## 3 Space Time Block Code (STBC)
### OSTBC System Model
On the other hand, the effect of having different sizes of reflecting elements is investigated by deploying two scenarios (16 and 64 IRS reflecting elements). This will help to assess the impact of the number of serving IRS reflecting elements versus the obtained BER. From the perspective of the wireless channel model, the Rayleigh fading channel is used throughout the whole work that is presented in this paper. Table 2 shows all the simulation parameters that are adjusted throughout all the simulations in this paper. Figure 3a,b shows BER versus \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) for both Alamouti and OSTBC, respectively. Figure 3a validates that the computed QPSK BER of Single Input Single Output (SISO) and Alamouti STBC 2 \(\times\) 1 is the same as the previously published work in [25]. \begin{table}
\begin{tabular}{c c} \hline
**Simulation Parameters** & **Value(s)** \\ \hline Modulation scheme & QPSK, 16-QAM, 64-QAM, 256-QAM \\ \hline Number of transmitting antennas (\(N_{i}\)) & 2 (Alamouti), 4 (OSTBC) \\ \hline Number of receiving antennas & 1 \\ \hline Number of simulated bits & \(10^{8}\) \\ \hline Channel models & Rayleigh flat fading, with \(\mathcal{CN}\) (0, 1) \\ \hline Number of IRS elements (N) & 16, 64 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 3: BER versus \(\text{E}_{\text{b}}/\text{N}_{\text{o}}\) for the QPSK modulation scheme (**a**) Alamouti STBC 2 \(\times\) 1 deployed (**b**) OSTBC 4 \(\times\) 1 deployed. In Figure 3a, as a point of comparison BER \(10^{-2}\) is taken. \(\rm E_{b}/N_{o}\) is 14 dB, 8 dB, 1 dB, \(-5\) dB for SISO, Alamouti STBC without IRS, Alamouti STBC with 16 reflecting elements, and Alamouti STBC with 64 reflecting elements, respectively. Furthermore, it has been established that an enhancement in error performance can be attained through the use of IRS and by increasing the number of reflecting elements in the IRS. In Figure 3b four transmitting antennas are used instead of two transmitting antennas, as in the case of Alamouti in Figure 3a. As a result of increasing the number of transmitting antennas, the BER decreases. This is due to the diversity gain between multiple simultaneous antennas where the data has been sent multiple times. When increasing the number of reflecting elements, the BER decreases. At BER \(10^{-2}\), \(\rm E_{b}/N_{o}\) is 14 dB, 6 dB, \(-1\) dB, \(-7\) dB for SISO, OSTBC without IRS, OSTBC with 16 reflecting elements, and OSTBC with 64 reflecting elements, respectively. Different from the previous published work, higher modulation schemes are deployed. Moreover, deploying different IRS reflecting elements is used to reduce the number of transmitting antennas to avoid system complexity at the gNodeB. The BER performance versus \(\rm E_{b}/N_{o}\) for different numbers of IRS reflecting elements and varying the modulation scheme used for both Alamouti 2 \(\times\) 1 and OSTBC 4 \(\times\) 1 is shown in Figure 4.

Figure 4a,b shows the error performance of the proposed system for Alamouti and OSTBC using 16-QAM as the modulation scheme, respectively. To demonstrate the impact of the improvement obtained via the implementation of IRS, the BER is taken to be \(10^{-2}\) for various systems (for the purpose of comparison). It was determined that the required \(\rm E_{b}/N_{o}\) decreases by approximately 7 dB and 13 dB when using an IRS with 16 and 64 reflecting elements, respectively, in comparison to the proposed system without using IRS. Thus, the deployment of IRS enhances the prediction probability of the received symbol. This is due to the gain of constructive combination of multiple reflective signals from different IRS elements, this is achieved instead of having a more complex system. The complexity analysis will be carried out in our future work. Figure 4c,d shows BER versus \(\rm E_{b}/N_{o}\) for Alamouti and OSTBC using 64 QAM.