## 2 System Model and Problem Formulation  
### System Model  
In this subsection, we present two communication cases to describe the considered system model. The first case is a non-D2D (ND) scenario in which the BS transmits signals to the CU, but the DT does not send any signals. Let \(h_{\text{lc}}\) and \(P_{b}\) denote the complex channel coefficient from the BS to the CU and the transmit power of the BS, respectively. For the SWIPT, with a power-splitting ratio \(0\leq\rho_{c}^{\text{ND}}\leq 1\), the CU divides the received signals into two parts: one part, with power \(\rho_{c}^{\text{ND}}P_{b}|h_{bc}|^{2}\), is allocated to energy harvesting, while the other part, with power \((1-\rho_{c}^{\text{ND}})P_{b}|h_{bc}|^{2}\), is used for information decoding. Over the block time \(T\), the CU's harvested energy and data rate are expressed as follows:  
\[E_{c}^{\text{ND}} =\zeta\rho_{c}^{\text{ND}}TP_{b}|h_{bc}|^{2}, \tag{1}\] \[R_{c}^{\text{ND}} =\log_{2}\left(1+\frac{P_{b}|h_{bc}|^{2}}{\sigma_{c,\text{ant}}^ {2}+\sigma_{c,\text{cov}}^{2}/(1-\rho_{c}^{\text{ND}})}\right), \tag{2}\]  
where \(0<\zeta\leq 1\) denotes the power conversion efficiency, \(\sigma_{c,\text{ant}}^{2}\) represents the antenna noise power at the CU, and \(\sigma_{c,\text{cov}}^{2}\) is the conversion noise power at the CU. In Section 2.2, the harvested energy in (1) and the data rate in (2) are used as thresholds for the CU's performance constraints.  
As shown in Figure 1, the second case is a D2D scenario where both the BS and DT simultaneously transmit signals. In a centralized manner, the BS manages both cellular and D2D communications. Let \(h_{bd}\), \(h_{dc}\), and \(h_{dd}\) represent the complex channel coefficients from the BS to the D2D receiver (DR), from the DT to the CU, and from the DT to the DR, respectively. The BS maintains a fixed transmit power of \(P_{b}\). To facilitate energy harvesting at the CU, the DT sends both information and energy signals. Since the energy signals are predetermined, they do not interfere with information decoding at the CU and DR; they can be canceled out prior to information decoding [17]. Under the coordination of the BS, the CU cooperates to cancel the received energy signals. The DT's transmit powers for the information and energy signals are denoted as \(P_{d,\text{J}}\) and \(P_{d,\text{E}}\), respectively. In this D2D case, the CU must adjust its power-splitting ratio to ensure its previously achieved energy and data rates, as expressed in (1) and (2). This adjusted power-splitting ratio is denoted by \(0\leq\rho_{c}\leq 1\). Also, for the SWIPT of D2D communications, the DR divides the received signals into two parts with a power-splitting ratio \(0\leq\rho_{d}\leq 1\). Then, the harvested energies and data rates at the CU and DR are given by  
\[E_{c} =\zeta T\rho_{c}(P_{b}|h_{bc}|^{2}+P_{d,\text{J}}|h_{dc}|^{2}+P_{ d,\text{E}}|h_{dc}|^{2}),\] (3) \[R_{c} =\log_{2}\left(1+\frac{P_{b}|h_{bc}|^{2}}{P_{d,\text{J}}|h_{dc}|^  
\[R_{d}=\text{log}_{2}\Bigg{(}1+\frac{P_{d,\text{J}}|h_{dd}|^{2}}{P_{b}|h_{bd}|^{2}+ \sigma_{d,\text{ant}}^{2}+\sigma_{d,\text{ant}}^{2}/(1-\rho_{d})}\Bigg{)}, \tag{6}\]  
where \(\sigma_{d,\text{ant}}^{2}\) is the antenna noise power at the DR, and \(\sigma_{d,\text{cov}}^{2}\) is the conversion noise power at the DR. It is important to note that both the information signals and energy signals transmitted from the DT assist the CU in energy harvesting. On the other hand, the information signals transmitted from the DT interfere with the information decoding at the CU, while the energy signals do not interfere.