## 2 Antenna Design
The proposed superstrate, positioned at \(0.18\lambda_{0}\), increases the thickness but improves gain and isolation while maintaining impedance matching across the band, creating a trade-off. Port Isolation and Reflection Coefficient Analysis:  
The scattering parameters of the antenna, both with and without MTM, are analyzed in Figure 6. The reflection coefficients of all ports with and without MTM remain less than \(-10\) dB for almost the whole band of concern (i.e., 3.5-3.8 GHz). In comparison, using MTM \(\mid\)S111, the resonating frequency shifts from 3.6 GHz to dual frequencies, 3.6 GHz and 3.75 GHz. Specifically, the maximum port isolation scattering parameters of adjacent ports in the case of without MTM are above \(-30\) dB. However, using the MTM superstrate, the port isolation is reduced compared to the case without MTM. Despite a minor shift in the reflection coefficient dip caused by the MTM, the structure improves the proposed antenna's mutual coupling capability. Figure 5: Four-port MIMO antenna with metamaterial. Isometric view of (**a**) Simulated and (**b**) Image of Fabricated antenna. Figure 6: S-Parameters of intended Antenna array (**a**) simulated without MTM, (**b**) simulated with MTM, (**c**) measured with and without MTM. MIMO Antenna Gain and Efficiency Analysis:  
As shown in Figure 7, incorporating the MTM superstrate substantially enhances the MIMO antenna's performance, elevating its gain from the original 1.2-3 dB range to a stable 4.5-5 dB throughout the entire 3.5-3.8 GHz frequency band. A superstrate with near-perfect transmission (0 dB) and minimal reflection (\(-35\) dB) in the concerned band acts as an efficient impedance matching layer between the MIMO antenna and free space, allowing maximum power transfer with minimal losses. Additionally, it creates a resonant cavity effect that helps shape the radiation pattern and increase directivity, ultimately enhancing the overall gain of the MIMO antenna. Radiation Pattern Analysis:  
A comparison of the antenna's effectiveness with and without metamaterial integration is presented in Figure 8, which depicts the simulated radiation patterns for both (a) E-field and (b) H-field distributions. The E-field pattern demonstrates that the metamaterial implementation maintains the radiation characteristics while enhancing the pattern stability around the broadside direction. The H-field plots reveal improved cross-polarization suppression with the inclusion of metamaterials, achieving levels between \(-30\) and \(-60\) dB. This enhancement in polarization purity and pattern symmetry across both fields validates the effectiveness of the metamaterial structure. Figure 9 compares 3D radiation patterns at 3.6 GHz for the MIMO antenna with (a) and without (b) a metamaterial (MTM) layer. With the MTM, the patterns are more focused, showing higher intensity and directionality, which increases gain and reduces coupling between ports, improving isolation. This highlights the MTM's role in enhancing directivity and port isolation. Figure 7: Simulated Gain with and without MTM and Proposed antenna measured Gain, Left \(y\)-axis. Simulated Efficiency with and without MTM superstrate on the Right \(y\)-axis. MIMO Diversity Parameters:  
Four key diversity parameters must be considered for proper MIMO antenna operation in a wireless communication system: envelope correlation coefficient, total active reflection coefficient, diversity gain, and channel capacity loss. For antenna elements in a MIMO system, ECC measures the correlation between radiation patterns. The ECC ranges from 0 (complete isolation) to 1 (complete correlation). Generally, \(\rho<0.5\) is considered acceptable for the appropriate operation of MIMO. The proposed MIMO antenna exhibits a very low value of ECC for any adjacent radiating element about less than 0.002 as shown on the left \(y\)-axis of Figure 10a. ECC is calculated from the formula given in Equation (10). It is noted that ECC remains lower when the MTM superstate is used for frequencies ranging from 3.6 to 3.8 GHz.