# A Partitioned IRS-Aided Transmit SM Scheme for Wireless Communication
## 5 Simulation Results  
In this section, the analytical and numerical results of the BER performance of the proposed PIRS-TSM scheme with different system configurations are demonstrated through Monte Carlo simulations. Furthermore, the comparisons among the proposed PIRS-TSM, unpartitioned IRS-aided transmit SM (IRS-TSM), PIRS-TSSK [20], PIRS-TGSSK [22], and PIRS-FGSSK [22] schemes are conducted to demonstrate the effectiveness of IRS partitioning and symbols carrying in enhancing system performances. To ensure fair performance comparisons, this study evaluates the BER of different schemes under the same SE. Meanwhile, in order to facilitate the configuration of \(N_{t}\) and \(M\) under the same SE and evaluate \begin{table}
\begin{tabular}{|c|c|c|} \hline
**Scheme** & **RMs** & **RAs** \\ \hline PIRS-TSSK & \((8N-\frac{7N}{N_{t}}+3)N_{t}\) & \((6N-\frac{5N}{N_{t}})N_{t}\) \\ \hline PIRS-TGSSK & \((8N-\frac{7N}{N_{t}}+4)N_{t}\) & \((6N-\frac{5N}{N_{t}})N_{t}+C\) \\ \hline PIRS-TSM & \((12N-\frac{9N}{N_{t}}+2)N_{t}M\) & \((8N-\frac{7N}{N_{t}})N_{t}M\) \\ \hline \end{tabular}
\end{table} 
Table 1: Detection complexity analysis summary. Figure 2: Comparison of computational complexity between PIRS-TGSSK, PIRS-TSSK, and PIRS-TSM (N = 128, SE = 4 bit/s/Hz). the impact of different SM configurations on PIRS-TSM system performance, we adopt SE = 4 bit/s/Hz for simulations. The system performances are compared by the SNR values (X-axis) of schemes at a certain BER value (Y-axis). Figure 3 shows the simulated and theoretical BER performance for various values of \(N\) (64, 128, 256), with the configuration of \(N_{t}=2\) and \(M=8\) and \(N_{t}=8\) and \(M=2\), respectively. As seen in Figure 3, as the number of reflecting elements increases, the BER performance of the system is superior, demonstrating the improvement of the channel propagation environment caused by the phase shift of IRS. Moreover, the theoretical results are very close to the experimental results in the area of high SNR. For the same N, the BER performance of the configuration with \(N_{t}=2\) and \(M=8\) outperforms that of \(N_{t}=8\) and \(M=2\), and its theoretical results show closer agreement with experimental data in the low-SNR region. Figure 4 demonstrates the agreement between theoretical and experimental BER performance at two SE examples. First, SE = 4 bit/s/Hz with configurations \(N_{t}=8\) and \(M=2\); \(N_{t}=4\) and \(M=4\); and \(N_{t}=2\) and \(M=8\). Second, SE = 6 bit/s/Hz with configurations \(N_{t}=8\) and \(M=8\); \(N_{t}=4\) and \(M=16\); and \(N_{t}=2\) and \(M=32\). The legend parameters are set in the format (SE, \(N_{t}\), \(M\)). It can be seen that the theoretical results fit the simulation results very closely. In addition, lower \(N_{t}\) with higher \(M\) configurations (e.g., (4, 2, 8) (6, 2, 32) vs. (4, 8, 2)(6, 8, 8)) achieve superior BER performance. The reason is that only one group of reflecting elements completely cancels out the channel phases in our IRS partitioning method. Therefore, with the same total number of reflecting elements, the more transmit antennas there are, the more groups are divided on the IRS, and the fewer reflecting elements each group has, leading to some degradation of the IRS beamforming. Quantitatively, as seen in Figure 4, when BER = \(10^{-3}\), PIRS-TSM at SE = 4 bit/s/Hz with \(N_{t}=2\), \(M=8\) contributes approximately 2.5 dB SNR gain over \(N_{t}=4\), \(M=4\) and 7.5 dB SNR gain over \(N_{t}=8,M=2\). When BER = \(10^{-2}\) and SE is 6 bit/s/Hz, PIRS-TSM with \(N_{t}=2\), \(M=32\) obtains about 7.5 dB SNR gain over \(N_{t}=4\), \(M=16\) and 14.5 dB SNR gain over \(N_{t}=8,M=8\). This shows that as the SE increases, the PIRS-TSM in the configuration with fewer antennas exhibits a more pronounced performance advantage. Figure 3: Theoretical and computer simulation results for PIRS-TSM with different \(N\) when SE is 4 bit/s/Hz (\(N_{t}=2\), \(M=8\) and \(N_{t}=8,M=2\)).