## 8 Numerical Results and Discussion
### The Effect of the Number of Epochs on Received Power in the VLC Scenario  
Figure 8 presents the relationship between the number of epochs and the received power for the ADR geometries and signal processing schemes. The results show that ADRs that utilize MRC (both pyramidal and hemispherical) achieve the highest received power levels, converging to approximately 10.92 dB and 12.11 dB, respectively. The figure demonstrates that RNN-based optimization facilitates rapid convergence, with MRC configurations stabilizing within the first 40 and 50 epochs and exhibiting minimal variation afterward. This underscores the efficiency of RNN in achieving optimal IRS placement quickly. Figure 7: The distribution of SNRs in an indoor VLC scenario where IRS positioning is optimized using an RNN, evaluated across various ADRs, employing either signal selection or combination strategies. In contrast, SBC-based configurations display lower received power levels, converging to approximately 10.59 dB for the pyramidal ADR and 11.94 dB for the hemispherical ADR. Although SBC configurations require more epochs (approximately 60) to stabilize, they also show improvements in received power, particularly for the hemispherical ADR. The enhanced performance highlights the RNN's ability to dynamically adapt IRS positions, even for less efficient signal processing mechanisms such as SBC. These findings emphasize the importance of MRC in maximizing received power and achieving rapid convergence, making it the preferred choice for scenarios with stringent performance requirements. Additionally, the comparison between pyramidal and hemispherical ADRs shows that, while the ADR geometry influences the performance, the choice of signal combination mechanism (MRC or SBC) plays a more significant role. The results validate the effectiveness of the RNN in optimizing IRS placements for VLC systems, regardless of the ADR configuration or processing scheme. On the other hand, the RNN framework was chosen for its ability to handle sequential optimization tasks efficiently, such as dynamically adjusting the IRS placement based on ADR feedback. To ensure the suitability of this approach, a comparison with alternative machine learning models, such as convolutional neural networks (CNNs) and backpropagation (BP) networks, has been conducted [25, 26]. This comparison aims to evaluate and verify the performance of these mechanisms in the VLC environment. Although CNN and BP networks are viable alternatives, their inherent characteristics limit their performance for iterative optimization in the VLC context. It is important to mention that in order to obtain the comparative parameters in Table 3, the characteristics of the VLC and IRS scenarios were always maintained. A hemidodecahedral ADR with MRC was evaluated because it presented better performance in the VLC scenario, together with the parameters in Table 1 for the three methodologies to generate fair comparisons. In this sense, the theoretical comparison, based on the metrics observed in this study, is summarized below. Figure 8: Received power vs. the number of epochs for different ADRs and processing mechanisms in the VLC system optimized with an RNN. The total computational complexity for each model was evaluated and adapted according to the parameters in this study and followed the same mechanism to obtain the computational complexity of the RNN (Equation (50)). The CNN processes the spatial features of the VLC environment, focusing on extracting patterns from IRS and ADR data. The complexity is expressed as follows:  
\[O(N_{\text{epochs}}n_{c}\cdot k^{2}\cdot n_{x}\cdot N_{\text{receivers}}), \tag{51}\]  
where \(n_{c}\) is the number of channels, \(k\) is the kernel size, and \(n_{x}\) is the input spatial size. CNNs require additional computation due to convolution operations, particularly for large input grids and kernel sizes. The BP network is a fully connected feedforward neural network that optimizes IRS positions based on static input-output relationships.