## 3 Performance Evaluation
### Average Number of Transmission Times (\(T_{avg}\))  
At first, we can see that the Cov-Scm scheme always uses \(2N_{\text{max}}\) transmission times of the FC packets for each successful data exchange, i.e., \(T_{\text{avg}}^{\text{Cov-Scm}}=2N_{\text{max}}\). For Mod-Scm, we again assume that \(\text{SS}_{i}\) transmits its data first, and it stops its transmission after \(N_{i}(N_{i}\leq N_{\text{max}})\) attempts. By re-using Equation (22), we obtain the probability that \(\text{SS}_{j}\) sufficiently collects \(H_{\text{min}}\) packets \(p_{i}\) after \(N_{i}\) transmission times of \(\text{SS}_{i}\) as  
\[\text{Pr}\big{(}r_{j}=H_{\text{min}}\big{|}N_{i}\big{)}=C_{N_{i}-1}^{H_{\text{ min}}-1}(1-\Phi_{i})^{H_{\text{min}}}(\Phi_{i})^{N_{i}-H_{\text{min}}}. \tag{28}\]  
Next, let \(N_{j}\) denote the number of transmission times of \(\text{SS}_{j}\), where \(H_{\text{min}}\leq N_{j}\leq 2N_{\text{max}}-N_{i}\). Also, the probability that \(\text{SS}_{i}\) collects enough \(H_{\text{min}}\) packets \(p_{j}\) after \(N_{j}\) transmission times of \(\text{SS}_{j}\) is written as  
\[\text{Pr}\big{(}r_{i}=H_{\text{min}}\big{|}N_{j}\big{)}=C_{N_{j}-1}^{H_{\text{ min}}-1}\big{(}1-\Phi_{j}\big{)}^{H_{\text{min}}}(\Phi_{j})^{N_{j}-H_{\text{min}}}. \tag{29}\]  
Now, we can formulate the average number of transmission times of two sources per successful data exchange in Mod-Scm as  
\[T_{\text{avg}}^{\text{Mod-Scm}}=\frac{\sum\limits_{N_{i}=H_{\text{min}}}^{N_{ \text{max}}}\sum\limits_{N_{j}=H_{\text{min}}}^{2N_{\text{max}}-N_{i}}\big{(} N_{i}+N_{j}\big{)}\text{Pr}\big{(}r_{j}=H_{\text{min}}\big{|}N_{i}\big{)}\text{Pr} \big{(}r_{i}=H_{\text{min}}\big{|}N_{j}\big{)}}{\Big{(}1-\text{OP}_{1}^{\text {Mod-Scm}}\Big{)}\Big{(}1-\text{OP}_{2}^{\text{Mod-Scm}}\Big{)}}, \tag{30}\]  
where \(\big{(}N_{i}+N_{j}\big{)}\) is the total number of transmission times of two sources in Mod-Scm, and \(\Big{(}1-\text{OP}_{1}^{\text{Mod-Scm}}\Big{)}\Big{(}1-\text{OP}_{2}^{\text {Mod-Scm}}\Big{)}\) is the probability that the data exchange between two sources is successful. Substituting Equations (27)-(29) into Equation (30), we obtain an expression of \(T_{\text{avg}}^{\text{Mod-Scm}}\) as \(T_{\text{avg}}^{\text{Mod-Scm}}=A/B\), where  
\[A=\sum\limits_{N_{i}=H_{\text{min}}}^{N_{\text{max}}}\sum\limits_{N_{j}=H_{ \text{min}}}^{2N_{\text{max}}-N_{i}}\big{(}N_{i}+N_{j}\big{)}\Bigg{[} \begin{array} []{c}C_{N_{i}-1}^{H_{\text{min}}-1}(1-\[PERSON]_{i})^{H_{\text{min}}}(1-\[PERSON]_{i}) ^{N_{i}-H_{\text{min}}}\\ \times C_{N_{j}-1}^{H_{\text{min}}-1}\big{(}1-\[PERSON]_{j}\big{)}^{H_{\text{min}}} \big{(}\[PERSON]_{j}\big{)}^{N_{j}-H_{\text{min}}}\end{array} \Bigg{]}. \tag{31}\]  
\[B=1-\Bigg{[}1-\Bigg{[}1-\Bigg{.}\Bigg{.}\Bigg{. Figure 2 illustrates the probability of the unsuccessful transmission of the packet \(p_{i}\) as a function of \(\Delta\big{(}\Delta=P_{\text{SB}}/\sigma_{0}^{2}\big{)}\) in dB with \(x_{\text{SB}}=0.7\) and \(\alpha=0.35\). As seen, both \(\Phi_{1}\) and \(\Phi_{2}\) decrease as \(\Delta\) increases. This is due to the fact that increasing \(\Delta\) also increases the transmit power of SS\({}_{1}\) and SS\({}_{2}\). Additionally, \(\Phi_{1}\) and \(\Phi_{2}\) with \(K=5\) are lower than those with \(K=3\), which is due to the improved quality of the SS\({}_{i}\)\(\rightarrow\) SS\({}_{j}\) links at higher values of \(K\). We also observe from Figure 2 that \(\Phi_{2}\) is lower than \(\Phi_{1}\). This is because SS\({}_{2}\) is closer to SB than SS\({}_{1}\), resulting in a higher average transmit power for SS\({}_{2}\) as compared to SS\({}_{1}\). Figure 3 presents \(\Phi_{i}\) as a function of the fraction of time (\(\alpha\)) allocated for the EH operation. The system parameters in this figure are set to \(\Delta=15\) (dB) and \(K=4\). We can see that both \(\Phi_{1}\) and \(\Phi_{2}\) change significantly with variations in \(\alpha\). It is straightforward that with very low values of \(\alpha\), the transmit power of SS\({}_{i}\) is also low, resulting in the low channel capacity and high \(\Phi_{i}\).