## 3 C/N Penalty of RoF Link  
The DPF of the RoF link can be seen through the carrier-to-noise (C/N) penalty curve. The C/N penalty in this paper is defined by the ratio between RF power received at distance \(L\) or \(P_{rec}(L)\) compared to the output power at MZM modulator, and it has distance \(L=0\) or \(P_{rec}(L=0)\). The difference value between Prec (\(L\)) and Prec (\(L=0\)) occurs because of the relative phase difference between sideband and carrier. Therefore, the noise term is the phase noise. Moreover, the C/N penalty was also introduced by [32; 33; 34]. To calculate the C/N penalty of the RoF link, it is necessary to initially model and derive the \(P_{rec}(L)\) value. The RoF link model that uses DD-MZM with CA as the E/O converter can be seen in Figure 1. The RoF link consists of DD-MZM with CA as the E/O converter, a dispersive optical fiber with \(H(f)\) response and photodetector (PD) as the O/E converter. To simplify the analysis, Equation (19) can be rewritten as  
\[E_{TX}(t)=A_{c}e^{j2\pi f_{c}t}+\sum\limits_{n=1}^{\infty}\left\{A_{ln}e^{j2 \pi(f_{c}-nf_{m})t}+A_{un}e^{j2\pi(f_{c}+nf_{m})t}\right\} \tag{20}\]  
where  
\[A_{c}=\sqrt{2P_{in}}\left\{((1-r)+\frac{r}{2}J_{0}(m).\left(e^{jn\gamma}+1 \right)\right\},\]  
\[A_{ln}=\sqrt{2P_{in}}.\frac{r}{2}.j^{n}.J_{n}(m).\left(e^{jn\gamma}+e^{-jn \theta}\right),\text{ and}\]  
\[A_{un}=\sqrt{2P_{in}}.\frac{r}{2}.j^{n}.J_{n}(m).\left(e^{jn\gamma}+e^{jn \theta}\right).\]  
The transfer function of the dispersive fiber link is given by [35]  
\[H(f)=e^{\frac{jnDL\lambda_{c}^{2}(f-f_{c})^{2}}{c}} \tag{21}\]  
where \(D\) is the chromatic dispersion in ps/(nm.km). The \(\lambda_{c}=c/f_{c}\) is the optical wavelength, \(f\) is the frequency offset of the optical carrier, \(c\) is the speed of light in a vacuum, and \(L\) is the fiber length. When \(E_{TX}(t)\) is transmitted through the fiber link, there is a phase difference between the optical carrier and the first-order sideband, \(\phi\), given by  
\[\phi=\frac{\pi DL\lambda_{c}^{2}f_{m}^{2}}{c} \tag{22}\]  
while the phase difference between the optical carrier and any random sideband is the square of the frequency range \((\pm nf_{m})\) given by [36]  
\[\phi_{n}=n^{2}\phi \tag{23}\]  
Therefore, the optical field arriving at the receiver (\(E_{RX}(t)\)) can be expressed as  
\[E_{RX}(t)=A_{c}e^{j2\pi f_{c}t}+\sum\limits_{n=1}^{\infty}\left\{A_{ln}e^{j2 \pi(f_{c}-nf_{m})t}+A_{un}e^{j2\pi(f_{c}+nf_{m})t}\right\}.e^{jn^{2}\phi} \tag{24}\]  
At the receiver, \(E_{RX}(t)\) is detected using a photodetector, which is a squared envelope operator, given by [2]  
\[\left|E_{RX}(t)\right|^{2}=E_{RX}(t).E_{RX}^{*}(t) \tag{25}\]  
By simply taking the \(f_{m}\) term,  
\[E_{TX}(t)=A_{c}e^{j2\pi f_{c}t}+\sum\limits_{n=1}^{\infty}\left\{A_{ln}e^{j2 \pi(f_{c}-nf_{m})t}+A_{un}e^{j2\pi(f_{c}+nf_{m})t}\right\} \tag{20}\]0  
The \(X_{rec}(t)\) power is the square of the amplitude term in Equation (27) [2], so that the recovered RF signal power as the \(L\) function, \(P_{rec}(L)\), is given by  
\[E_{TX}(t)=A_{c}e^{j2\pi f_{c}t}+\sum\limits_{n=1}^{\infty}\left\{A_{ln}e^{j2 \pi(f_{c}-nf_{m})t}+A_{un}e^{j2\pi(f_{c}+nf_{m})t}\right\} \tag{20}\]1  
where  
\[E_{TX}(t)=A_{c}e^{j2\pi f_{c}t}+\sum\limits_{n=1}^{\infty}\left\{A_{ln}e^{j2 \pi(f_{c}-nf_{m})t}+A_{un}e^{j2\pi(f_{c}+nf_{m})t}\right\} \tag{20}\]2  
\[E_{TX}(t)=A_{c}e^{j2\pi f_{c}t}+\sum\limits_{n=1}^{\infty}\left\{A_{ln}e^{j2 \pi(f_{c}-nf_{m})t}+A_{un}e^{j2\pi(f_{c}+nf_{m})t}\right\} \tag{20}\]3  
Equation (28) shows that the recovered RF signal is obtained by multiplying the \(n\)th order lower sideband with the \((n+1)\)th order conjugated lower sideband plus the multiplication of the \(n\)th order conjugated upper sideband with the \((n+1)\)th order upper sideband, where \(n\) is an integer. It can be seen from Equation (28) that \(P_{rec}(L)\) is dependent on \(\gamma\) and \(\theta\).