## 2 System Model
Here, we also assume that the CSI estimation at PR is perfect._  
It is worth noting that various diversity transmitting/receiving techniques such as TAS/maximal ratio combining (MRC), maximal ratio transmission (MRT)/SC, and MRT/MRC can be used to enhance the OP performance for the primary network. However, the MRT and MRC techniques require both the amplitude and phase information of the channel coefficients. As a result, the implementation of the MRT and MRC techniques is more complex than that of TAS and SC. Moreover, as with using the MRT technique, PT has to use all its transmit antennas, which can cause more co-channel interference on the secondary network. Next, for \(\text{SS}_{1}\) and \(\text{SS}_{2}\), the SINRs obtained for decoding \(x^{*}\) can be formulated, respectively, as  
\[\Omega_{\rm PT_{u}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm PTB}, \ \Omega_{\rm APR_{r}}\stackrel{{\Delta}}{{=}}\Omega_{\rm APR},\ \Omega_{\rm ASR_{m}}\stackrel{{\Delta}}{{=}}\Omega_{\rm ASR},\ \Omega_{\rm SR_{m}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm SRB},\ \forall u,v,m. \tag{2}\]0  
We note from (18) that when \(x^{*}\equiv x_{1}\), this means that \(\text{SR}_{b}\) only sends \(x_{1}\) to \(\text{SS}_{2}\) at the second time slot, and hence \(\text{SS}_{1}\) is the outage in this case. When \(x^{*}\equiv x_{\oplus}\), the secondary source \(\text{SS}_{i}(i=1,2)\) attempts to decode \(x_{\oplus}\) so that it can obtain the desired data by using the XOR rule, i.e., \(x_{i}\oplus x_{\oplus}=x_{j}\), where \(j=1,2\) and \(j\
eq i\). This paper evaluates OP for the primary and secondary networks. For the primary network, OP in the first and second time slots can be formulated, respectively, as  
\[\Omega_{\rm PT_{u}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm PTB}, \ \Omega_{\rm APR_{r}}\stackrel{{\Delta}}{{=}}\Omega_{\rm APR},\ \Omega_{\rm ASR_{m}}\stackrel{{\Delta}}{{=}}\Omega_{\rm ASR},\ \Omega_{\rm SR_{m}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm SRB},\ \forall u,v,m. \tag{2}\]1  
where \(\theta_{\text{PH}}\) is a pre-determined threshold of the primary network. For the secondary network, we consider OP at \(\text{SS}_{1}\) and \(\text{SS}_{2}\). At first, the OP of \(\text{SS}_{1}\) is formulated as  
\[\Omega_{\rm PT_{u}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm PTB}, \ \Omega_{\rm APR_{r}}\stackrel{{\Delta}}{{=}}\Omega_{\rm APR},\ \Omega_{\rm ASR_{m}}\stackrel{{\Delta}}{{=}}\Omega_{\rm ASR},\ \Omega_{\rm SR_{m}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm SRB},\ \forall u,v,m. \tag{2}\]2  
where \(\theta_{\text{SH}}\) is a pre-determined threshold of the secondary network. In (20), \(\text{Pr}\big{(}\psi_{\text{SR}_{b}\text{,}x_{1}}\geq\theta_{\text{SH}},\psi_{ \text{SR}_{b}\text{,}x_{2}}\geq\theta_{\text{SH}},\varphi_{\text{SS}_{1}}\geq \theta_{\text{SH}}\big{)}\) is the probability that \(\text{SS}_{1}\) can correctly receive the data \(x_{2}\), i.e., \(x_{2}\) is successfully obtained by \(\text{SR}_{b}\) at the first time slot \(\big{(}\psi_{\text{SR}_{b}\text{,}x_{1}}\geq\theta_{\text{SH}},\psi_{\text{SR} _{b}\text{,}x_{2}}\geq\theta_{\text{SH}}\big{)}\), and the transmission from \(\text{SR}_{b}\) to \(\text{SS}_{1}\) at the second time slot is successful \(\big{(}\varphi_{\text{SS}_{1}}\geq\theta_{\text{SH}}\big{)}\). Then, the OP of \(\text{SS}_{2}\) can be formulated as  
\[\Omega_{\rm PT_{u}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm PTB}, \ \Omega_{\rm APR_{r}}\stackrel{{\Delta}}{{=}}\Omega_{\rm APR},\ \Omega_{\rm ASR_{m}}\stackrel{{\Delta}}{{=}}\Omega_{\rm ASR},\ \Omega_{\rm SR_{m}B}\stackrel{{\Delta}}{{=}}\Omega_{\rm SRB},\ \forall u,v,m. \tag{2}\]3  
where \(\text{Pr}\big{(}\psi_{\text{SR}_{b}\text{,}x_{1}}\geq\theta_{\text{SH}},\varphi_ {\text{SS}_{2}}\geq\theta_{\text{SH}}\big{)}\) is the probability that \(x_{1}\) is successfully decoded by \(\text{SR}_{b}\) and \(\text{SS}_{2}\) at the first and second time slots, respectively.