## 2 System Model  
In this paper, the SWIPT-enabled CRN model as in [18; 20] is considered. As in [18], all nodes are half-duplex and equipped with a single antenna. All nodes have perfect channel state information (CSI). All the nodes' noise is modeled as addictive white Gaussian noise (AWGN) with zero mean and \(\sigma^{2}\) variance. All signal and interference channels are independent of each other. And all channels undergo the quasi-statically symmetric complex Gaussian distribution. At the same time, as stated in [26], the SWIPT-enabled CRN can relieve the constraints of energy-constrained and spectrum resources for massive and small-sized nodes. Therefore, it can also be used in a variety of application scenarios, such as in the fields of IoT and UAV networks.  
With the above system setting, the SWIPT-enabled CRN model is shown in Figure 1. From Figure 1, we can find that it consists of a primary network and a secondary network. In the primary network, there is one primary transmit user (PTU) and one primary destination user (PDU). The PTU and PDU can transmit signals by direct transmission. In the secondary network, there are two SUs (SU\({}_{1}\), SU\({}_{2}\)) and \(m\) energy-constrained relay nodes \(SR_{k}\), where \(k=1,2,...,m\). The \(SR_{k}\) can transmit signals with the amplify-and-forward (AF) protocol [27]. The SU\({}_{1}\) and SU\({}_{2}\) can both act as transmit and receive nodes to exchange signals. And they can achieve bidirectional transmission through the energy-constrained best relay node SR\({}_{\text{b}}\) or the DL with the adaptive transmission. Namely, SU\({}_{1}\) and SU\({}_{2}\) can achieve bidirectional transmission through the BRT or the BDT modes. At the same time, the node which shows superiority in the consideration of both SNR and global channel gain will be SR\({}_{\text{b}}\). In addition, SR\({}_{\text{b}}\) will split the received signals into two parts with the SWIPT-PS protocol, namely, one part for energy harvesting (EH) and the other for signal processing (SP) [13].  
To better show the transmission process of the SWIPT-enabled CRN model, the specific time slots model of the signal transmission is given in Figure 2. In Figures 1 and 2, the green solid line and purple dashed line respectively represent the transmit signals in time slots 1 and 2. At the same time, the gray dashed line represents the interference signals. With Figures 1 and 2, we can further assume that the signals sent by the PTU, SU\({}_{1}\) and SU\({}_{2}\) are respectively \(x_{p}\), \(x_{1}\), and \(x_{2}\) with \(\mathbb{E}\Big{\{}\big{|}x_{p}\big{|}^{2}\Big{\}}=\mathbb{E}\Big{\{}|x_{1}|^{ 2}\Big{\}}=\mathbb{E}\Big{\{}|x_{2}|^{2}\Big{\}}=1\). The transmit powers of PTU, SU\({}_{1}\), and SU\({}_{2}\) are respectively \(P_{p}\), \(P_{1}\), and \(P_{2}\). The channel coefficient from SU\({}_{1}\) to SU\({}_{2}\) is \(h\) with \(h\sim CN\big{(}0,\sigma_{h}^{2}\big{)}\). The channel coefficients from SU\({}_{1}\) and SU\({}_{2}\) to SR\({}_{\text{b}}\) are \(f_{b}\) and \(g_{b}\) with \(f_{b}\sim CN\big{(}0,\sigma_{1}^{2}\big{)}\) and \(g_{b}\sim CN\big{(}0,\sigma_{2}^{2}\big{)}\), respectively. The interference channel coefficients from PTU to SU\({}_{1}\), SU\({}_{2}\), and SR\({}_{\text{b}}\) are respectively \(l_{1}\), \(l_{2}\), and \(l_{r}\) with \(l_{1}\sim CN\big{(}0,\sigma_{p_{1}}^{2}\big{)}\), \(l_{2}\sim CN\big{(}0,\sigma_{p_{2}}^{2}\big{)}\), and \(l_{r}\sim CN\big{(}0,\sigma_{p_{r}}^{2}\big{)}\).  
Figure 1: SWIPT-enabled CRN model.