and initial phase of each electrical comb line. The optical signals are received by employing a photo-detector using dark current (10 nA), responsivity (1 A/W) and thermal power density (100 \(\times\) 10 \({}^{-24}\) W/m\({}^{3}\)). On the receiver side, the signal is purified from the NLPns and other dispersion losses including that of amplified spontaneous emission (ASE) with the help of the proposed DSP and soft detecting-based decision block. The decision block comprises DC blocking, normalizing, optimizing decision, gray code and differential coding that mitigate the NLPns effects from LDOTNs; furthermore, the presented model performance is evaluated, applying the electrical constellation visualizer (ECV) and bit error rate (BER). The inner propagation steps of the installed DSP, aiming to minimize the influences of NLPns in LDOTNs, is mentioned in Figure 5, which contains all the prominent stages for refining the collected information. Adding to the internal structure of DSP, the DSP is formed from 24 taps slightly spaced by least mean square (LMS). The LMS adaptive equalizer is followed by a pilot-aided blind phase search-maximum likelihood (BPS-ML) phase recovery. The internal procedure of the proposed LMS adaptive equalizer is mentioned in Figure 6, wherein the input signals are transformed into an independent \(N\) number of tap filters. The outputs of the tap filters are estimated as  
\[ \begin{bmatrix}FIR_{outx}\\ FIR_{outy}\end{bmatrix} =e^{j\theta(t)} \begin{bmatrix}j_{xx}(t)&j_{xy}(t)\\ j_{yx}(t)&j_{yy}(t)\end{bmatrix}\begin{bmatrix}s_{x}\\ s_{y}\end{bmatrix}  \tag{12}\]  
where \(FIR_{outx}\) and \(FIR_{outy}\) represent the FIR filter outputs, \(s_{x}\) and \(s_{y}\) are the two transmitted polarization signals and \(j(t)\) denotes the Jones matrix. Tables 1 and 2 summarize the list of parameters, selected for valuing the proposed work and obtaining the entropy. Figure 4: Dual-polarization 16/64-QAM-based proposed model for evaluating NLPns in LDOTNs. Figure 5: Proposed DSP structure for minimizing the impact of NLPns in LDOTNs.