## 5 Effect of Optical Fiber Dispersion  
In this section, the effect of dispersion is studied to investigate the performance of the RoF system and the signal power of the mm-wave at different optical fiber lengths. The simulation results of the proposed architecture showed acceptable performance of the RoF system: the system obtained a BER of 2.6 \(\times\) 10\({}^{-10}\) and Q factor of 6.2 for the 1.25 Gbps signal. Figure 6 shows the relationship between BER and the received optical power (ROP) at 0 km and 20 km fiber length. From the graph, it can be seen that the power penalty is 1.5 dBm between the 0 km and 20 km lines at a BER of 10\({}^{-9}\), where the system achieves error-free transmission. Figure 5: Effect of both optical splitting ratio \(\gamma\) and the phase imbalance \(\phi\) on the 4\(m\) order sideband. Figure 6: BER vs. the received optical power (ROP) at 0 km and 20 km fiber length. To show the dispersion effects, the optical fiber length was varied from 0 km to 40 km and dispersion was considered at 16 ps/(nm/km). The parameters for CW laser, PD, EDFA1 and EDFA2 were kept at the same settings. The results in Figure 7a-e show the effects of dispersion on the DSB-CCS system and how it contributes to changing the output spectrum of 40 GHz. Figure 7: _Cont_. Figure 7a shows the 40 GHz output spectrum with a 0 dBm peak and 80 dB SNR at 0 km fiber length. Figure 7b shows that the SNR decreases to 54 dB, while the peak of 40 GHz remains at 0 dBm at 10 km fiber length. At this length, the components of 20 GHz and 60 GHz appear with amplitudes of \(-27\) dBm and \(-38\) dBm, respectively. Figure 7c shows that the peak of 40 GHz output spectrum is \(-5\) dBm and the SNR value drops to 44 dB at 20 km fiber length. The component amplitudes of 20 GHz and 60 GHz are \(-45\) dBm and \(-36\) dBm, respectively. Figure 7d shows that the peak of the 40 GHz output spectrum is \(-10\) dBm and the value of the SNR is 42 dB at 30 km fiber length, while the component amplitudes of 20 GHz and 60 GHz are \(-43\) dBm and \(-38\) dBm, respectively. Finally, Figure 7e shows that the peak of the 40 GHz output spectrum is \(-14\) dBm and the SNR is 42 dB at 40 km fiber length, whereas the component amplitudes of 20 GHz and 60 GHz are \(-41\) dBm and \(-45\) dBm, respectively. It is obvious that the 40 GHz amplitude and the SNR is decreasing with the increase in optical fiber length. The amplitude of 40 GHz is reduced to \(-14\) dB after increasing the fiber length to 40 km. Additionally, the amplitude of SNR drops to 44 dB after 40 km fiber length. Therefore, the effect of optical fiber dispersion occurs with the increase in optical fiber length. To investigate more into dispersion parameter, we can refer to the formula [29]:  
\[D=-\frac{2\pi C}{\lambda^{2}}\ \beta_{2} \tag{8}\]  
where \(D\) is the dispersion [ps/(nm/km)], \(C\) represents the light speed in (ps), \(\lambda\) represents the wavelength in (nm), and \(\beta_{2}\) represents the second-order propagation constant. The \(D\) value degrades the RoF system due to the high utilization of optical bandwidth, as displayed in Figure 7. The degradation of system influences more on the DSB system than the OCS. This because the speed of the sideband is different from the speed at which the carrier propagates in the fiber. Later, both arrive with an introduced delay and inter-mix with the optical signal at the detector. Therefore, the system would experience power loss and signal broadening, which makes it difficult to decode the received data. Another study provides a comprehensive description of dispersion and its influence on the DSB-OCS output [30]. Figure 8 illustrates the relationship between the mm-wave signal amplitude in dBm and different optical fiber distance. In this graph, the optical fiber length varies from 0 to 40 km distance, while the amplitudes for the mm-wave signals range from 0 dBm to \(-80\) dBm.