## 3 Space Time Block Code (STBC)
### OSTBC System Model
In Figure 4e there is a reduction in the required \(\rm E_{b}/N_{o}\) of about 2 dB when utilizing two antennas (Alamouti STBC) at the transmitting side instead of using one antenna when taking BER \(10^{-2}\) as a comparative point. In addition, 256 QAM performance for both Alamouti and OSTBC is shown in Figure 4e,f, respectively. To conclude, when employing 16 reflecting elements, the utilization of IRS results in a 7 dB decrease in the required \(\rm E_{b}/N_{o}\) when compared to the scenario without IRS. Similarly, with 64 reflecting elements, the required \(\rm E_{b}/N_{o}\) reduced by 13 dB. Remarkably, this improvement remains consistent for all modulation techniques employed, including QPSK, 16 QAM, 64 QAM, and 256 QAM. Table 3 shows the required \(\rm E_{b}/N_{o}\) at BER \(10^{-2}\) for the case of Alamouti and OSTBC for all the modulation schemes. It shows that the required \(\rm E_{b}/N_{o}\) decreases by 7 dB and by 13 dB when deploying the 16 and 64 IRS elements respectively when compared to the non-IRS system for all modulation schemes. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**M\_QAM**} & \multicolumn{3}{c}{**Alamouti**} & \multicolumn{3}{c}{**OSTBC**} \\ \cline{2-7}  & **No IRS** & **N = 16** & **N = 64** & **No IRS** & **N = 16** & **N = 64** \\ \hline
**QPSK** & 8 dB & 1 dB & \(-5\) dB & 6 dB & \(-1\) dB & \(-7\) dB \\ \hline
**16 QAM** & 11 dB & 4 dB & \(-2\) dB & 9 dB & 2 dB & \(-4\) dB \\ \hline
**64 QAM** & 15 dB & 8 dB & 2 dB & 13 dB & 6 dB & 0 dB \\ \hline
**256 QAM** & \(\rm N/A\) & 12 dB & 6 dB & \(\rm N/A\) & 10 dB & 4 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(\rm E_{b}/N_{o}\) for Alamouti and OSTBC at BER \(=10^{-2}\) for different modulation schemes. Figure 4: BER versus \(\rm E_{b}/N_{o}\) (**a**) Alamouti STBC employing 16 QAM scheme (**b**) OSTBC employing 16 QAM scheme (**c**) Alamouti STBC employing 64 QAM scheme (**d**) OSTBC employing 64 QAM scheme (**e**) Alamouti STBC employing 256 QAM scheme (**f**) OSTBC employing 256 QAM scheme. Figure 5 illustrates the BER versus \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) for both Alamouti and OSTBC utilizing the 16 QAM technique using 64 reflecting elements for IRS. OSTBC outperforms Alamouti due to the more diversity the system has in order that the received signal will be recognized correctly more than by the Alamouti technique. This is done via the diversity gain between multiple simultaneous antennas where the data has been sent multiple times. In Alamouti the symbol is sent twice, while in OSTBC (4 \(\times\) 1) the symbol is sent four times. So, the prediction of the symbol will be improved. At BER 10\({}^{-4}\), \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) is 4 dB, and 10 dB when utilizing two antennas (Alamouti 2 \(\times\) 1), and four antennas (OSTBC 4 \(\times\) 1) at the transmitting side, respectively. Thus, the required \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) reduced by 6 dB. The increase of the number of transmitting antennas directly improves symbol detection, resulting in a decrease in BER. This is due to diversity gain. Moreover, the system has been simulated for constant \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) equal to 0 dB while investigating the effect of having different numbers of reflecting elements of the IRS, to evaluate the effect of increasing the number of reflecting surfaces on BER. It is assumed that the IRS is in a square orientation. The number of reflecting elements on one side ranges from 4 to 17, incrementing by 1. Figure 6 demonstrates that increasing the number of reflecting elements leads to an enhancement in detecting the received bits, which leads to less BER in the system. Moreover, when employing a higher modulation order, the BER increases as a result of the increased challenge in detecting the received bits. Table 4 shows BER for different reflecting elements and modulation schemes at \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) equal to zero.