## 2 System Model  
Figure 1 shows the system model of the proposed FC-based TWRCR model, where secondary sources (SS\({}_{1}\) and SS\({}_{2}\)) exchange data with each other. Let \(m_{1}\) and \(m_{2}\) denote the data sent by SS\({}_{1}\) and SS\({}_{2}\), respectively. Since direct communication between SS\({}_{1}\) and SS\({}_{2}\) is outage due to their far distance, a reconfigurable intelligent surface (RIS) is deployed to assist these data exchange. Let \(K(K\geq 2)\) represent the number of small reflective elements in the RIS. Additionally, a power beacon station (denoted by SB) is deployed in the secondary network to provide energy for SS\({}_{1}\) and SS\({}_{2}\). To prevent co  
Figure 1: The proposed FC-based TWR CR scheme. channel interference, the frequencies used for energy harvesting differ from those used for the data transmission. The transmit power of \(\text{SS}_{1}\) and \(\text{SS}_{2}\) is constrained by an interference threshold established by a primary user (PU). Assume that all channels experience block Rayleigh fading and that all devices are single-antenna nodes. The proposed scheme can be applied to IoT networks, where \(\text{SS}_{1}\) and \(\text{SS}_{2}\) are IoT devices with limited power and energy. Therefore, the station power (SB) is deployed to provide energy for two source nodes. Moreover, due to spectrum scarcity, the underlay cognitive radio technique is employed for the IoT networks. Following the operational principle of FC, \(\text{SS}_{i}(i=1,2)\) divides \(m_{i}\) into small, equally sized packets, which are then used to create FC packets. Let \(p_{i}\) denote one FC packet of \(\text{SS}_{i}\). To successfully recover \(m_{i}\), \(\text{SS}_{j}(j=1,2,j\
eq i)\) must collect at least \(H_{\text{min},i}\) packets \(p_{i}\). In addition, let \(N_{\text{max},i}\) as the maximum number of FC packets sent by \(\text{SS}_{i}\). For simplicity in presentation and analysis, we can assume that \(H_{\text{min},i}=H_{\text{min},j}=H_{\text{min}}\) and \(N_{\text{max},i}=N_{\text{max},j}=N_{\text{max}}\ \forall i,j\). In the conventional FC-TWRCR scheme (Cov-Scm), \(\text{SS}_{1}\) continuously transmits packets \(p_{1}\) to \(\text{SS}_{2}\) through the RIS. After \(N_{\text{max}}\) transmission times, \(\text{SS}_{1}\) stops the transmission. If \(\text{SS}_{2}\) correctly receives at least \(H_{\text{min}}\) packets \(p_{1}\), the data transmission is successful, and otherwise, \(\text{SS}_{2}\) experiences an outage. Then, \(\text{SS}_{2}\) in turn transmits packets \(p_{2}\) to \(\text{SS}_{1}\) through the RIS, also using \(N_{\text{max}}\) transmission times. Similarly, for the successful recovery of \(m_{2}\), \(\text{SS}_{1}\) must receive at least \(H_{\text{min}}\) packets \(p_{2}\) by the end of this transmission. In the modified FC-TWRCR scheme \((\text{Mod-Scm})\), \(\text{SS}_{i}(i=1,2)\) first transmits packets \(p_{i}\) to \(\text{SS}_{j}(j=1,2,j\
eq i)\). If \(\text{SS}_{j}\) gathers enough \(H_{\text{min}}\) packets \(p_{i}\) after \(N_{i}\) transmission times \((N_{i}\leq N_{\text{max}})\), \(\text{SS}_{j}\) sends an ACK message back to \(\text{SS}_{i}\). Upon receiving the ACK message, \(\text{SS}_{i}\) ends its transmission, and \(\text{SS}_{j}\) begins its transmission. Notably, if \(N_{i}=N_{\text{max}}\), \(\text{SS}_{j}\) does not need to send feedback to \(\text{SS}_{i}\) because \(\text{SS}_{i}\) must stop its transmission, regardless of whether \(\text{SS}_{j}\) has received enough \(H_{\text{min}}\) packets \(p_{i}\) or not. Otherwise, if \(N_{i}<N_{\text{max}}\), the remaining transmission times \((N_{\text{max}}-N_{i})\) can be allocated to \(\text{SS}_{j}\) in the second transmission phase, i.e., allowing \(\text{SS}_{j}\) to send at most \(N_{\text{max}}+(N_{\text{max}}-N_{i})\) packets \(p_{j}\) to \(\text{SS}_{i}\). Similarly, as soon as \(\text{SS}_{i}\) receives enough \(H_{\text{min}}\) packets \(p_{j}\), it also sends an ACK message to inform \(\text{SS}_{j}\). **Remark 1**.