## 4 Results and Discussion  
The simulations are carried out in the MATLAB R2022b environment and the simulation parameters considered for the performance analysis of the proposed IRS-assisted bidirectional FD-MTC system are shown in Table 1. In the proposed IRS-assisted bidirectional FD-MTC system, it is assumed that IRS is placed halfway between the two source nodes \(S_{1}\) and \(S_{2}\); hence, both outage probability and BER performance analysis behave similarly for both source nodes \(S_{n},n=1,2\). The MC simulations of the outage performance for the IRS-assisted bidirectional FD-MTC system with a different number of reflecting elements (\(N=16,32,64\)) in the Rayleigh fading environment is shown in Figure 5 and it is verified using the derived analytical expression. For the target outage probability value of \(10^{-3}\) in Figure 5, there is \(\approx\)6 dB improvement in the proposed system model by doubling the number of meta surface elements \(N\) in IRS. From Equation (19), it is inferred that, if the ratio \(\frac{X_{Tbl}}{\rho_{S_{n}}}\) is held constant, the outage probability decreases with respect to the number of meta surface elements \(N\) in IRS. Similarly, if the value of \(N\) is fixed, an increase in the ratio of \(\frac{X_{Tbl}}{\rho_{S_{n}}}\) causes a decrease in the outage probability. Therefore, increasing the \(\frac{X_{Tbl}}{\rho_{S_{n}}}\) leads to an improvement in the outage performance for a fixed value of meta surface elements \(N\). The comparison of the outage probability for IRS-assisted bidirectional FD-MTC system with HD-MTC system with various values of meta surface reflecting elements (\(N=16,32\)) and \(SI=5\) dB, 10 dB, 15 dB, and 20 dB are shown in Figures 6-9. From Figures 6-9, it is observed that, when the \(SI\) at the source node is increased from 5 dB with an incremental step size of 5 dB up to 15 dB, the outage probability value of IRS-assisted bidirectional FD-MTC system increases and gets closer to the performance of HD-MTC system. For 20 dB \(SI\), the outage probability value degrades more than the HD-MTC system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline \(N\) (number of meta surface elements in IRS) & \(16,32,64\) \\ \hline Self-Interference (SI) & 5 dB, 10 dB, 15 dB, 20 dB \\ \hline SNR in dB & \(-30\) to \(10\) \\ \hline Required data rate & \(2\) bps\(/\) Hz \\ \hline MC Simulation & \(5000\) \\ \hline Power transmitted & \(50\) mW \\ \hline \(C_{0}\) & \(-30\) dB \\ \hline The path loss exponent \(\zeta\) & \(2\) \\ \hline \multirow{3}{*}{Distance between IRS and \(S_{1}\) in meters} & Near case: \(10,20,30\) \\  & Far case: \(90,80,70\) \\  & Equal case: \(50\) \\ \hline \multirow{3}{*}{Distance between IRS and \(S_{2}\) in meters} & Near case: \(10,20,30\) \\  & Far case: \(90,80,70\) \\  & Equal case: \(50\) \\ \hline Phases of 1-bit discrete phase shifter & \(0\), \(\pi\) \\ \hline Phases of 2-bits discrete phase shifter & \(0\), \(\pi/2\), \(\pi\), \(3\pi/2\) \\ \hline Phases of 3-bits discrete phase shifter & \(0\), \(\pi/4\), \(\pi/2\), \(3\pi/4\), \(\pi\), \(5\pi/4\), \(3\pi/2\), \(7\pi/4\) \\ \hline Target outage probability & \(10^{-3}\) \\ \hline Target BER & \(10^{-6}\) \\ \hline Noise variance (\(N_{0}\)) & Normalized to \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 5: Outage probability for IRS-assisted bidirectional FD-MTC system. Figure 6: Outage probability of IRS-assisted bidirectional HD vs. FD MTC system at SI = 5 dB. Figure 7: Outage probability of IRS-assisted bidirectional HD vs. FD MTC system at SI = 10 dB. The BER performance of the IRS-assisted bidirectional FD-MTC system with different numbers of meta surface reflecting elements (\(N=16,32,\,64\)) in a Rayleigh fading environment is shown in Figure 10. From Equation (27), it is inferred that, if the ratio \(a_{pt}=\frac{\sigma_{m}^{2}}{N_{0}}\), is held constant, the BER decreases with respect to the number of meta surface elements \(N\) in IRS.