## 5 MIMO Performance Parameters  
The MIMO performance of the proposed antenna systems were evaluated. These parameters included Envelope Correlation Coefficient (ECC), Diversity Gain (DG) and Mean Effective Gain (MEG).The Envelope Correlation Coefficient reveals the degree of radiation pattern independence between two antennas. Therefore, the two radiating structures would have a correlation of 0 if one was totally horizontally polarized and the other was completely vertically polarised. The ECC of these antennas would also be zero if one antenna exclusively radiated energy towards the sky and the other just radiated energy towards the earth. Therefore, Envelope Correlation Coefficient considers the polarization, shape, and even the relative phase of the fields between the two antennas of the antennas. The ECC is evaluated using far field characteristics of proposed antenna using Equation (1) [27; 28; 29]. The ECC among any two radiating elements were found to be \(<\)0.005. Stand-alone antenna gain is not a trustworthy measure of antenna performance because the antenna is frequently used outside of an anechoic chamber. The antenna is used in a specific situation for a specific application. It is essential to look into how the surroundings influence the antenna's radiation properties in order to evaluate its performance. The MEG shows how well the antenna will behave in a multi-path environment and is calculated using Equation (2) [30; 31; 32; 33; 34]. The diversity gain is calculated using Equation (3). All the evaluated performance parameters results were found to be in adequate limits and thus satisfying the performance criteria for the proposed system. Table 1 shows the MEG of the MIMO Antenna. Also Figure 13 shows the MIMO parameters of the proposed system  
\[ECC=\frac{|\iint_{4\pi}(\vec{B}_{i}(\theta,\phi))\times(\vec{B}_{j}(\theta, \phi))\,d\Omega|^{2}}{\iint_{4\pi}|(\vec{B}_{i}(\theta,\phi))|^{2}\,d\Omega \iint_{4\pi}|(\vec{B}_{j}(\theta,\phi))|^{2}\,d\Omega} \tag{1}\]  
Figure 12: Co- and cross-polarization (**a**) Antenna 1 (**b**) Antenna 2 (**c**) Antenna 3 (**d**) Antenna 4.  
where \(\vec{B}_{i}(\theta,\phi)\) denotes the 3D radiation pattern upon excitation of the \(i\)-th antenna and \(\vec{B}_{j}(\theta,\phi)\) denotes the 3D radiation pattern upon excitation of the \(j\)-th antenna. \(\Omega\) is the solid angle. \[MEG=\int_{-\pi}^{\pi}\int_{0}^{\pi}[\frac{r}{r+1}G_{\theta}(\theta,\phi)P_{ \theta}(\theta,\phi)+\frac{1}{1+r}G_{\phi}(\theta,\phi)P_{\phi}(\theta,\phi)] sin\theta d\theta d\phi \tag{2}\]  
where \(G_{\phi}(\theta,\phi)\) and \(P_{\theta}(\theta,\phi)\) are angle of arrival and \(r\) is the cross-polar ratio which can be expressed as Equation (3). \[r=10 log_{10}(\frac{P_{ppa}}{P_{ppa}}) \tag{3}\]  
The power received by the vertically polarized and horizontally polarized antenna is represented as \(P_{ppa}\) and \(P_{hpa}\), respectively. \[DG=10\sqrt{1-(ECC^{2})} \tag{4}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frequency (GHz)** & **MEG1** & **MEG2** & **MEG3** & **MEG4** \\ \hline
28 & \(-\)3.13 & \(-\)3.25 & \(-\)3.16 & \(-\)3.88 \\
38 & \(-\)3.56 & \(-\)3.77 & \(-\)3.88 & \(-\)3.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MEG of the proposed antenna system. Figure 13: Olympicak antenna MIMO parameters (**a**) ECC Sim (**b**) ECC Mean (**c**) Diversity Gain. Table 2 shows a comparison of the proposed MIMO antenna system with the recent state-of-the-art published literature in terms of the number elements in the system, the frequency coverage of the system, the size of the system, the realized gain, the isolation levels between antenna elements and the Effective Channel Capacity. It is seen from the table that the proposed antenna not only covers the widest bandwidth but also supports dual band operations in the 5G mmwave bands. The isolation performance of the proposed antenna is one of best based on the overall antenna size.