## 3 C/N Penalty of RoF Link
### C/N Penalty of RoF Link with ODSB Modulation  
The calculation of the C/N penalty aims to observe the DPF on the RoF link that uses DD-MZM as the E/O converter with ODSB modulation. This is done because IM on the RoF link generally produces modulated optical signals with a double sideband spectrum. Based on Equation (14), DD-MZM will generate a modulated optical signal with a double sideband spectrum only if it is set with parameters \(\gamma=\
icefrac{{1}}{{2}}\) and \(\theta=180^{\circ}\). The following steps are completed to calculate the C/N penalty of the RoF link with the modulated ODSB. This study focused on the effect of dispersion so that attenuation was eliminated. In addition, the attenuation at optical fiber is minimal.  
1. Calculate \(P_{rec}(L)\) using Equation (28) with r = 1 (without CA), \(P_{in}\) = 1 mw (0 dBm), \(\gamma=\
icefrac{{1}}{{2}}\), \(\theta=180^{\circ}\), \(m=0.5\), \(\lambda_{c}=1550\) nm (\(D=17\) ps/(nm.km)), and \(f_{m}=60\) GHz with \(L\) = 0, 0.1, 0.2,... 5 km.
2. From the obtained \(P_{rec}(L)\) in (a), calculate the C/N penalty using Equation (29).
3. Repeat steps (a) and (b) for \(m=1\), 1.5, 2, 2.5, 3, 3.5, and 4.
4. The result of the calculation is shown in Figure 3a,b.  
The vertical axis in Figure 3 shows the C/N penalty in dB, whereas the horizontal axis depicts the fiber length in km. The C/N penalty of the RoF link curve with ODSB modulation at \(m\leq 2\) is shown in Figure 3, while Figure 3 shows the C/N penalty at \(m>2\). Observed from the physical meaning side, the C/N value was influenced by constructive/destructive sideband interference. Therefore, the received power followed the cosine function, and it did not strictly increase/decrease. The RoF link with ODSB modulation at \(m=0.5\), 1, and 1.5 experiences deep fade (a massive power decline) at \(L=1\) and 3.1 km; at \(m=2\), deep fade occurs at \(L=0.2\) and 3.9 km. By using Equation (30), the DF value of the RoF link is obtained with ODSB modulation at \(m=0.5\), 1, 1.5 and 2 as much as 6.5, 5.5, 4.2 and 10.5, respectively. The RoF link at \(m=2.5\), 3, 3.5 and 4 undergoes deep fade at different \(L\) and has an irregular pattern. The DFs from the RoF link with ODSB modulation at \(m=2.5\), 3, 3.5 and 4 are 6.9, 5.5, 10.9, and 7.4, respectively. This shows that the level of the chromatic dispersion effect or the DPF value on the RoF link with ODSB modulation is very high.  
It should be noted that several values of C/N have high positive values. This does not mean that the power of the signal was amplified. The C/N value is the ratio of the power of \(P_{rec}(L)\) with \(P_{rec}(L=0)\). The C/N is positive when \(P_{rec}(L)\) is higher than \(P_{rec}(L=0)\). This condition can be found when \(P_{rec}(L=0)\) has low power due to destructive interference and \(P_{rec}(L)\) has high power due to constructive interference. Therefore, the C/N can be a positive or negative value.  
This condition does not only apply to the irregular phase method but also to the ODSB (conventional) method. The value of \(\theta\) will affect the spectrum shape of the optic signal. Moreover, the index modulation (\(m\)) will affect the value of \(n\), and the value of \(n\) will affect the number of side bands. For instance, if we apply this equation to the ODSB (\(\theta=180^{\circ}\)) system with parameter i.e., r = 1, \(P_{in}=1\) mw (0 dBm), \(\gamma=1/2\), \(\theta=180^{\circ}\), \(\lambda_{c}=1550\) nm (\(D=17\) ps/(nm.km)), and \(f_{m}=60\) GHz, as shown in Table 1,the value of \(P_{rec}(L=0)\) is different for different values of \(m\), and it was close to zero (very small). By this calculation, we use the different values of \(P_{rec}(L=0)\). Therefore, the role of \(\theta\) is clear for the irregular phase as well as for ODSB.