## 3 Research of the Key Elements
### Calculation of Equilibrium between Fiber Optical Repeater and Cellular Phone  
Implementation of the downlink gain in the fiber optical repeater involves controlling the output power of the fiber optical repeater. It is necessary to consider the upstream and downstream balance between the optical fiber optical repeater and the mobile station [18]. As an equilibrium guarantees the transmission power to UL and downlink, the fiber optical repeater should satisfy the following:  
\[P_{o-rep}-P_{o-cellular\ phone}+NF_{cellular\ phone}-NF_{rep} \tag{14}\]  
Here, \(P_{o-rep}\) is the output power of the fiber optical repeater, \(P_{o-cellular\ phone}\) is the _MU_ of output power, \(NF_{cellular\ phone}\) is the noise figure of the cellular phone, and \(NF_{rep}\) is the noise figure of the fiber optical repeater. The maximum of the cellular phone output power is \(P_{o-cellular\ phone}\) = 33 dBm, the noise figure of the cellular phone is \(NF_{cellular\ phone}\) = 6 dBm, and the noise figure of \(FR\) is \(NF_{rep}\) = 5 dBm. Therefore, the maximum fiber optical repeater output power is \(P_{o-rep}\) = 33 + 6 - 5 = 34 dBm. MDP-RRH latency introduced by the fiber optical repeater is not the only delay to take into account. In fact, delays introduced by coaxial cables and fiber optic links used in the application must be considered. The delays analyzed by the equipment are summarized as follows [19]:  
1. Repeater absolute delay time, T\({}_{\text{d-Rep}}\), is 6-8 \(\upmu\)s.
2. Coaxial cable delay time, T\({}_{\text{d-Coax}}\), is D/0.88 \(\times\) C.
3. Optic fiber delay time, T\({}_{\text{d-Opt}}\), is D/0.66 \(\times\) C.  
where:  
C is the speed of light (m/s). D is the length of the coaxial cable or of the optic fiber (m). There are two types of delay time (absolute and relative) that need to be considered in the design. When an eNB or a MU receives both direct and through repeater paths, the relative time delay difference between the two paths will determine the correct functioning of the system. Relative delays larger than the searcher window will probably cause the call to drop when moving from the repeater coverage area to the eNB, since the system cannot handle the handover between the two paths. The absolute repeater delay can cause positioning systems to not work correctly. This really depends on the type of positioning system employed. In the Cell ID method, the repeater delay will not affect the identification of the serving cell whose serving area is used to identify the MU location. In the round-trip time (RTT) method, the estimation of MU location strongly depends on the delay time between the MU and eNB. \begin{table}
\begin{tabular}{c c} \hline \hline \(\begin{array}{c}\mathit{UILAN}_{eNB}\text{: }\mathit{UL}\ G_{rep}=L_{p}+NF_{eNB}-NF_{rep}+ \Delta N_{eNB}\\ =39+2-5+(-9)\ (\text{dB})\end{array}\) & \(\begin{array}{c}\text{Uplink }G_{rep}\ (\text{dB})\\ \text{Noise Floor, }NF_{eNB}\end{array}\) \\ 5 & \(\begin{array}{c}\text{Noise Floor, }NF_{rep}\end{array}\) \\ \hline \(\begin{array}{c}\text{Path Loss},L_{p}\ (\text{dB})=\text{Coupling Loss}+\text{Cable Loss}+\text{Combiner Loss}\equiv 39 \end{array}\) & \(\begin{array}{c}\text{Path Loss},L_{p}\ (\text{dB})\\ \text{Path Loss},L_{p}\ (\text{dB})\end{array}\) \\ 30 & \(\begin{array}{c}\text{Coupling Loss}\\ \text{Combiner Loss}\end{array}\) \\ 7 & \(\begin{array}{c}\text{Cable Loss}\end{array}\) \\ \hline \(\begin{array}{c}\text{\Delta N}_{eNB}\text{: number of fiber optical repeaters ($n$)}\end{array}\) & \(\begin{array}{c}\text{$n$}\end{array}\) \\ \hline \(\begin{array}{c}-9\\ -6\end{array}\) & \(\begin{array}{c}2\\ 1\\ 0\end{array}\) & \(\begin{array}{c}0\end{array}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation of link budget for the fiber optical repeater. Two examples of the signal path delay calculus are depicted in Figure 8 for eNB to FR and in Figure 9 for FR to FR:  
1. One signal arrives directly from the eNB while the other is retransmitted via optical equipment.