## 3 Results and Discussion
### Four-Port MIMO Array  
The MIMO configuration of this design is customized for a four-port MIMO antenna array computed at the resonance frequency of 28.8 GHz. Special attention is paid to the spacing between antenna elements to boost isolation, reduce mutual coupling, and enhance MIMO system performance. This MIMO antenna setup comprises four individual radiating elements compactly arranged within an 80 \(\times\) 68 mm\({}^{2}\) area, utilizing the same substrate as the single-array antenna. Figure 5 provides top and bottom views of the MIMO antenna structure, featuring sub-miniature version A (SMA) connectors for each port. Figure 3: Computed reflection coefficient of single-port antenna versus frequency. The dashed line highlights the \(-\)10 dB borderline and the highlighted area represents the bandwidth range, in which the S11 parameter is less than \(-\)10 dB. The achieved significant reduction in mutual coupling due to the key role of the designed MTM cell is depicted in Figure 6. The extracted relative permittivity (\(\epsilon_{\pi}\)), relative permeability (\(\mu_{\pi}\)), and refractive index (n) exhibit both positive and negative values that vary with frequency. Specifically, the design outputs feature negative values of \(\varepsilon\pi\) across the target frequency range and demonstrate resonant behavior. This underlines the behavior of the cell as an MTM. Regarding gain, the gain is enhanced by the effects of the MTM to focus EM energy in specific directions. Additionally, concerning isolation, it absorbs or prevents surface wave propagation in specific directions. The split-ring-like MTM cells operate similarly to bandstop filters, filtering out unwanted interference and thus improving the attenuation of mutual coupling. The metamaterial unit cell experienced further investigation through dispersive analysis, as depicted in the frequency dispersion diagram presented in Figure 6f. The eigensolutions of the electromagnetic wave equation revealed broadband bandgaps evident in the lower-order modes, alongside a narrower bandgap spanning 2.6 GHz within the frequency range from 27.4 to 30 GHz, encompassing the required frequency of 28 GHz. This observation solidifies the role of the unit cell in acting as a bandgap structure, effectively mitigating coupling between MIMO elements within the examined frequency band of interest. Consequently, this boosts isolation capabilities, thereby optimizing the performance of the proposed antenna structure. Figure 4: Computed peak gain of single-port antenna versus frequency. Figure 6: Unit cell MTM in (**a**) top and (**b**) bottom views and its extracted parameters: (**c**) \(\epsilon_{r}\), (**d**) \(\mu_{e}\), (**e**) n. (**f**) Dispersive diagram exhibiting EM bandgaps detected in the unit cell structure and (**g**) current distribution resulting from excitation of port 3. In Figure 8, the graphical representation illustrates the computed frequency-dependent ECC and DG of the MIMO structure. Throughout the frequency spectrum, the ECC values consistently remain below 0.00010, which is much lower than the ECC conventional threshold of 0.5, indicating significant isolation between antenna elements and minimal signal correlation. Simultaneously, the DG approaches the 10 dB, indicating robust signal reception in that direction alongside effective fading mitigation. Moreover, the CCL values demonstrate commendable performance. Specifically, at 28 GHz, the CCL is computed to be 0.11 bit/Hz/s, which is lower than the standard reference of 0.4 bit/Hz/s, signifying a substantial reduction in channel capacity loss and enhanced system efficiency. Figure 9 depicts the computed radiation pattern of the MIMO antenna. At 28 GHz and in the E-plane direction, the antenna achieves a gain of 14.4 dBi, with the main lobe pointed at \(\theta\) = 2\({}^{\circ}\) and a beamwidth of 70\({}^{\circ}\). In the H-plane, the main lobe exhibits a gain of 15.5 dBi, directed at \(\theta\) = 3\({}^{\circ}\), with a beamwidth of 10.4\({}^{\circ}\).