## 8 Numerical Results and Discussion
### Convergence Time Analysis of the RNN Framework  
The convergence time of the RNN-based optimization framework is a critical factor in evaluating the practicality and efficiency of the proposed VLC system. This analysis evaluates how different system components, such as ADR configurations and signal selection mechanisms, influence the convergence behavior. Table 4 presents the convergence \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Max** & **Min SNR** & **Convergence** & \multirow{2}{*}{**Adaptability**} & \multirow{2}{*}{**Computational Complexity**} \\  & **SNR (dB)** & **(dB)** & **Epochs** & & \\ \hline RNN & **105.94** & 69.65 & **50** & High & \(O(N_{\text{epochs}}T(n_{h}\cdot n_{x}+n_{l}^{2}+n_{o}\cdot n_{l}+N_{\text{receivers}}))\) \\ CNN & 95.67 & \(\sim\)60.00 & 80 & Moderate & \(O(N_{\text{epochs}}n_{c}\cdot k^{2}\cdot n_{x}\cdot N_{\text{receivers}})\) \\ BP Network & 89.45 & \(\sim\)50.00 & 120 & Low & \(O(N_{\text{epochs}}n_{l}\cdot n_{x}^{2}\cdot N_{\text{receivers}})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of machine learning models for IRS optimization in VLC systems. times for the proposed RNN-based optimization framework for the different configurations of the VLC system. The analysis demonstrates the adaptability of the RNN framework, achieving convergence within a reasonable timeframe across all configurations. The two ADR configurations exhibit distinct convergence characteristics, as we can see in Table 4. Pyramidal ADRs demonstrate faster convergence due to their focused angular coverage, which reduces the complexity of IRS placement optimization. The simpler structure requires fewer iterations for the RNN to refine the IRS positions effectively. On the other hand, hemispherical ADRs provide broader angular coverage and increase the search space for optimization, leading to slightly longer convergence times. This is due to the RNN needing to take into account signals coming from a wider range of directions, which introduces additional complexity. The signal processing mechanisms (MRC and SBC) also significantly affect the convergence time. MRC consistently achieves faster convergence across both ADR configurations. By aggregating signals from multiple photodiodes, the MRC stabilizes the feedback to the RNN, allowing it to refine the optimization parameters efficiently. For example, the pyramidal ADR with MRC achieves convergence in approximately 4.23 s, while the hemispherical ADR requires 5.12 s. SBC is inherently less efficient, as it selects only the strongest signal, which introduces variability in the optimization process. Consequently, SBC requires more iterations for the RNN to achieve convergence, with times of approximately 6.64 s for the pyramidal ADR and 7.01 s for the hemispherical ADR. The results highlight the interaction between the ADR geometry and the signal combination mechanisms to determine the convergence speed. MRC-based configurations are more suitable for scenarios where rapid optimization is required, as they take advantage of signal diversity to stabilize the optimization process. SBC-based configurations, while slower, may still be effective in scenarios with limited computational resources or when simplicity is prioritized. These findings underscore the adaptability of RNN-based optimization to different system designs, making it a robust solution for real-time VLC applications. The convergence time results were computed using simulations conducted on an Intel Core i7-12700H CPU @ 2.70 GHz with 16 GB of RAM. These simulations were performed in MATLAB, leveraging its optimization toolbox for gradient-based updates. The convergence time in seconds is directly influenced by the computational hardware, as the performance of the RNN depends on the efficiency of matrix operations and iterative calculations. For this reason, the reported times apply specifically to the given hardware configuration and software environment.