## 5 Numerical Results  
In Figure 2, the D2D data rate \(R_{d}\) versus \(\rho_{c}^{\text{ND}}\in[0,1]\) is plotted to demonstrate the effectiveness of the proposed scheme in maximizing the D2D data rate. Although a related study is presented in [15], making a fair comparison of the performance of our proposed  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Power-Splitting Ratio Condition** & **Performance Comparison Result** \\ \hline Area 1 & \(0\leq\rho_{c}^{\text{ND}}\leq g(0)\) & \(R_{d}^{\text{O}}\geq R_{d}^{\text{BL}}=0\) \\ \hline Area 2 & \(g(0)<\rho_{c}^{\text{ND}}<g(P_{d}^{\text{max}})\) & \(R_{d}^{\text{O}}>R_{d}^{\text{BL}}>0\) \\ \hline Area 3 & \(g(P_{d}^{\text{max}})\leq\rho_{c}^{\text{ND}}\leq 1\) & \(R_{d}^{\text{O}}=R_{d}^{\text{BL}}>0\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison between the optimal and BL schemes for SWIPT D2D communications in cellular networks.  
scheme with [15] is challenging, as our study focused on the power-splitting architecture, which offers a larger energy rate region than the time-switching architecture considered in [15]. Therefore, we compared the performance of our proposed scheme with that of the baseline scheme in (19)-(22) unlike in [15]. The channel power gains are modeled as \(|h_{i}|^{2}=\frac{10^{-3}}{d^{3}}\) for \(i\in\{bc,bd,dc,dd\}\), where \(d_{i}\) is the normalized distance. We set \(d_{bc}=d_{bd}=1\), \(d_{dc}=0.5\), \(d_{dd}=0.2\), \(\zeta=1\), \(T=1\) s, \(P_{b}=30\) dBm, \(P_{d}^{\max}=20\) dBm, \(\sigma^{2}=\sigma_{c,\text{ant}}^{2}=\sigma_{c,\text{cov}}^{2}=\sigma_{d,\text {ant}}^{2}=\sigma_{d,\text{cov}}^{2}\), \(\frac{P_{d}^{\max}|h_{d}|^{2}}{\sigma^{2}}=10\) dB, and \(Q_{d}=1.3\) dBm, \(8.3\) dBm, and \(10.8\) dBm. Under these simulation parameters, we have \(g_{2}(0)=0.4624\) and \(g_{2}(P_{d}^{\max})=0.6482\). As predicted by the results of Area 1 and Area 2 in Theorem 1, Figure 2 shows that the proposed optimal scheme outperforms the baseline scheme when \(0\leq\rho_{c}^{\text{ND}}\leq g_{2}(P_{d}^{\max})\). When \(0\leq\rho_{c}^{\text{ND}}\leq 0.4624\) (Area 1), the optimal scheme can transmit data, whereas the BL scheme cannot. When \(0.4624\leq\rho_{c}^{\text{ND}}\leq 0.6482\) (Area 2), both the optimal and BL schemes can transmit data, whereas when \(0.6482\leq\rho_{c}^{\text{ND}}\leq 1\) (Area 3), the BL scheme performs the same as the optimal scheme because the optimal scheme allocates all of the DT's transmit power to the information signals in the same way as the baseline scheme. In summary, when a smaller portion of the received energy is required for energy harvesting at the CU, the proposed scheme is more effective in improving D2D performance.  
To demonstrate the applicability of the proposed scheme to fading channels, which correspond to the scenarios of mobile CU and D2D nodes, Figures 3 and 4 show the D2D performance for Rayleigh fading channels. In Figures 3 and 4, the ergodic rate \(\mathbb{E}[R_{d}]\) and outage probability \(\Pr\{R_{d}<R_{d}^{\dagger}\}\) for the fast and slow fading channels are plotted versus \(\rho_{c}^{\text{ND}}\in[0,1]\), respectively. The target rate \(R_{d}^{\dagger}\) is set to \(R_{d}^{\dagger}=0.5\) bits/s/Hz, and the channels are modeled as \(h_{i}\sim CN\bigg{(}0,\frac{10^{-3}}{d_{i}^{3}}\bigg{)}\) for \(i\in\{bc,bd,dc,dd\}\), where \(d_{i}\) is the normalized distance. The other simulation parameters are the same as those in Figure 2. As predicted by Theorem 2, when the required energy of the CU is small (or large), the optimal scheme outperforms (or performs the same as) the BL scheme. Also, we can observe that the proposed optimal scheme demonstrates robust performance in fading channels.