## 3 Analytical Model  
In Section 2, the proposed model is described based on a block diagram and system model used for the simulation work. This section discusses the basic theoretical model of the proposed work for 100 Gbps (and above) optical fiber communication network system with including nonlinear issues. The effect of nonlinearities due to the fiber transmission and their mitigation using the proposed receiver are explained, as follows: The output of the laser source is given by [18; 19; 20]  
\[F_{o}=F_{i}^{juct} \tag{1}\]  
\[E_{o}=E_{i}/2[e^{(i\pi v_{1}(t))/v_{\pi}}+\gamma e^{((i\pi v_{2}(t)+v_{bias})/v _{\pi})})] \tag{2}\]  
The optical fields are modulated by modulator using the pulses that are induced by the medium, explained below as [16]  
The \(V_{1}\) and \(V_{2}\) are given as  
\[V_{1}=-V_{2}=(P(t))/2 \tag{3}\]  
The variables used in the above equations are input optical field denoted by \(E_{i}\), \(V_{\pi}\) shows the magnitude of the modulator, bias of the modulator circuit explored by \(V_{bias}\), \(V_{1}\) and \(V_{2}\) explain the electrical pulses voltage, \(F_{i}^{juct}\) denotes the laser output and coefficient of the refractive index denoted by \(\gamma\). Mathematical explanation of the \(\gamma\) is presented by Equation (4) [21]  
\[\gamma=(\pi N_{2})/(\lambda A_{e}C) \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subsystem** & **Component** & **Parameter** & **Value** \\ \hline Transmitter & CW laser & frequency & 193.1 THz with 25 and 50 GHz \\  & Linewidth & frequency & 1 MHz \\  & Total Power & Launch power & 6 dBm \\  & MZM & Insertion Loss & 5 dB \\  & MZM & Half-wave RF voltage & 5 V \\  & (V\(\pi\)) & (V\(\pi\)) & 32 \\  & Channel & Quantity & 32 \\  & Pulse generator & NRZ & aggregate 100 Gbps \\  & WDM Mux/DeMux & Insertion loss & 3 dB \\  & 25/50 GHz spacing filter & Optical bandpass & 5 GHz \\  & & bandwidth & \\ \hline Optical link & Fiber & Transmission Length & 300 km \\  & & Attenuation & 0.2 dB/km \\  & & Reference wavelength & 1553 nm \\  & & \(\beta_{2}\) & \(-18\) ps\({}^{2}\)/km \\  & & \(\beta_{3}\) & \(-3\) ps\({}^{3}\)/km \\  & & Nonlinear refractive & \(2.6\times 10^{-17}\) m\({}^{2}\)/W \\  & Amplifier & EDFA Gain & 30 dB \\  & Impairments & Dispersion & 17 ps/nm \\  & Filter & Optical Filter order & 8 \\ \hline Receiver & Photo-detector & Responsivity & 1 A/W \\  & Low pass filter & Cutoff frequency & 0.75\(\times\) bit rate Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used at the transmitter end. Here \(N_{2}\), \(A_{e}\), \(\lambda\), and \(C\) denote non-linear regime of the compensating fiber, effective area of the transmitting fiber, wavelength, and weighing constant, respectively. The generalize model of the Schrodinger equation can be written as [17,22]  
\[\partial U/\partial Z+\alpha/2U-\sum_{(i\geq 2)}n^{(i+1)/i}\beta_{i}( \partial^{i}U)/(nT_{i})=\] \[n\gamma(1+n\tau_{i}\partial U/\partial T) \tag{5}\]  
where \(U\) is the complex magnitude of the electric field, \(T\) define the retarded time, \(\alpha\) is the fiber impairments, and \(\beta_{i}\) is the linear and nonlinear dispersive term with function of \(z\). The \(\beta_{2}\) presents linear term, while \(\beta_{3}\) denotes nonlinear dispersion. The induced polarization by electric dipoles is given by [23,24]  
\[p=\varepsilon_{0}(x^{n}E_{n}) \tag{6}\]  
The parameter \(\varepsilon_{0}\) is permittivity of free space and equal to \(8.85\times 10^{-12}\)F/m, \(x^{n}\) explains order of susceptibility and n is equal to 1, 2, 3,... \(N\). The final element \(E_{n}\) denotes the electric field. Initial term of the nonlinearity starts from \(x^{3}\) and it is called as third order susceptibility, which concludes that both nonlinearity and order of susceptibility can be mitigated by a simple estimation of the third order nonlinear transfer function. The relation of the number of channel, \(N\), with these parameter is expressed [21,22], as follows.