## 2 Proposed Optimization Method
In the second phase, the regression DNN that is constructed by the LSTM layers is utilized for predicting the optimal design parameters of constructed initial antenna design. The total obtained datset consists of 1000 sequences where each sequence includes multi-segment S\({}_{11}\), S\({}_{12}\) and TARC values over the operatio \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Design Parameters** & **Value** & **Design Parameters** & **Value** \\ \hline T\({}_{1}\) (mm) & 22 & W\({}_{\text{p}}\) (mm) & 12.86 \\ R\({}_{1}\) (mm) & 3.47 & L\({}_{\text{p}}\) (mm) & 17.91 \\ W\({}_{\text{f}}\) (mm) & 3 & W\({}_{\text{ps}}\) (mm) & 4.94 \\ L\({}_{\text{ps}}\) (mm) & 4 & L\({}_{\text{ts}}\) (mm) & 1 \\ L\({}_{\text{f}}\) (mm) & 13 & S\({}_{1}\) (mm) & 5 \\ S\({}_{2}\) (mm) & 3.5 & S\({}_{3}\) (mm) & 6 \\ S\({}_{4}\) (mm) & 1.5 & W\({}_{\text{ground}}\) (mm) & 150 \\ L\({}_{\text{ground}}\) (mm) & 120 & \(\varepsilon_{r,\text{(substrate)}}\) & 11.2 \\ \(\varepsilon_{r,\text{(bone)}}\) & 11.38 & \(\varepsilon_{r,\text{(liquid)}}\) & 52.7 \\ \(\varepsilon_{r,\text{(plexiglass)}}\) & 3.4 & t (mm) & 0.035 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design parameters of optimized implanted MIMO antenna in Figure 2.

Figure 3: Regression DNN for predicting the best design parameters of implanted MIMO antenna. hyperparameter achieved from BO method represents n = 3 LSTM layers with 50 neurons in each layer. As the capability of each DNN is validated by the training/testing accuracy, the normalized training error for the regression DNN is around 0.09. ## 4 Simulation Results of the Optimized Implanted MIMO Antenna

This section presents the simulated output of the optimized implanted MIMO antenna using the TDO and DNN methods. Sequentially, the biological layers are mounted together and the MIMO antenna is placed on Al\({}_{2}\)O\({}_{3}\) substrate. Afterwards, the proposed and trained DNN is employed for sizing the implanted MIMO antenna that are optimized in terms of S-parameters and TARC specification. Table 1 presents the achieved optimal design parameters for the configured antenna. The presented MIMO antenna covers the two frequency bands of 4.34-4.61 GHz and 5.86-6.64 GHz. Figure 4 presents the output results of optimized antenna in terms of S-parameters. Another important specification of the implanted MIMO antenna is TARC: it is less than \(-10\) dB in the two mentioned frequency bands. Figure 5 reports the obtained TARC value. The radiation pattern (co-pol term) of optimized antenna in the E- and H planes are depicted in Figure 6 for the centered frequencies of the two bands, i.e., 4.5 GHz and 6.2 GHz. The plots correspond to excitation of both ports with equal amplitude. Effects of the variable coupling between the antennas (even if low, see Figure 4 (right)) can be observed, that is further influenced by the dispersive behaviour of the resonators around them. Additionally, the variation of the frequency in the wide range--almost 50% (from 4.5 GHz to 6.3 GHz)--corresponds to a change in the relative (\(d/\lambda\)) normalized distance, that in turn will affect the radiation pattern. In the present investigation, aiming to demonstrate the validity of the optimisation process, no attention has been paid to the effect of the ground plane, since in a further step the antennas will be positioned on a cylindrical/conical configuration, hence eliminating any diffraction effects from the finite dimension ground plane present here [23; 24]. The reported value of the gain of the embedded MIMO antenna can be considered in case of link budget estimation. Figure 4: S\({}_{11}\) (**left**) and S\({}_{12}\) (**right**) of optimized implanted MIMO antenna array. Figure 5: TARC of optimized implanted MIMO antenna. ## 5 Conclusions

Designing and optimizing high performance antennas, especially the implanted antennas with MIMO structure are not straightforward and require challenging efforts.