## 2 Proposed Radio over Fiber Network
The waves explain in Equation (4) are interfered by HC with 50 MHz frequency [29], which output is given as  
\[N_{out}(t)=D[I(t)cos(2\pi f_{c}t+\omega_{c})- \tag{3}\] \[Q(t)sin(2\pi f_{c}t+\omega_{c})]+a\]  
Here electrical input signals are shown by \(I\) and \(Q\), \(D\) means gain of element, \(f_{c}\) is the carrier frequency and \(\omega_{c}\) is phase of the signal. To estimate the PAPRTs, considering liNb MZM transmission with \(n\) sub-carriers with frequencies (\(f_{i},i=1,2,...,n\)). The continuous time signal \(S(t)\) based on modulation interval \(T\) and \(nT\) duration of inter symbol interference (ISI) [30; 31; 32] is defined as  
\[S(t)=\frac{0\leq t<nT^{max}|\zeta(t)|^{2}}{E|\zeta(t)|^{2}} \tag{4}\]  
The parameter \(E[\zeta(t)]\) explains the expectation. The gain of electrical amplifier which suppress the high PAPRIs [33; 34; 35; 36] is measured as  
\[\frac{P_{out}}{P_{in}}=10^{b/10} \tag{5}\]  
The outcomes of Equation (7) are measured in \(dB\), which gives the amplifies electrical signals and is presented as  
\[E_{out}=E_{in}\surb b \tag{6}\]  
At the presence of PAPRIs and NLIs the power spectral density (PSD) function is induced and calculated as  
\[PSD=\surd P_{noise}.f_{s} \tag{7}\]  
Here \(P_{noise}\) means the noise power and \(f_{s}\) denotes the frequency grid spacing which is defined as  
\[f_{s}=\frac{R_{s}}{\psi_{s}} \tag{8}\]  
In order to transmit the RF signals over optical CN the laser source is needed. So, in this model CW optical laser source is used. The electric field intensity of CW laser is define as  
\[E_{1}=E_{0}e^{\beta 2\pi f_{c}t} \tag{9}\]  
From Equation (1) to Equation (10) the cosine of RF signal \(S(t)\) is calculated as  
Figure 2:0  
where \(V_{RF}\) shows the driving voltage of RF. The optical field at output of intensity modulatot (IM) is given as  
Figure 2:1where \(V_{DC}\) is the DC bias voltage and \(V_{\pi}\) explains the IM half wave voltage. Assuming \(\xi=\pi V_{RF}/V_{\pi}\) and \(\varpi=\pi V_{DC}/V_{\pi}\), which explain the modulation index and initial phase caused by \(V_{DC}\) of the IM respectively. From Equation (13) the \(E_{1}\) can be extended as  
Figure 2:2 \[ \begin{cases}cos\varpi[J_{0}(\xi)+2\Sigma_{i=1}^{\infty}(-1)^{i}J_ {2i}(\xi)cos(4i\pi f_{s}t)]\\ +sin\varpi[2\Sigma_{i=1}^{\infty}(-1)^{i}J_{2i-1}(\xi)cos(2i-1)2\pi f_{s}t] \end{cases}  \tag{12}\]  
Here \(J_{i}\) means the \(i\)th order of Bessel function. The transfer function of the transmitted signal is measured as  
\[H(f)= \begin{cases}\alpha&(|f|<f_{1})\\ \beta&(f_{1}\leq|f|<f_{2})\\ 0&f_{2}<|f|\end{cases}  \tag{13}\]  
where \(\beta\) is written as  
\[\beta=\sqrt{0.5\alpha^{2}.1}+cos((|f|-f_{1}/r_{p}.\delta).\pi) \tag{14}\]  
Here \(\alpha\) denotes insertion loss, \(r_{p}\) means roll of factor and \(f_{1},f_{2}\) are calculated as  
\[f_{1}=1-r_{p}f_{c}(0\leq r_{p}\leq 1) \tag{15}\]  
\[f_{2}=1+r_{p}f_{c}(0\leq r_{p}\leq 1) \tag{16}\]  
To describe, measuring the NLIs in the propagation of light wave in fiber are given below:  
\[i\partial A/\partial z-\beta_{2}(\partial^{2}A)/(\partial t^{2} )-i\beta_{3}\partial^{3}A)/(\partial t^{3})+\gamma|A|^{2}A\] \[=-i\alpha/2A. \tag{17}\]  
where complex term of electromagnetic field is defined by \(A\), \(z\) is the fiber distance, \(t\) is the time, \(\beta_{2}\) and \(\beta_{3}\) are the group velocity dispersion (GVD) and nonlinear dispersion, respectively. The term \(\gamma\) is used for nonlinear coefficient and \(\alpha\) means attenuation of the fiber. The nonlinear coefficient is further calculated as in terms of nonlinear refractive index \(n_{2}\) and carrier wavelength \(\lambda_{0}\).