# Directly Matching an MMIC Amplifier Integrated with MIMO Antenna through DNNs for Future Networks
## 2 Proposed Optimization Method
### LSTM-Based DNN for Modeling Antenna (Phase-1)
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency** & \(\text{IMD}_{3}\) **(3)** & \(\text{IMD}_{5}\) **(4)** & \(\text{IMD}_{7}\) **(5)** \\ \hline \(\text{f}_{1}\) & \(\text{a}_{1}\) & \(\text{b}_{1}\) & \(\text{c}_{1}\) \\ \hline \(\text{f}_{2}\) & \(\text{a}_{2}\) & \(\text{b}_{2}\) & \(\text{c}_{2}\) \\ \hline \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) \\ \hline \(\text{f}_{n}\) &\[\text{Linearity}(\text{dBc})=\text{L}_{1}(\text{IMD}_{\text{3 opt}})+\text{L}_{2}( \text{IMD}_{\text{5 opt}})+\text{L}_{3}(\text{IMD}_{\text{7 opt}}) \tag{8}\]  
By the generated dataset and the constructed target function (i.e., linearity), the LSTM-based DNN is trained as the procedure presented in Step-6 and the BO method is applied for finding the optimal hyperparameters (Step-11). Finally, with two LSTM-based DNNs such that one is used for modeling PA and the other is for the modeling antenna, the whole system is optimized. The modeled PA is optimizing the linearity performance of whole system by the directly matching to the optimal predicted impedance from the modeled antenna through DNN (Step-12). **Phase 1 (Antenna modeling)**  
**1**: Create co-simulation environment between CST and MATLAB;  
**2**: Design the initial structure of the antenna;  
**3**: Employ the GA method for optimizing the design parameters;  
**4**: Achieve a suitable dataset size, i.e., training and testing dataset, by performing the parametric sweep;  
**5**: Achieve the optimal hyperparameters of DNN used for modeling the antenna through BO method;  
**6**: Train the LSTM-based DNN enabling the prediction of the optimal impedance that is perfectly matched to the drain impedance transistor over the large frequency band;  
**Phase 2 (PA modeling and optimization in terms of linearity along with the modeled antenna)**  
**7**: Construct co-simulation environment between ADS and MATLAB;  
**8**: Configure the PA structure with the SRFT method and run the GA method to obtain the optimal design parameters;  
**9**: Obtain the dataset in terms of gain, efficiency, and IMDs for constructing the LSTM-based DNN;  
**10**: Employ Multivariate Newton's Method for optimizing the linearity specification;  
**11**: Train the regression DNN for the PA where the optimal hyperparameters are achieved using the BO method:  
**12**: Run the modeled antenna and PA concurrently for optimizing the whole linearity specification of communication systems over the determined frequency band. **3. Practical Execution for Training Two DNNs**  
Employing a successful methodology requires a suitable implementation environment. For this case, we start the proposed methodology at CPU environment with the characteristics of Intel Core i7-4790 CPU @ 3.60 GHz with 32.0 GB RAM. In this study, we design and optimize MIMO antenna with a monolithic microwave integrated circuit (MMIC) design that is a class-AB amplifier. In the first phase, the structure of MIMO is constructed, and after employing the GA method the optimal design parameters are obtained. Figure 5 presents the MIMO antenna structure with the ground plane of 120 mm and 120 mm, along x and y directions, respectively and Table 2 presents the optimal values of parameters. The presented MIMO antenna consists of two single antennas with rings between two patch-like radiators aiming to reduce the surface waves coupling between them. The MIMO antenna is implemented on the FR-4 substrate with \(\varepsilon_{r}\) of 4.3 and and loss tangent of \(\delta=1\times 10^{-3}\). After sizing the antenna, the parametric sweep is employed with the different ranges of \(\mp\)5%, and \(\mp\)10% to obtain the suitable amount of dataset, including training and testing data. Afterwards, the hyperparameters of DNN are achieved through the BO method where 3 LSTM layers with 135 neurons are used for modeling the antenna with the use of DNN. In total, 1500 data are achieved at various frequencies, where the input layer includes characteristics are: S\({}_{11}\), gain, and E-plane with H-plane radiation patterns.