# A Sub-6 GHz MIMO Antenna Array for 5G Wireless Terminals
## 2 Antenna Geometry  
### Single Element  
The front view of the antenna element is shown in Figure 1. RT5880 with a thickness of 0.787 mm is used as a substrate. The length and width of the substrate is 50 \(\times\) 40 mm\({}^{2}\). The radiating portion of the antenna exhibits a circular, patch-like geometry, with a circular-shaped slot in the center with an inner radius of 6.75 mm and an outer radius of 11.54 mm. A slot-termed gap is created at the edge of the patch to tune the resonant frequency to the desired frequency band. The feed contains an impedance transformer for the purpose of matching the transmission line with the radiating portion of the antenna. The back side of the proposed antenna is fully copper-coated. The parameters in Table 1 have been calculated via the known equations of the transmission line theory for the circular patch [25] and have then been optimized to achieve resonance at the desired frequency band.  
\[\text{rad}_{1}=\frac{\text{F}}{\left\{1+\frac{2\hbar}{\pi e_{r}\text{F}}\left[ \text{ln}\left(\frac{\pi\text{F}}{2\hbar}\right)+1.7726\right]\right\}^{\frac {1}{2}}} \tag{1}\]  
\[\text{F}=\frac{8.791\times 10^{9}}{f_{r}\sqrt{\varepsilon_{r}}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** \\ \hline L & 6.00 & F & 1.00 \\ gap & 1.00 & R1 & 11.54 \\ W1 & 2.38 & L1 & 10.0 \\ L2 & 9.7 & R2 & 6.75 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the dimensions of the proposed design.  
The voltage standing wave ratio (VSWR) and reflection coefficient graphs are shown in Figure 2. It is seen that the magnitude of the reflection coefficient is below 15 dB, which is acceptable for optimum power transmission. The VSWR is also observed below 2 dB within the operating bandwidth, which depicts low loss and a good matching between the feedline and the radiating portion of the proposed antenna. The \(-10\) dB bandwidth of almost 50 MHz is obtained with a range from 5.55 to 5.6 GHz, with the central frequency noted to be 5.57 GHz, which is dedicated for 5G Sub-6 GHz applications [18].  
Figure 1: Front view of the antenna element.  
Figure 2: Antenna element: (**a**) reflection coefficient; (**b**) VSWR.  
The parametric study for the proposed antenna element by varying the values of different key parameters is shown in Figure 3. It is observed that the value of the parameters' variations has a significant effect on the reflection coefficient of the proposed design. All three parameters, such as R1, R2 and gap are helpful to bring the antenna element to resonate at 5.57 GHz. In the case of R1, the resonance for the selected parameter is at 5.6 GHz, while simultaneously varying R2 and gap parameter with the R1 moves the resonance to 5.57 GHz. Alongside, the matching circuit helps to improve the magnitude of the reflection coefficient. Thus, after careful consideration and analysis, final values are taken, and the antenna element can proceed towards the array concept.  
The peak gain patterns for the proposed antenna element are presented in Figure 4. The polar and 3D gain patterns are observed in Figure 4a and Figure 4b, respectively. The gain pattern in the 90-degree plane is analyzed, and the side l  
Figure 3: Antenna element reflection coefficient analysis by **(a-c)** varying different parameters.  
be \(-13.8\) dB, while the magnitude of the main lobe is 6.65 dB. Further, the angular 3 dB beamwidth is seen to be \(110.4\) degrees. The 0-degree plane gain pattern is with the side lobe level of \(-24.1\) dB, whereas a main lobe magnitude of 5.93 dB with a 3 dB beamwidth is 69.9 degrees. The gain achieved is 6.66 dB as shown in the 3D radiation pattern (Figure 4b) of the proposed antenna. The greater level of side lobe reduction makes the proposed design less lossy, whereas the back lobes level is also very low as shown in the E plane of Figure 4a.