## 4 Simulation Results and Analysis
Furthermore, a similarity is observed in the system performance of the Baseline Scheme 1, Baseline Scheme 2, and Baseline Scheme 3 algorithms. However, when \(N=64\), the proposed AO-EE algorithm surpasses them, achieving approximately 12.41% higher system energy efficiency. Comparing the proposed AO-EE algorithm with the NO-IRS and Random Phase schemes, the system energy efficiency is improved by approximately 35.26% and 37.96%, respectively. Hence, the proposed AO-EE algorithm strikes a favorable balance between computational complexity and system energy efficiency. Figure 2: EE versus the number of IRS elements. Figure 3 presents the relationship between the BS transmit power and the system energy efficiency for different algorithms with \(M=32\) and \(N=64\). It can be observed that, as the BS transmit power increases, the system energy efficiency gradually improves. This improvement arises because the BS transmit power affects the range of values for BS transmit beamforming. However, due to saturation effects, when the BS transmit power reaches a certain threshold, further increasing the power will lead to a plateau in the system energy efficiency. Under the same BS transmit power, the proposed AO-EE algorithm outperforms the baseline schemes in terms of achieving higher system energy efficiency. Furthermore, the performances of the Random Phase and NO-IRS schemes show few differences from each other. Therefore, for IRS-assisted HST communication systems, optimizing the IRS phase shift is essential to enhancing the system energy efficiency. In conclusion, Figure 3 demonstrates that increasing the BS transmit power can lead to improved system energy efficiency. The proposed AO-EE algorithm consistently achieves better performance than the baseline schemes. Additionally, optimizing the IRS phase shift is crucial for enhancing the energy efficiency of IRS-assisted HST communication systems. Figure 4 illustrates the relationship between the number of BS antennas (M) and the system energy efficiency for different algorithms, with \(N=64\) and \(P_{\text{max}}=42\) dBm. It can be observed that, as the number of BS antennas increases, the system energy efficiency gradually improves. This improvement is attributed to the higher array gain achieved when there are more BS antennas, leading to increased system energy efficiency. With the same number of BS antennas, the proposed AO-EE algorithm consistently outperforms the baseline schemes in terms of achieving higher system energy efficiency. Furthermore, the energy efficiency of the IRS-assisted system surpasses that of the NO-IRS scheme, validating the effectiveness of deploying IRS in HST communication systems. In conclusion, Figure 4 demonstrates that increasing the number of BS antennas results in improved system energy efficiency, owing to the higher diversity gain obtained with more antennas. The proposed AO-EE algorithm consistently outperforms the baseline schemes, and the deployment of IRS in HST communication systems proves to be effective in enhancing energy efficiency. Figure 3: EE versus maximum transmit power \(P_{\text{max}}\). Figure 5 illustrates the variation in system energy efficiency with the number of IRS reflecting elements for \(M=32\) using the proposed AO-EE algorithm at different transmit powers. It can be observed that the three curves exhibit the same trend: as the number of IRS elements increases, the system energy efficiency also improves for different BS transmit powers. Furthermore, when operating with the same number of IRS reflecting elements, the system energy efficiency increases with the growth of the transmit power. This is because a higher transmit power allows the BS to allocate more power for signal transmission to meet the power constraint, leading to an increase in system energy efficiency. However, as indicated in Figure 3, due to the saturation effect, the relationship between transmit power and system energy efficiency does not increase in a linear manner.