## 4 Numerical Results  
For simplicity, this study assumed the coupled IoT relays are closed to each other. Therefore, the distances from IoT hub \(S\) to coupled relays \(R_{1}\) and \(R_{2}\) are \(d_{R_{1}}=d_{R_{2}}=10\) m. The IoT network shows the number of \(N=3\) IoT devices. Distances from coupled IoT relays to IoT device \(D_{n}\) are equally (\(d_{R_{1},D_{n}}=d_{R_{2},D_{n}}\) for \(n\in N\)). In this section, the paper conducts the analysis and Monte Carlo simulation results. The outcomes presented in this paper are given by parameters as shown in Table 2.  
The study examined the impact of crucial factors, i.e., PS factor \(\lambda_{R_{r}}\) and pre-defined IoT devices' threshold \(\mathcal{R}\). Figure 2(a) plotted the impact of PS factor \(\lambda_{R_{r}}\) onto OP performance at coupled IoT relays \(R_{r}\) and IoT devices by fixed pre-defined bit-rate threshold \(\mathcal{R}=0.1\,\mathrm{b/s/Hz}\). Allocated unsuitability of PS factor \(\lambda_{R_{r}}\) leads to OP performance at either coupled IoT relays or IoT devices tending to one. On the other hand, Figure 2(b) also sketched OP performance at coupled IoT relays and IoT devices; however, considering the impact of pre-defined bit-rate threshold \(\mathcal{R}\). A lower pre-defined bit-rate threshold \(\mathcal{R}\) leads to better OP performance (\(OP\to 0\)), however, lower system throughput (\(throughput=(1-OP)\mathcal{R}\)). Observing Figure 2(b), it is worth noticing that if the pre-defined bit-rate threshold \(\mathcal{R}<0.5\,\mathrm{b/s/Hz}\) and SNR \(\rho\to\infty\), the OP at all IoT nodes then tends to \begin{table}
\begin{tabular}{l l} \hline \hline Number of devices & \(N=3\) \\ Distances & \(d_{S,R_{r}}=10\) m, \(d_{R,D_{1}}=5\) m, \(d_{R,D_{2}}=7\) m, \(d_{R,D_{3}}=12\) m, \(d_{R,E}=4\) m \\ Path-loss exponent & \(\epsilon=4\) \\ Channel gains & \(\sigma_{S,R_{r}}=0.01\), \(\sigma_{R,D_{1}}=0.04\), \(\sigma_{R,D_{2}}=0.0204\), \(\sigma_{R,D_{3}}=0.0069\), \(\sigma_{R,E}=0.0625\) \\ Fixed bit-rate thresholds & \(\mathcal{R}=\mathcal{R}_{1}=\mathcal{R}_{2}=\mathcal{R}_{3}=0.1\,\mathrm{b/s/Hz}\) \\ Optimal bit-rate thresholds & \(\mathcal{R}=0.499\,\mathrm{b/s/Hz}\) as given by (54) with tolerance factor for \(v=0.001\) \\ Fixed PS factor & \(\lambda_{R_{r}}=0.4\) \\ PS factor & \(\lambda_{R_{r}}=0.3056\) as given by (55) \\ PA factors & \(\alpha_{1}=0.1667\), \(\alpha_{2}=0.3333\), and \(\alpha_{3}=0.5\) as given by [21; 37] \\ SNRs \(\rho\) & \(\{0,\ldots,50\}\) dB \\ Status of jamming signal & \(\delta=1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of parameters (denoted \(r=\{1,2\}\)). zero. on the other hand, if pre-defined bit-rate threshold \(\mathcal{R}\geq 0.5\,\mathrm{b/s/Hz}\), the OP at all IoT nodes then always tends to one since \(\mathcal{R}=0.5\,\mathrm{b/s/Hz}\) is the ceiling bit-rate threshold. Figure 3(a) presented OP performance at coupled IoT relays and IoT devices, where fixed pre-defined bit-rate threshold \(\mathcal{R}=0.1\,\mathrm{b/s/Hz}\) and PS factor \(\lambda_{R_{1}}=\lambda_{R_{2}}=0.4\). The OP performance of IoT devices are approximate and tend to zero when \(\mathrm{SNR}\,\rho\to\infty\). Figure 3(b) also plotted OP performance of coupled IoT coupled relays and IoT devices; however, where pre-defined bit-rate threshold \(\mathcal{R}=0.499\) given by (54) and PS factor \(\lambda_{R_{r}}\) as given by (55). Although OP performance of IoT devices also tended to zero as shown in Figure 3(b); however, the OP performance of IoT devices are worse than the obtained results as shown in Figure 3(a). Since the pre-defined bit-rate threshold \(\mathcal{R}=0.499\,\mathrm{b/s/Hz}\) in Figure 3(b) is greater than the pre-defined bit-rate threshold \(\mathcal{R}=0.1\,\mathrm{b/s/Hz}\) in Figure 3(a), therefore, SNR in Figure 3(b) is higher SNR in Figure 3(a). Figure 4: OP performance at IoT relays and devices with (**a**) fixed PS factor \(\lambda_{R_{r}}=0.4\) and fixed bit-rate threshold \(\mathcal{R}=0.1\), (**b**) optimized bit-rate threshold and PS factors.