# Machine-Learning-Based Optimization for Multiple-IRS-Aided Communication System
## 5 Simulation Results
### Performance Analysis for the Static UE Scenario  
In this subsection, we present the numerical results for the static UE scenario, where the location of UEs is generated from one random realization, as depicted in Figure 4.  
For our proposed new GRNN-based algorithm, training and validation are performance keys; hence, we first present the effects of key parameters (i.e., the spread factor) to facilitate the selection of training and validation sets. Here, supervised offline learning is used to train the proposed algorithm network based on a generalized dataset of 220,000 samples collected from AO results, where the SINR requirements are in the range of [\(-10\) dB to \(0\) dB]. Figure 5 plots the mean absolute value versus the spread factor by considering a 10-fold cross-validation, which means that the model is trained with 90% of the data set while 10% is used for the validation testing. From the figure, we can see  
Figure 4: 2D deployment. that all folds achieved the lowest validation errors at a range [0.28-0.34] of the spread factor, while spread values greater than this value range induce model overfitting. Moreover, the curve with fold 1 can achieve the best MAE among the different numbers of folds. This is because the training network across fold 1 outperforms the other folds in the validation performance. Then, we study the training and validation performance in the validated range of [0.28-0.34] that has the lower MAE. Table 2 shows the training and validation mean error values under different spread factors. \(V_{MAE}\) and \(V_{MSE}\) denote the validation mean absolute and square errors, respectively. \(T_{MAE}\) and \(T_{MSE}\) denote the training mean absolute and square errors, respectively. In the table, it can be seen that as the spread factor increases, the validation errors decrease, but the training error increases. Nonetheless, when the spread factor equals 0.3, the validation error remains constant and then increases. Thus, to compromise between validation and training errors, a 0.3 spread factor is chosen to train the model, which corresponds to the best performance. We then compare our proposed GRNN-based algorithm with the considered benchmark schemes in terms of the optimized total transmit power. Figure 6 plots the optimized transmit power at the source BS versus the SINR threshold for UEs under different schemes, where each simulated point is averaged through 200 random initializations. From the figure, it is clear that the optimized transmit power from our proposed GRNN-based algorithm is the lowest compared to other benchmark schemes, demonstrating our algorithm's superiority. Compared to the scenarios with deployed IRSs, the power consumption for the scenario without IRSs is the highest, indicating the energy performance gain brought by the deployed IRSs. Then, the random phase scheme has the second-worst performance. This implies that the phases of IRS elements should be optimized rather than randomly chosen, to achieve the maximum gain from their deployment. Moreover, when comparing the iterative scheme with the AO algorithm, we can see that the performance of the AO algorithm is better than the performance of the iterative algorithm. This is because the performance of both approaches depends on the starting phase and stopping criteria. The iterative approach updates its beamforming during iterations with values that lead to the minimum transmit power until 200 iterations are reached; however, the AO stopping criterion is that the fractional decrease in objective value is less than the AO threshold level \(\epsilon\), as defined before. Clearly, AO optimizes the beamforming at every iteration, leading to less power than the optimized one in the previous iteration. Nonetheless, the iterative approach depends on the random phases generated at every iteration, which may be the  
Figure 5: Measured MAE versus spread factor values for 10 folds. reason for the power reduction noticed after some iterations.