## 2 Proposed Optimization Method
\[\text{TARC}=\sqrt{((\mathsf{S}_{11}+\mathsf{S}_{12})^{2}+(\mathsf{S}_{21}+ \mathsf{S}_{22})^{2})/2} \tag{1}\]

Lastly, the hidden layers are constructed using the LSTM layers where the optimal hyperparameters are determined using the BO [19] for predicting the optimal number of layers and neurons. For training any DNN, suitable amount of dataset including training, validation, and testing data is needed that can be achieved, for example, by running a parametric sweep. For this case, firstly the initial constructed antenna is generated in the CST Studio Suite (Dassault Systemes). Then, an automated environment is created that is the collaboration of CST and numerical analyzer as MATLAB. CST has two important duties as (i) providing the output responses for the simulated design parameters and also (ii) preparing the outcome file includes all the simulation input and results. MATLAB collects all the input data namely as \(X_{Train}\), \(X_{Validation}\), and \(X_{Test}\) and also the corresponding output data (\(Y_{Train}\), \(Y_{Validation}\), and \(Y_{Test}\)). The training, validation, and testing data is split with the range of 70%, 15%, and 15%. This amount of data is generated by employing the Latin hypercube sampling technique [20] within the \(\pm 10\) and \(\pm 15\) range of current points achieved from the initial MIMO design in (Step-3) (Step-5). The input feature of optimization are the ones presented in Table 1 and the output features of optimization are the \(\mathsf{S}_{11}\), \(\mathsf{S}_{21}\), and TARC specifications that are collected by MATLAB. Afterwards, the hyperparameters of the regression DNN include number of neurons and number of LSTM layers are determined using the BO method (Step-6). For the proposed optimization method, the used activation function and loss function are the rectified linear unit (ReLU) and mean squared error, respectively. in the following, the DNN is constructed using the 'trainNetwork' function in the MATLAB environment (2). \[\text{net}=\text{trainNetwork}(X_{Train},Y_{Train},\text{layers},\text{ options}) \tag{2}\]

After training the DNN, for ensuring about the accuracy of the network, the 'predict' function is used to measure the difference between the actual \(Y_{Test}\) and the predicted output through the constructed DNN as (3) that is expected to be more than 90% (Step-7). \[Y_{Pred}=\text{predict}(\text{net},X_{Test}) \tag{3}\]

Finally, the constructed DNN is used for predicting the design parameters and optimizing the MIMO design up to achieving the optimal solutions (Step-8). ## 3 Practical Implementation of the Optimization-Oriented Method

The presented automatic methodology is employed in the CPU execution environment: it involves an Intel Core i7-4790 CPU @ 3.60 GHz with 32.0 GB RAM. As described in Section 2, firstly the TDO method is used for constructing the initial antenna geometry. For this case, sequentially biological tissues as: bone, liquid like %1 sodium chloride (NaCI) and %40 sugar dissolved in distilled water, and plexiglass are mounted over together. Then aluminium oxide (Al2O3) substrate with large ground plane are placed for constructing the MIMO antenna. The dielectric properties of tissues can be obtained from [21, 22]. After constructing the various tissues and planes, the MIMO antenna must be generated. Figure 2 shows the general structure of MIMO configuration considered in this paper. It consists of two single antennas with T\({}_{1}\) transform distance surrounded by a 1-D periodic ring series around and in between the patch antennas. These rings are considered aiming to reducing the surface waves, hence the mutual coupling between the single patches. The ground plane has a large extension of 150 mm and 120 mm, along \(x\) and \(y\) directions, respectively. Such a dimension guarantees eliminating the diffraction effects that would not be present for a conformal configuration, when the antennas are bend around a medical implant.