## 3 Antenna Design
### De-Coupling Structure of Dumbbell Shape MTM Unit Cell  
As the distance between the elements of the MIMO antenna is responsible for the mutual coupling issue, the performance of the antenna seriously deteriorates as this distance decreases. The three configurations of the MIMO antenna introduced above suffer from mutual coupling problems, so, a de-coupling structure is needed to overcome this problem. A complimentary new shape of Dumbbell-structure MTM unit cell is etching in the ground plane with a strong band rejection characteristic (Band-stop Filter) illustrated in Figure 12 and its dimensions listed in Table 1. The S-parameter curve depicted in Figure 13 illustrates that the Dumbbell-structure MTM unit cell has a high band-stop characteristic \(\mid\)S\({}_{21}\mid\). The permittivity and permeability of the unit cell in Figure 14a,b reveal that this structure is an MTM unit cell with a negative value if (\(\varepsilon_{r}\) and \(\mu_{r}\)) in the desired bandwidth. The MTM unit cell of the Dumbbell-structure that is etched in the ground plane will reduce the mutual coupling between the two elements of the graphene MIMO configurations due to its band rejection characteristic at the desired frequency band. As mentioned before, in the proposed three configurations there is only one mode responsible for the coupling between the two elements (mode 2) in all configurations. So, this mode should be returned to improve the isolation. The MTM unit cell is designed to produce a current flow distribution in the opposite direction of the coupling mode current (mode 2). The characteristic mode theory (CMA) has a vital role in illustrating the behavior of the graphene MIMO systems with and without introducing the Dumbbell-structure unit cell by the usage of model significant and model current distribution. The Ant. C is the best choice to invoke the MTM unit cell on its ground plane as it has a good characteristic rather than the other configurations. In Ant. C configuration, with the presence of an MTM unit cell as depicted in Figure 15, the model current distribution of the first four modes is shown in Figure 16. It can be seen that the mutual coupling is reduced and the path of the current through the MTM design is orthogonal to the path of the current that occurred due to the coupling mode (mode 2). So, the net interference between the two patches is remarkably reduced. This result can be assured from the model significance curve illustrated in Figure 17, we can note that the first four modes of operations and only mode 1 affects the desired bandwidth (\(M_{s}\geq 0.707\)). Mode 2, which is responsible for the coupling is moved away from the bandwidth in the condition that the resonance mode 1 does not affect and stays the same. Moreover, modes 3 and 4 do not affect the desired bandwidth which can be seen from the model current distribution and model significant curves. At last, from the study of the CMA analysis in the three proposed configurations of graphene MIMO antenna, introducing the Dumbbell-structure MTM unit cell in the ground plane has a good impact on the MIMO antenna parameters, especially in the interference problem between the patches that enhance the overall performance of the antenna. Ant. C, in the presence of an MTM unit cell, is the preferable configuration of the two-element graphene plasmonic MIMO structure, which gives high isolation between the patches as shown in Figure 18, which presents the \(\,\mathrm{|S_{11}|}\,\mathrm{|}\) and \(\,\mathrm{|S_{21}|}\,\mathrm{|}\) of the proposed antenna with and without the presence of the MTM unit cell. Figure 10: Model Significant of the proposed MIMO configurations (**a**) Ant. A, (**b**) Ant. B, and (**c**) Ant. C.  
Figure 11: Model current distribution (\(\eta_{\text{n1}}\)–\(\eta_{\text{n4}}\)) of the proposed MIMO configurations (**a**) Ant. A, (**b**) Ant. B, and (**c**) Ant. C.  
Figure 12: Simulation set up and dimensions for the Dumbbell-structure MTM unit cell. Figure 13: S–Parameters of Dumbbell-structure MTM unit cell.