## 3 Antenna Design
### Analysis of MIMO Antenna Parameters  
In this section, we discuss the most important parameters of the MIMO antenna structure. These parameters are very crucial in the MIMO systems. As the demand for a higher data rate for long-distance transmission is one of the major motivations behind the MIMO configuration to ensure the compatibility of the graphene plasmonic MIMO antenna in the THz frequency band. The envelope correlation coefficient (ECC), diversity gain (DG), and channel capacity loss (CCL) are evaluated and discussed [36; 37]. The ECC is defined as the correlation between the patches in the chosen MIMO configuration. The lower amount of ECC between the MIMO elements means higher MIMO performance. There are two methods to extract the ECC parameters, the first one is by extracting from the S-Parameters as in [38]. \[ECC=\rho_{ij}=\frac{\left|S_{11}^{*}S_{12}+S_{21}^{*}S_{22}\right|^{2}}{\left(1- \left(\left|S_{11}\right|^{2}+\left|S_{21}\right|^{2}\right)\right)\left(1- \left(\left|S_{22}\right|^{2}+\left|S_{12}\right|^{2}\right)\right)} \tag{16}\]  
Figure 19: S–Parameters of Ant. C with CST and ADS equivalent circuit model. Figure 20: Equivalent circuit model of the proposed structure of two-element MIMO configurations with the MTM unit cell. where \(S_{11}^{*}\) and \(S_{21}^{*}\) represent the conjugate of \(S_{11}\) and \(S_{21}\), respectively. The second one is by extracting from the 3D radiation pattern as illustrated in [25]. \[ECC=\rho_{ij}=\frac{\left|\iint_{4\pi}\left[F_{i}(\theta,\varphi)\bullet F_{j}( \theta,\varphi)\right]d\Omega\right|^{2}}{\iint_{4\pi}\left[F_{i}(\theta,\varphi )\right]^{2}d\Omega\ \iint_{4\pi}\left[F_{j}(\theta,\varphi)\right]^{2}d\Omega} \tag{17}\]  
where \(F_{n}(\theta,\varphi)\) is the 3D field radiation pattern of the elements associated with the nth port, \(\bullet\) denotes the Hermitian product operator and \(\Omega\) represents the solid angle. The evaluation of the ECC using a far-field radiation pattern is a complex method, so the S-Parameters method is very convenient to calculate the ECC between the two antenna elements as it is faster and easy to be used as it depends only on the port parameters of the antenna system. The agreeable limit of the ECC is lower than 0.5. The proposed graphene plasmonic MIMO antenna is simulated and ECC is calculated and displayed in Figure 21a. This figure reveals the comparisons between the MIMO elements with and without introducing the complementary Dumbbell-structure MTM unit cell in the ground plane. The ECC without MTM has a value of 0.0189, while the ECC with MTM is reduced to 0.000168 through the entire bandwidth of operation. The lower value of ECC indicates a lower correlation between antenna elements. This value guarantees good MIMO performance of the proposed antenna. Another way to describe and evaluate the performance of the MIMO antenna structure is the diversity gain (DG), which describes the losses that occur in the transmitted power. The formula given in [39] is used to calculate the DG value:  
\[DG=10\sqrt{1-\left(ECC\right)^{2}} \tag{18}\]  
Figure 21: (**a**) Envelop correlation coefficient (ECC), (**b**) Diversity gain (DG), and (**c**) channel capacity loss (CCL) of Ant. C with and without the presence of the MTM unit cell. It can be seen that the DG depends on the value of ECC, moreover, equation (18) states that the small value of ECC produces a higher value of DG and makes the MIMO antenna suitable for diverse applications. Figure 21b depicts the DG value of the proposed MIMO structure in the presence and absence of the MTM structure it has a value of 9.999 and 9.904, respectively. Channel capacity loss (CCL) is one of the most significant MIMO parameters that describe the potential loss of channel capacity due to the correlation between the MIMO antenna elements, in other words, CCL defines the maximum limit of information transmission rate without significant loss. It should be less than 0.5 bits/s/Hz for a well-designed MIMO configuration. The CCL is indicated in (19) as reported in [39].