# Slotted Circular-Patch MIMO Antenna for 5G Applications at Sub-6 GHz
## 3 A 2-Port MIMO System Using Two Flipped Parallel 1 \(\times\) 2 Arrays Antenna
### Measurement Results Discussion of Two 1 \(\times\) 2 Arrays MIMO
#### 3.3.2 MIMO Performance Results of Two \(1\times 2\) Arrays MIMO  
The reliance on MIMO antenna configurations in modern wireless communication systems is enhancing overall system performance. To ensure optimal MIMO functionality, it is essential to achieve isolation, which mitigates the need for an external decoupling network. Additionally, several key factors influencing MIMO performance, such as the CCL, ECC, DG, TARC, and MEG [33; 34; 35]. Figure 17 presents the calculation results of a MIMO of two \(1\times 2\) antenna arrays. Figure 16: The measured and the simulated gain of the MIMO of two \(1\times 2\) arrays. Figure 15: A Comparison of: (**a**) measured and simulated (E-plane) at 3.5 GHz, (**b**) at 5.8 GHz, of MIMO of two \(1\times 2\) arrays, and (**c**) radiation pattern and gain setup. The CCL represents the minimum practical losses experienced by a MIMO system, and for it to be considered an acceptable standard, it is preferred to be below 0.4-bit/s/Hz. CCL can be estimated using Equations (3)-(8). Figure 17a illustrates a comparison of CCL values  
Figure 17: MIMO parameters of Two 1 \(\times\) 2 Arrays: (**a**) measured and simulated CCL, (**b**) the ECC, (**c**) the DG, (**d**) the TARC, and (**e**) the MEG. from both measured data and simulations, showing that they remain under 0.4-bit/s/Hz, particularly at the resonant frequency band. \[\text{CCL}=-log_{2}(det(a)). \tag{3}\]  
\[\text{a}= \begin{vmatrix}\xi_{11}&\xi_{12}\\ \xi_{21}&\xi_{22}\end{vmatrix} , \tag{4}\]  
\[\xi_{11}=1-\left(\left|\text{S}_{11}\right|^{2}+\left|\text{S}_{12}\right|^{2} \right), \tag{5}\]  
\[\xi_{12}=-(\text{S}^{*}{}_{11}\text{S}_{12}+\text{S}^{*}{}_{21}\text{S}_{12}), \tag{6}\]  
\[\xi_{21}=-(\text{S}^{*}{}_{22}\text{S}_{21}+\text{S}^{*}{}_{12}\text{S}_{12}), \tag{7}\]  
\[\xi_{22}=1-\left(\left|\text{S}_{22}\right|^{2}+\left|\text{S}_{21}\right|^{2} \right), \tag{8}\]  
The ECC parameter quantifies the changes in the diversity factor, indicating the relationship between antennas within a MIMO system. It can be determined using S-parameters, as in Equation (9). Figure 17b illustrates a comparison of simulation results and measurements, revealing that both are closely similar. ECC approach zero between 2.9 GHz and 5.1 GHz, with values of 0.006 dB at 2.8 GHz and 0.0025 dB at 5.2 GHz, which is considered an effective antenna as it trends towards zero. \[\rho_{eij}=\frac{\left|\text{S}^{*}{}_{11}\text{S}^{*}{}_{12}+\text{S}^{*}{}_{2 1}\text{S}^{*}{}_{22}\right|^{2}}{\left(1-\left|\text{S}_{11}\right|^{2}- \left|\text{S}_{21}\right|^{2}\right)\left(\left(1-\left|\text{S}_{22}\right| ^{2}-\left|\text{S}_{12}\right|^{2}\right)\right)}. \tag{9}\]  
The DG serves as a metric for assessing the quality and reliability of a MIMO antenna. It is derived from the envelope correlation coefficient (ECC), as in Equation (10), and is considered favorable when it approaches 10 dB across the operating frequency range. In comparing simulation results with actual measurements, Figure 17c indicates that both yield a diversity gain of 10 dB that contributes to an efficient antenna design. \[\text{DG}=10\sqrt{1-\left|\rho_{eij}\right|^{2}}\,. \tag{10}\]  
The TARC is defined as the square root of the ratio between the total power that is reflected and the power that is incident. TARC can be calculated from Equation (11). For effective antenna design, TARC values should be below \(-10\) dB. As illustrated in Figure 17d, the TARC remains below \(-10\) dB, especially at the resonant frequency. \[\text{TARC}=\sqrt{\frac{\left|\left(\text{S}_{11}+\text{S}_{12}\text{e}^{ \text{i}o}\right)\right|^{2}+\left|\left(\text{S}_{21}+\text{S}_{22}\text{e}^ {\text{i}o}\right)\right|^{2}}{2}}. \tag{11}\]  
The MEG is considered the total adequate average power received over the total average power received by an isotropic antenna. MEG can be calculated from Equation (12). For MIMO systems to meet acceptable performance standards, MEG should be between zero and \(-3\) dB. MEG1 and MEG2 values close to \(-6\) dB that because to bidirectional radiation.