## 3 MIMO Antenna Parameters  
ECC is calculated using the electric field's magnitude in Equation (1). The ECC solid angle components are indicated by ith and jth. It is time-consuming and labor-intensive to evaluate ECC using far-field radiation characteristics. Equation (2) demonstrates an alternate way of calculating ECC with the help of S-parameters, as described in [32]. \[\rho_{ij}=\frac{\iint\left(E_{\theta_{i}}\cdot E_{\theta_{j}}^{*}+E_{\varphi} :E_{\varphi_{ij}}^{*}\right)d\Omega}{\iint\left(E_{\theta_{i}}\cdot E_{\theta_ {i}}^{*}+E_{\varphi_{ij}}\cdot E_{\varphi_{ij}}^{*}\right)d\Omega\iint\left(E_ {\theta_{j}}\cdot E_{\theta_{j}}^{*}+E_{\varphi_{ij}}\cdot E_{\varphi_{ij}}^{ *}\right)d\Omega}\Bigg{|}^{2} \tag{1}\]  
\[\rho_{ij}=\frac{\left|S_{11}^{*}S_{12}+S_{21}^{*}S_{22}\right|^{2}}{\left(1- \left(\left|S_{22}\right|^{2}+\left|S_{12}\right|^{2}\right)\right)\left(1- \left(\left|S_{11}\right|^{2}+\left|S_{21}\right|^{2}\right)\right)} \tag{2}\]  
The results of the ECC calculations for antenna Design 5 are shown in Figure 12. Figure 12 shows that the antenna has an ECC of less than 0.001 for its principal frequency range of operation. Incorporating these ECC thresholds has increased the system's robustness. When the ECC value of an antenna is low, there are fewer links between its individual parts. Due to the low numbers, it is considered that the antenna's MIMO performance is excellent. Mixing antenna elements with different fading characteristics helps reduce the fading's impact. \[DG=10\sqrt{1-|ECC|^{2}} \tag{3}\]  
\[MEG_{i}=0.5\eta_{ij,rad}=0.5\Bigg{[}1-\sum_{j=1}^{M}\left|S_{ij}\right|^{2} \Bigg{]} \tag{4}\]  
For a given channel, the diversity gain [30] may be calculated by comparing the SNR of the diversity antenna system to that of a comparable single diversity antenna system. Using Equation (3), we can calculate the maximum theorized 10 dB diversity gain for a given ECC and DG. These two factors should be considered together. As diversity gain increases, multi-user MIMO antenna patches become more and more separated from one another. That being said, diversity gain's appropriate value is at least 9 dB, as shown in Figure 13. DG values are projected to surpass 10 dB in all operating bands of both antennas. As such, it ensures that the proposed MIMO design has acceptable diversity performance. The graph of the different DG values seems to overlap with each other because of the similar response for different port excitations that has been observed in numerical calculations. Two isotropic antennas combined average power in the absence of noise is less than or equal to the noise-averaged power delivered to a diversity antenna, as measured by the mean error gain (MEG) parameter (or interference). It demonstrates how environmental factors influence the enhanced performance of a MIMO antenna. The MEG may be validated by using Equation (4), which is based on the equation proposed in [33]. In this formula, M represents the total number of ports in the MIMO configuration, and, \(\eta_{i,rad}\) is the performance in terms of radiation efficiency of the proposed MIMO configurations. Setting the mean effective gain to \(-3\)dB will maximize diversity performance on all of the device's  
Figure 12: Calculated values of the ECC for antenna Design 5. Figure 13: Calculated values of the DG for antenna Design 5.  
interfaces. In addition, there should be no more than a 0 dB divergence between the two ports. The MEG \(-\)3 dB values for all three modes of operation are shown in Figure 14.  
In cases where more than one port is being utilized, the total active reflection coefficient (TARC) provides the most precise measurement of radiation performance and frequency response. This is because TARC is the most trustworthy metric. The mathematical expression for determining this value is as follows: (total power incident on the item) (the total reflected power's square root) (total power incident on the object).