## 3 Proposed Scheme
### Numerical Analysis
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\tau_{A}\) & \(\tau_{B}\) & \(\tau_{C}\) \\ \hline Figure & & & \\ \hline \(D_{avg}\) & 0.608 & 1.175 & 1.540 \\ \hline  & \(\tau_{D}\) & \(\tau_{E}\) & \(\tau_{F}\) \\ \hline Figure & & & \\ \hline \(D_{avg}\) & 0.706 & 1.08 & 1.225 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average distance coefficient according to type of neighboring zone. where \(u_{s,D2D}=\
u u_{s,CE}\). After arranging the common coefficients and constants related with the \(ffr\) design, Equation (10) is derived again as follows:  
\[I_{CE,ffr}=\ell\mathcal{P}_{t}\Psi_{CE,ffr}\mathbf{1}, \tag{11}\]  
where \(\ell=u_{s,CE}hr^{-\alpha}\), \(\mathbf{1}=[1,1,1]\), and \(\mathcal{P}_{t}=[P_{t,CE},\
u P_{t,D2D}]\). In addition, \(\Psi_{CE,ffr}\) is denoted as  
\[\Psi_{CE,ffr}= \begin{bmatrix}n_{D2D,CE,ffr,r_{A}}\tau_{A}^{-\alpha}&n_{D2D,CE, ffr,r_{B}}\tau_{B}^{-\alpha}&n_{D2D,CE,ffr,r_{C}}\tau_{C}^{-\alpha}\\ n_{CE,CE,ffr,\tau_{D}}\tau_{D}^{-\alpha}&n_{CE,CE,ffr,r_{E}}\tau_{E}^{-\alpha} &n_{CE,CE,ffr,r_{F}}\tau_{F}^{-\alpha}\end{bmatrix} . \tag{12}\]  
Accordingly, Equation (1) can be derived with adopting Equation (11) as  
\[SINR_{ffr,CE} =\frac{P_{r,CE}}{I_{CE,ffr}+I_{sh,ffr}+N_{0}} \tag{13}\] \[=\frac{P_{r,CE}}{\ell\mathcal{P}_{t}(\Psi_{CE,ffr}+\Psi_{D2D,ffr} )\mathbf{1}+N_{0}}. \tag{14}\]  
To simplify, \(\ell\mathcal{P}_{t}(\Psi_{CE,ffr}+\Psi_{D2D,ffr})\mathbf{1}\) can be replaced by \(\gamma_{ce}^{ffr}P_{t,CE}+\delta_{D2D}^{ffr}P_{t,D2D}\) because others are constants excepts the power variables, \(P_{t,CE}\) and \(P_{t,D2D}\). Then, Equation (14) is redefined as  
\[SINR_{ffr,CE} =\frac{P_{r,CE}}{\gamma_{CE,CE}^{ffr}P_{t,CE}+\delta_{D2D,CE}^{ffr }P_{t,D2D}}, \tag{15}\] \[T_{ffr,CE} =\frac{B}{6u_{z,CE}}\log_{2}\left(1+SINR_{ffr,CE}\right), \tag{16}\]  
where \(T\) is defined as throughput with the Shannon capacity. \(B\) is total system bandwidth per a cell. A zone uses \(\frac{B}{6}\) of bandwidth because a cell has six zones. We assume that the bandwidth is allocated equally and sequentially to the users in the zone. It means that the same portion of the bandwidth is allocated to each user. Similarly, throughput for D2D link in \(ffr\) mode also can be derived as  
\[T_{ffr,D2D}=\frac{2B}{6u_{z,D2D}}\log_{2}\left(1+SINR_{ffr,D2D}\right), \tag{17}\]  
where D2D link in \(ffr\) mode uses double bandwidth because the two frequency domains which are allocated for cellular are used as the D2D link in the other two zones. On the other hand, in the semi-static method, system bandwidth is divided into cellular and D2D links. We assume that it is separated with considering ratio of the number of users for each link. Therefore, \(T_{ss,CE}\) and \(T_{ss,D2D}\) are derived as \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Mode** & **Link** & \(\mathbf{\tau_{A}}\) & \(\mathbf{\tau_{B}}\) & \(\mathbf{\tau_{C}}\) & **Link** & \(\mathbf{\tau_{D}}\) & \(\mathbf{\tau_{E}}\) & \(\mathbf{\tau_{F}}\) \\ \hline \(ffr\) & \(CE\to CE\) & 0 & 1 & 2 & \(CE\to D2D\) & 0 & 0 & 3 \\ \(ffr\) & \(D2D\to CE\) & 2 & 2 & 4 & \(D2D\to D2D\) & 0 & 0 & 3 \\ ss & \(CE\to CE\) & 0 & 6 & 12 & \(CE\to D2D\) & 0 & 0 & 0 \\ ss & \(D2D\to CE\) & 0 & 0 & 0 & \(D2D\to D2D\) & 1 & 2 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of interferer zones in neighboring zones, \(n\). \[T_{ss,CE} = \frac{u_{z,CE}}{u_{z,CE}+u_{z,D2D}}\frac{B}{6u_{z,CE}}\log_{2}\left( 1+SINR_{ss,CE}\right) \tag{18}\] \[= \frac{B}{6\
u(1+u_{z,CE})}\log_{2}\left(1+SINR_{ss,CE}\right),\] \[T_{ss,D2D} = \frac{u_{z,D2D}}{u_{z,CE}+u_{z,D2D}}\frac{B}{6u_{z,D2D}}\log_{2} \left(1+SINR_{ss,D2D}\right)\] (19) \[= \frac{B}{6\
u(1+u_{z,CE})}\log_{2}\left(1+SINR_{ss,D2D}\right),\]  
where the bandwidth is allocated to a cell in semi-static mode. For instance, \(6u_{z,CE}\) users use \(\frac{u_{z,CE}B}{u_{z,CE}+u_{z,D2D}}\).