## 3 Analysis of SCSRR-Based DGS MIMO Antennas with Different Feed Networks
### MIMO Antenna Performance  
The ECC is used to define how one antenna is correlated with other antennas present in their region of interference and it is calculated using Equation (7) [99, 100]. ECC was below 0.05 in the operating frequency band, as shown in Figure 29, indicating that the proposed MIMO antenna is a good candidate for practical applications.  
\[ECC=\frac{|\int\int_{0}^{4\pi}\left|\overrightarrow{\mathrm{F}_{\mathrm{i}}}( \theta,\phi)\times\overrightarrow{\mathrm{F}_{\mathrm{j}}}(\theta,\phi)d \Omega\right|\,|^{2}}{\int\int_{0}^{4\pi}\left|\overrightarrow{\mathrm{F}_{ \mathrm{i}}}(\theta,\phi)\right|\,|^{2}\,d\Omega\int\int_{0}^{4\pi}\left| \overrightarrow{\mathrm{F}_{\mathrm{j}}}(\theta,\phi)\right|\,|^{2}\,d\Omega} \tag{7}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Without SCSRR** & **With SCSRR** \\ \hline \(f_{c}\) [GHz] & 5.84 & 5.85 \\ \hline Peak return loss [dB] & 24 & 31 \\ \hline BW [MHz] & 210 & 225 \\ \hline Peak gain [dBi] & 6.3 & 6.33 \\ \hline Peak isolation [dB] & 18 & 17 \\ \hline RE [\%] & 94.9 & 94.8 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Performance comparison of aperture-coupled feed MIMO antennas with and without SCSRR-based DGS.  
Figure 28: Current distribution of aperture-coupled feed MIMO antennas (**a**) without and (**b**) with SCSRR-based DGS.  
Figure 27: The 3D gain patterns of aperture-coupled feed MIMO antennas with SCSRR-based DGS.  
where \(\overrightarrow{\mathrm{F}_{i}}(\theta,\phi)\) and \(\overrightarrow{\mathrm{F}_{j}}(\theta,\phi)\) indicates, respectively, the \(i^{th}\) and \(j^{th}\) elements of the antenna's radiation patterns.  
DG describes the amount of improvement of MIMO configuration that is estimated by using Equation (8) [100]. DG was close to 10 dB in the operating frequency band, as shown in Figure 30, confirming that the proposed MIMO antenna is an adequate option for real-world applications.  
\[DG=10\sqrt{1-\left|\rho_{eij}\right|^{2}} \tag{8}\]  
The CCL details the channel capacity losses of the system during the correlation effect, and it is evaluated by Equations (9)-(12) [100]. Figure 31 proves that CCL was within the limits of practical standard of 0.4 bit/s/Hz [101] for the entire operating band, which justifies the proposed system's successful transmission at the operating frequency.  
\[CCL=log_{2}det(\alpha), \tag{9}\]  
\[\alpha=\begin{bmatrix}\sigma_{ii}&\sigma_{ij}\\ \sigma_{ji}&\sigma_{ji}\end{bmatrix} \tag{10}\]  
\[\sigma_{ii}=1-(\left|S_{ii}\right|^{2}-\left|S_{ij}\right|^{2}) \tag{11}\]  
\[\sigma_{ij}=(S_{ii}^{*}S_{ij}+S_{ji}S_{ji}^{*}), \tag{12}\]  
Figure 30: DG of MIMO antennas with SCSRR-based DGS for each feeding methods.  
Figure 29: ECC of MIMO antennas with SCSRR-based DGS for each feeding methods.  
The MEG is defined as the mean received power in the fading environment, and it is calculated using Equation (13) [100]. For acceptable diversity performance of the MIMO, the MEG needs to be between \(-3\) dB and \(-12\) dB [101], which is validated for the obtained MEG values of all MIMO antennas of the proposed designs, as demonstrated in Figure 32.  
\[MEG=0.5(1-\sum_{j=1}^{N}\abs{S_{ij}}) \tag{13}\]