# Eight Element Wideband Antenna with Improved Isolation for 5G Mid Band Applications
## 5 Results and Discussion
### MIMO Performance  
The antenna was analyzed using MIMO metrics like envelope correlation coefficient (ECC), diversity gain (DG), mean effective gain (MEG), total active reflection coefficient (TARC), and multiplexing efficiency (ME) to examine MIMO diversity. Furthermore, the proposed eight-element antenna's ergodic channel capacity was estimated and compared with the ideal 8\(\times\)8 MIMO antenna, taking into consideration an SNR value of 20 dB. The above-mentioned investigations and the corresponding results are given in the upcoming sections.  
Figure 21: S-parameters of the proposed antenna: (**a**) simulated reflection coefficient; (**b**) simulated transmission coefficient; (**c**) measured reflection coefficient; and (**d**) measured transmission coefficient.  
Figure 22: Radiation pattern measurement: (**a**) photograph of measurement set-up in anechoic chamber; and (**b**) gain and radiation efficiency v/s frequency plots.  
ECC is a parameter that explains how well the individual elements are isolated within the MIMO system. This can be computed using the radiation pattern and Equation (1) [29].  
\[\text{ECC}_{p}=\frac{\left|\iint_{4\pi}[\text{E}_{1}(\theta,\phi).\text{E}_{2}( \theta,\phi)\text{d}\Omega]\right|^{2}}{\iint_{4\pi}\left|\text{E}_{1}(\theta, \phi)\right|^{2}\text{d}\Omega\iint_{4\pi}\left|\text{E}_{2}(\theta,\phi) \right|^{2}\text{d}\Omega} \tag{1}\]  
Here, representation of the electric field product is  
\[\text{E}_{1}(\theta,\phi).\text{E}_{2}(\theta,\phi)=\text{E}_{\theta 1}(\theta,\phi)\text{E}_{02}^{*}(\theta,\phi)+\text{E}_{\phi 1}( \theta,\phi)\text{E}_{\phi 2}^{*}(\theta,\phi)\]  
The value of ECC should be smaller than 0.5 to provide an efficient MIMO environment. Figure 24a shows the ECC computed using the 3D radiation pattern and the value falls to 0.07 for the operating frequency range which ensures the effectiveness of the MIMO. DG, on the other hand, is the metric that evaluates how desirable the diversity is, shown in Figure 24b, and can be computed using the correlation coefficient and Equation (2) [31].  
\[\text{DG}=10\sqrt{1-\text{ECC}^{2}} \tag{2}\]  
Figure 23: Proposed antenna radiation characteristics at 5.03 GHz.  
Figure 24: _Cont._  
MEG is the ratio between the accepted and incident power of the MIMO elements concerning the isotropic antenna and is shown in Figure 24c. ME is the parameter that describes the relationship between each component of the MIMO system and the same has been shown in Figure 24d. Conversely, TARC explains the MIMO antenna performance and is depicted in Figure 24e. It provides information about the power levels of the incident and reflected waves. These parameters can be computed using Equations (3)-(5) [31].  
\[\text{MEG}_{\text{i}}=0.5\Big{(}1-\Sigma_{\text{j}=1}^{\text{M}}\big{|}S_{ \text{ij}}\big{|}\Big{)} \tag{3}\]  
\[\text{TARC}=\sqrt{\frac{\big{(}|S_{\text{ii}}+S_{\text{ji}}\text{e}^{\text{j }\text{i}}|^{2}\big{)}+\big{(}|S_{\text{ji}}+S_{\text{ji}}\text{e}^{\text{j} \text{i}}|^{2}\big{)}}{2}} \tag{4}\]  
\[\text{ME}=\sqrt{\eta_{1}\eta_{2}\Big{(}1-\Big{|}\rho_{\text{ij}}\Big{|}\Big{)}} \tag{5}\]  
Figure 24a-e displays the diversity performance of the proposed eight-element antenna. From the figure, it can be inferred that the proposed antenna provides good diversity values with ECC \(<\) 0.07, DG \(\sim\) 10, MEG ratio \(\sim\) 0, TARC \(<\) \(-\)10 dB, and ME \(<\) \(-\)0.5 throughout the operating bandwidth which implies that the antenna is appropriate for MIMO scenarios.  
Figure 24: Diversity metrics of the eight-element antenna (**a**) ECC; (**b**) DG; (**c**) MEG; (**d**) ME; and (**e**) TARC.