## 3 Results and Discussion
\[\rho_{ij}=\left|\frac{\iint\ \left(E_{\theta_{i}}\cdot E_{\theta_{j} }^{*}+E_{\varphi}:E_{\varphi_{j}}^{*}\right)^{d\Omega}}{\iint\ \left(E_{\theta_{i}}\cdot E_{\theta_{j}}^{*}+E_{\varphi_{i}} \cdot E_{\varphi_{j}}^{*}\right  
Figure 4: Directivity response for the Type-1 antenna under the consideration of port-1 as an exciting port. (**a**) 2D response of directivity with co- and cross-polarization. (**b**) 3D directivity response.  
Figure 5: (**a**) Variation in S-parameters (S11) for the different radius values for type-5 antenna. Calculated directivity in (**b**) 2D (with co- and cross-polarization) and (**c**) 3D, by considering a radius of 20 \(\upmu\)m.  
Figure 6: Calculated gain for the different types of antenna.  
Figure 7: Variation in gain for the different modes of port excitation, along with co- and cross-polarization effects. Three-dimensional directivity with co- and cross-polarization for port excitation conditions of (P1, P2, P3, P4): **(a)** (1, 0, 0, 0), **(c)** (0, 1, 0, 0), **(e)** (0, 0, 1, 0), and **(g)** (0, 0, 0, 1). Two-dimensional directivity with co- and cross-polarization for port excitation conditions of (P1, P2, P3, P4): **(b)** (1, 0, 0, 0), **(d)** (0, 1, 0, 0), **(f)** (0, 0, 1, 0), and **(h)** (0, 0, 0, 1). co- (green line) and cross-polarization (red line).  
Figure 10a depicts the relationship between ECC and frequency for the suggested type 1 antenna for the different port excitations. On the other hand, it can be noticed that the ECC of the antenna remains below 0.001 over its whole operational bandwidth (1-10 THz and 15-30 THz). These ECC values make the system stable. The lower value of the ECC obtained suggests less correlation between the antenna components themselves. The values are much lower than the allowed limit of 0.5, ensuring that the suggested antenna would provide satisfactory MIMO performance. Fading is reduced by combining antenna components that have distinct fading characteristics. To calculate diversity gain [23], one must compare a diversity antenna system to its equivalent single diversity antenna system in a given channel and determine the difference in signal-to-noise ratio. DG may be evaluated in terms of a theoretical maximum diversity gain of 10 dB and an envelope correlation coefficient, as shown in Equation (8). The MIMO antenna patch components are more isolated when the diversity gain increases. In other words, the DG should be at least 9 dB higher than that. The estimated DG values are over 20 dB over all three working bands of the antenna, as shown in Figure 10d. This assures that the suggested MIMO structure diversity performance is good.  
Figure 8: Variation in gain for the different modes of port excitation, along with co- and cross-polarization effects. Three-dimensional directivity with co- and cross-polarization for port excitation conditions of (P1, P2, P3, P4): (**a**) (0, 0, 1, 1), (**c**) (1, 0, 0, 1), and (**e**) (1, 0, 1, 0). Two-dimensional directivity with co- and cross-polarization for port excitation conditions of (P1, P2, P3, P4): (**b**) (0, 0, 1, 1), (**d**) (1, 0, 0, 1), and (**f**) (1, 0, 1, 0). co- (green line) and cross-polarization (red line).  
Antenna diversity methods, which combine antenna parts that suffer from various types of fading, are used to lessen the effect of fading. By applying the DG equation [23], as shown in Equation (8), the maximum theoretical diversity gain (10 dB) and the envelope correlation coefficient may be evaluated for this value (8). In MIMO antennas, a more considerable diversity gain indicates more isolation between the patch components, which is indicated by a lower value of diversity gain. To be considered loud, the DG must be more than 20 dB. In Figure 10d, it can be seen that the estimated values of DG over 20 dB over the whole working range of the antenna. As a result, the suggested MIMO structure has excellent diversity performance. The MEG parameter indicates that the amount of average power received by a diversity antenna in the presence of noise is greater than the sum of average powers received by two isotropic antennas in the absence of noise (or interference). It depicts the performance increase of a MIMO antenna while considering the impacts of the surrounding environment. We can determine whether the MEG is present at both ports of the planned structure by utilizing Equation (4), as shown in [25].  
\[DG=10\sqrt{1-\lvert ECC\rvert^{2}} \tag{3}\]  
\[\text{MEG}_{i}=0.5\eta_{i,\text{rad}}=0.5[1-\sum_{j=1}^{M}\lvert Sij\rvert^{2}] \tag{4}\]  
Figure 9: Variation in gain for the different modes of port excitation, along with co- and cross-polarization effects.