# Energy-Efficient RIS-Enabled SISO-OFDMA Communication via Lower Bound Optimization
## 4 Simulation Results  
In this section, we present the results of our proposed algorithm's performance evaluation through numerical simulations for downlink communications. All simulations were conducted using MATLAB 2019b. The simulation setup is based on an OFDM system with \(N=72\) subcarriers. The multiple single-antenna mobile users are considered to be randomly and uniformly distributed within the 100 m \(\times\) 100 m rectangular region on the right-hand side of the RIS in the x-y plane. All the provided illustrations represent averaged outcomes obtained from \(10^{3}\) independent scenarios involving variations in users' positions and channel characteristics. These scenarios were generated following the 3 GPP propagation environment detailed in [26], and the relevant parameters are outlined in Table 1. The performance of our proposed joint resource allocation was compared with two benchmark schemes, random passive beamforming and without RIS, where the first scheme considers the BS-user direct link and performs the OFDMA resource allocation. The results also compared with the optimization approach using the genetic algorithm (GA) for phase shift optimization [27]. However, detailed information regarding these schemes are omitted in this context. The specific simulation parameters are outlined in Table 3.  
It is noteworthy to point out that a majority of the papers listed in Table 1 primarily concentrate on optimizing the sum-rate. This poses a challenge when attempting to compare our results with the aforementioned papers. Moreover, the study in [21] focuses on maximizing EE and incorporates an active RIS in the system model, presenting a distinction from the system model considered in our work. The graph in Figure 2 illustrates the performance of achievable EE with respect to variations in \(P_{\text{max}}\) in dBm. In this depiction, we have set the minimum QoS constraint as \(R_{\text{min}}=2.5\) bps/Hz and fixed \(\alpha_{k,\text{RIS}}\) to 0.25 for all \(K\) users. Our study considers system parameters \(M=4\), \(K=4\), and \(N=72\). As depicted in Figure 2, an increase in \(P_{\text{max}}\) correlates with an increase in EE. Nevertheless, around \(P_{\text{max}}=12\) dBm, there is an underutilization of excess transmit power, resulting in a decline in energy efficiency. This can be attributed to the fact that the EE function does not exhibit a strictly increasing trend with the maximum BS transmit power, \(P_{\text{max}}\). Instead, it reaches a finite maximizer. It is essential to emphasize that the proposed algorithm for passive beamforming optimization using PSO outperforms the one using GA, random passive beamforming optimization, as well as the scenario without RIS in terms of EE. Moreover, Figure 3 illustrates the average SE versus \(P_{\text{max}}\) for different schemes. It can be observed that with an increase in \(P_{\text{max}}\), there is an enhancement in the achievable SE for all the schemes. It also underscores that for low values of \(P_{\text{max}}\), the problem is frequently infeasible. This is expected since the BS lacks adequate transmit power to meet the rate requirements of the users, leading to significantly low SE values. Nevertheless, as \(P_{\text{max}}\) increases, the attainable SE starts to rise. Additionally, similar to the trend in Figure 2, the proposed algorithm for passive beamforming optimization using PSO outperforms other schemes. Besides, Figure 4 portrays the performance of EE concerning the number of RIS elements, denoted as \(M\). As observed, when \(M\) is relatively small, i.e., \(M\leq 10\), all designs except for the without-RIS scheme, exhibit the same trend. Particularly, EE performance increases as \(M\) increases. However, as \(M\) assumes moderate to intermediate values and beyond, EE undergoes a reduction, substantiating the existence of an optimal \(M\) for the maximization of EE objectives [28]. The proposed scheme exhibits a significant improvement when contrasted with a random passive beamforming mechanism.