# Using AI to Improve MIMO Antennas with SRR for 26 GHz by Analyzing Data
## 2 Model 1 for Antenna Dimension Prediction
The database is first preprocessed and normalized to ensure compatibility with learning models. Then, rather than using a single model, we trained the data using several different regression algorithms in order to compare their performance and identify the most suitable one. This comparison is summarized in Table 1, where each model is evaluated based on the mean-squared error (RMSE), the correlation coefficient (R\({}^{2}\)), and the mean absolute error (MAE). The algorithm offering the best trade-off between accuracy and generalization is then selected for the final prediction of the S11 coefficient. Once trained, the model is evaluated and validated by comparing its predictions with simulated results. Interestingly, the model reveals clear trends and allows us to identify optimal regions in the parameter space with minimized S11, sometimes even predicting resonance shifts and sharp notches, which are then cross-verified with EM simulations. This workflow significantly reduces the design time and helps guide future fabrication with improved accuracy. In this study, several machine learning models were evaluated for predicting antenna performance, including random forest (RF), multi-layer perceptron (MLP), support vector regression (SVR), XGBoost, and gradient boosting. While RF demonstrated the best overall results, with an R\({}^{2}\) of 0.992 and MSE of 0.197, the other models showed certain limitations. MLP, despite its ability to capture nonlinear relationships, suffered from overfitting on our dataset and required higher computational effort. SVR performed poorly (R\({}^{2}\) = 0.639), likely due to challenges in handling the complex nonlinearities and parameter tuning in the antenna design data. XGBoost and gradient boosting showed competitive accuracy (R\({}^{2}\) near 0.97), but demanded more extensive hyperparameter optimization and computational resources. Therefore, RF was chosen for its balance of high predictive accuracy, robustness against overfitting, interpretability, and computational efficiency. This selection is justified to provide a practical and reliable optimization framework for antenna design. A detailed comparison of these models is presented in Table 1.  
These metrics reflect the model's ability to capture complex nonlinear relationships between input design parameters and the S11 response across the full frequency band. Random forest's ensemble learning nature, which combines multiple decision trees, allows it to generalize well and avoid overfitting, even in the presence of noisy or limited data. This robustness and precision make it particularly well-suited for guiding rapid antenna \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **R\({}^{2}\)** & **MSE** \\ \hline XGBoost & 0.979 & 0.574 \\ \hline MLP & 0.970 & 0.839 \\ \hline Gradient Boost & 0.966 & 0.950 \\ \hline SVR & 0.639 & 10.00 \\ \hline Random Forest & 0.992 & 0.197 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of algorithm performance for antenna dimension prediction. optimization processes, especially when simulating or fabricating large numbers of design variants is computationally expensive. Figure 3 presents the final structure of the optimized antenna, derived from the predictions of the Random Forest model. This configuration was selected as the optimal design due to its superior performance, particularly in achieving a well-centered S11 response around 26 GHz. The dimensions of the proposed antenna are listed in Table 2.  
In this research, the random forest algorithm was used to forecast the reflection coefficient S11 for a patch antenna functioning in the 26 GHz frequency range. Two important hyperparameters of the model--the number of \"trees\" and the maximum \"depth\" of each tree--were methodically adjusted to assess their impact on prediction accuracy. The parameter that defines the number of estimators dictates how many separate decision trees are created and averaged to form the final forecast.