## 4 Results and Discussions
We compare our results with the baseline Stackelberg and the power-control-based algorithms in [46; 48]. The optimum values of \(\alpha\) and \(\beta\) are determined by the source, while the optimum jammer power values are determined by the jammer, as seen in the Stackelberg leader-follower game in Figure 3. In the non-relaying scheme of CJST [48], both the secrecy rate and utility rate would improve as the number of CJs increases. However, when relaying is invoked in our UR-MCJST scenario, it is interesting to see from Figure 6 that as \(N\) increases, the secrecy rate drops. Hence, the CJST scenario is not desirable when an untrusted relay is involved. By contrast, our proposed UR-MCJTDT scenario works well in the untrusted relaying system, where the secrecy rate improves as \(N\) increases, as seen in Figure 6. However, it appears that we only need \(N=3\) CJs in our case, when the SNR used is 10 dBm. We can also see from Figure 6 that our proposed algorithms outperform the baseline Stackelberg in [46] and the power control algorithm in [48]. The optimized \(\alpha^{*}\) and \(\beta^{*}\) chosen by the source, as well as the average optimized CJ power of all \(N\) CJs given by \(P^{*}_{CJ}=\frac{1}{N}\sum_{i}^{N}P^{*}_{CJ_{i}}\), are shown in Figures 6 and 7. For example, when \(N=2\), we have \(\alpha^{*}=0.93\), \(\beta^{*}=6\) and \(\tilde{P}^{*}_{CJ}=0.41\) (mWatts) for the orthogonal scenario. Furthermore, as seen in Figure 7, the per user utility rates of the UR-MCJTDT and UR-MCJST scenarios are similar. However, the CJs in the UR-MCJTDT scenario can achieve the same utility rate with less power, when compared to the UR-MCJST scenario. For example, as seen in Figure 7 when \(N=3\), the average CJ power is \(P_{CJ}^{*}=0.18\) (mWatts) and \(\bar{P}_{CJ}^{*}=0.93\) (mWatts) for the UR-MCJST and UR-MCJTDT scenarios, respectively. We also compared the utility rate results with the baseline Stackelberg and the power-control-based algorithms in [46; 48]. Here, we can see that the per user utility rate increases with increasing available \(CJs\) in the case of the baseline algorithms, but the overall utility rate will be higher in the proposed scheme, as we have employed multiple \(CJs\), while the baseline scheme chooses a better \(CJ\) among the available \(CJs\). Figure 4: UR-MCJST scenario with specified locations. \(S\) is at \((0,0)\), \(R\) is at \((25,25)\) and \(D\) is at \((50,50)\) while \(CJ_{1}\) is mobile, \(CJ_{2}\) is at \((22,43)\) and \(CJ_{3}\) is at \((26,50)\), \(\alpha=0.65\) and \(\beta=1\). (**a**) The secrecy rate with reference to the location of the mobile jammer. (**b**) Average utility rate for the mobile jammer. Figure 5: UR-MCJTDT scenario with specified locations. \(S\) is at \((0,0)\), \(R\) is at \((25,25)\) and \(D\) is at the location \((50,50)\) while \(C_{1}\) is mobile, \(C_{2}\) is at \((22,43)\) and \(C_{3}\) is at \((26,50)\), \(\alpha=0.65\) and \(\beta=1\). (**a**) The secrecy rate with reference to the location of mobile Jammer. (**b**) Average utility rate for the mobile jammer. Figure 6: Optimized secrecy rate comparison with the baseline Stackelberg in [46] and the power control algorithm in [48]. Figure 7: Optimized utility rate per user comparison with the baseline Stackelberg in [46] and the power control algorithm in [48].