## 3 Space Time Block Code (STBC)
### OSTBC System Model
In the case of QPSK, by increasing the number of reflecting elements from 49 to 100, the BER decreases by approximately a decade, and by increasing the number of reflecting elements more than 100, the BER decreases by around a decade. Moreover, for 100 reflecting elements at fixed \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) equal to zero, the BER increases by almost a decade for different modulation schemes. This is due to the challenge of detecting the received bits. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline M\_QAM\_N & **49** & **100** & **144** & **256** & **289** \\ \hline QPSK & \(2.50\times 10^{-4}\) & \(2.03\times 10^{-5}\) & \(5.29\times 10^{-6}\) & \(4.00\times 10^{-7}\) & \(2.90\times 10^{-7}\) \\ \hline
**16 QAM** & \(2.70\times 10^{-3}\) & \(3.40\times 10^{-4}\) & \(1.05\times 10^{-4}\) & \(1.37\times 10^{-5}\) & \(8.64\times 10^{-6}\) \\ \hline
**64 QAM** & \(1.80\times 10^{-2}\) & \(4.40\times 10^{-3}\) & \(1.79\times 10^{-3}\) & \(3.40\times 10^{-4}\) & \(2.31\times 10^{-4}\) \\ \hline
**256 QAM** & \(5.80\times 10^{-2}\) & \(2.68\times 10^{-2}\) & \(1.56\times 10^{-2}\) & \(5.20\times 10^{-3}\) & \(4.00\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: OSTBC BER for different reflecting elements and modulation schemes at \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) = 0 dB. Figure 5: BER for Alamouti STBC and OSTBC (4 \(\times\) 1) using the 16 QAM scheme. Figure 7 shows the BER versus the number of reflecting elements for Alamouti and OSTBC at \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) 0 dB using QPSK. BER decreases by the increase of the reflecting elements of the IRS. The BER is 4 \(\times\) 10\({}^{-7}\), 10\({}^{-4}\) for OSTBC, and Alamouti, respectively, when using 256 reflecting elements. OSTBC, the system with greater diversity, outperforms Alamouti, as it increases the precision of recognizing the received signal compared to the Alamouti technique. Thus, the number of antennas used at the transmitting side is directly proportional with the accuracy of the system. Figure 8a,b shows the BER performance for Alamouti and OSTBC versus the number of reflecting elements, respectively, for different \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) using QPSK as a modulation scheme as a proof of concept that the BER decreases by increasing of \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\). Moreover, by boosting the energy of the received signal via an increase in the number of reflecting elements of the IRS, BER decreases. Figure 6: BER performance versus the number of reflecting elements at \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) equal to 0 dB. Figure 7: BER performance versus the number of reflecting elements. Figure 9a,b shows the BER performance for Alamouti and OSTBC as a function of the number of reflecting elements, respectively, for different values of \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) using 256 QAM as a modulation scheme. BER decreases by increasing the reflecting elements. ## 5 Conclusions

In this paper, an IRS-assisted MISO system using the OSTBC scheme is studied. The performance of the proposed system was assessed by conducting simulations with different operation scenarios, including the number of transmitting antennas, the number of IRS reflecting elements, and the higher modulation schemes. The simulation outcomes provide evidence that the combination of OSTBC and IRS leads to notable improvements in terms of BER. The utilization of IRS with 16 and 64 reflecting elements yields a significant 7 dB and 13 dB reduction in the required \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) when compared to the non-IRS scenario. This improvement remains consistent across various modulation schemes, including QPSK,

Figure 8: BER for the QPSK modulation scheme versus the number of IRS reflecting elements (**a**) Alamouti STBC \(2\times 1\) deployed (**b**) OSTBC \(4\times 1\) deployed at different \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\).