## 2 System Model  
In Figure 1, we present the system model of the proposed underlay CRN applying TAS/SC for the primary network, and the DNC TWR and PRS techniques for the secondary network. In the primary network, the \(N_{\text{T}}\)-antenna primary transmitter (PT) uses TAS to serve the \(N_{\text{R}}\)-antenna primary receiver (PR) using SC. In the secondary network, the secondary sources \(\text{SS}_{1}\) and \(\text{SS}_{2}\) exchange their data (denoted by \(x_{1}\) and \(x_{2}\), respectively) with each other thanks to \(M\) secondary relays (denoted by \(\text{SR}_{m}\), where \(m=1,2,\ldots,M\)). In addition, only one relay (denoted by \(\text{SR}_{b}\)) is selected to assist the \(\text{SS}_{1}-\text{SS}_{2}\) data exchange. Assume that \(\text{SS}_{1}\) and \(\text{SS}_{2}\) cannot directly communicate with each other due to the great distance between them, and all secondary nodes only have one antenna. As mentioned earlier, the data exchange is performed via two orthogonal time slots: i) \(\text{SS}_{1}\) and \(\text{SS}_{2}\), at the first time slot send its data to \(\text{SR}_{b}\) which then uses ICT to decode the received data; ii) if \(\text{SR}_{b}\) can correctly decode both \(x_{1}\) and \(x_{2}\), it performs the XOR operation, i.e., \(x_{\oplus}=x_{1}\oplus x_{2}\), and then sends the XOR-ed data \((x_{\oplus})\) to \(\text{SS}_{1}\) and \(\text{SS}_{2}\) at the second time slot. If \(\text{SR}_{b}\) only correctly decodes \(x_{1}\) (or \(x_{2}\)), it will transmit \(x_{1}\) (or \(x_{2}\)) to \(\text{SS}_{2}\) (or \(\text{SS}_{1}\)) at the second time slot. The proposed scheme can be applied to wireless sensor networks and wireless ad hoc networks. For example, in wireless sensor networks, the secondary nodes are sensors while the primary nodes are base stations and/or mobile users in cellular mobile networks. Because of the limited size, the sensor nodes are only equipped with one antenna. Moreover, the sensor networks have to operate on the USS mode to be able to access the bands licensed to the primary nodes. Let \(h_{\text{AB}}\) denote the channel coefficient of the \(\text{A}\rightarrow\text{B}\) link, where \(\text{A}\) is a transmitter and \(\text{B}\) is a receiver, i.e., \(\text{A}\in\{\text{SS}_{1},\text{SS}_{2},\text{SR}_{m},\text{PT}_{u}\}\), \(\text{B}\in\{\text{SS}_{1},\text{SS}_{2},\text{SR}_{m},\text{PR}_{v}\}\), \(\text{PT}_{u}(u=1,2,\ldots,N_{\text{T}})\) denotes the \(u-\) th antenna of PT and \(\text{PR}_{v}(v=1,2,\ldots,N_{\text{R}})\) denotes the \(v-\) th antenna of PR. Then, we denote \(g_{\text{AB}}\) as the corresponding channel gain: \(g_{\text{AB}}=|h_{\text{AB}}|^{2}\), and \(d_{\text{AB}}\) as a link distance between A and B. We can assume that the secondary relays are close to each other, i.e., they are in one cluster. Hence, we can write that \(d_{\text{ASR}_{m}}\overset{{}_{\text{AB}}}{=}d_{\text{ASR}}\) and \(d_{\text{SR}_{m}\text{B}}\overset{{}_{\text{AB}}}{=}d_{\text{SRB}}\), \(\forall\text{A},\text{B},m\). Moreover, we can also assume that the secondary relays are closer to \(\text{SS}_{1}\) than to \(\text{SS}_{2}\) (i.e., \(d_{\text{SS}_{1}\text{SR}}\leq d_{\text{SS}_{2}\text{SR}}\)), and \(\text{SS}_{1}\) is closer to PR than \(\text{SS}_{2}\) (i.e., \(d_{\text{SS}_{1}\text{PR}}\geq d_{\text{SS}_{2}\text{PR}}\)). Figure 1: The DNC TWR model in the proposed underlay CRN. **Remark 1**. : _In the case where \(d_{SS_{1}PR}<d_{SS_{2}PR}\), we simply change the role of \(SS_{1}\) by that of \(SS_{2}\), and vice versa. Then, considering ultra-dense wireless networks [41; 42] where there are a lot of nodes that are between the radio range of \(SS_{1}\) and \(SS_{2}\), they can be considered the potential relays.