# Minimized Triple-Band Eight-Element Antenna Array for 5G Metal-frame Smartphone Applications
## 4 Experimental Results and Discussion  
To verify the proposed design, an antenna prototype was fabricated using the optimized dimensions described in Figure 1. Figure 5 is a photograph of the measurement setup. Figure 6 shows the simulated and measured coefficients. The antenna is measured by Keysight Vector Network Analyzer N5224A. It can be seen that the simulated and measured bandwidth can cover 3.3-3.8 GHz, 4.8-5 GHz, and 5.15-5.925 GHz. The isolation between different ports is larger than 13 dB. The slight frequency offset is due to excess solder. Figure 5: Photograph of the measurement setup; (**a**) vector network analyzer; (**b**) anechoic chamber; (**c**) fabricated antenna. Figure 7 shows all measured total efficiencies which are larger than 70%. The inconsistent efficiency of symmetrical antennas is due to the current skin effect caused by excess solder. Figure 6: Simulated and measured coefficients of the proposed antenna array: (**a**) simulated and measured reflection coefficient; (**b**) simulated and measured transmission coefficient. Figure 7: Measured total efficiencies of Ant. 1,2,3,4. In this study, the imaginary part and real part of the S-parameters are measured by VNA, and the calculated envelope correlation coefficient (ECC) of the proposed eight-antenna MIMO system according to Equation (1). \[\text{ECC}= \frac{\iint_{4\pi}\text{A}_{\text{ii}}(\theta,\phi)\sin(\theta)d \theta d\phi}{\sqrt{\iint_{4\pi}\text{A}_{\text{ii}}(\theta,\phi)\sin(\theta)d \theta d\phi\iint_{4\pi}\text{A}_{\text{ij}}(\theta,\phi)\sin(\theta)d\theta d\phi}} \tag{1}\]  
The calculated ECC of the proposed MIMO antenna system is shown in Figure 8. The values of ECC in the operating frequency bands are smaller than 0.09. The calculated diversity gain (DG) is related to ECC in Equation (2). \[\text{DG}=10\ (\text{dB})\ \times\sqrt{1-\left|\text{ECC}\right|^{2}} \tag{2}\]  
The calculated DG of the proposed MIMO antenna system is shown in Figure 9. The values of DG in the operating frequency bands are greater than 9.96. The multiplexing efficiency (ME) is related to ECC in Equation (3). \(\eta_{1}\) and \(\eta_{2}\) are total efficiencies in Figure 7.  
\[\text{ME}=\sqrt{\eta_{1}\eta_{2}(1-\left|\text{ECC}\right|^{2})} \tag{3}\]  
Figure 5:0 Calculated ECC. Figure 5:1 Calculated DG. The calculated ME of the proposed MIMO antenna system is shown in Figure 5:2 The values of ME in the operating frequency bands are greater than 70%. The channel capacity loss (CCL) is calculated from S-parameters using MATLAB in Equations (4) and (5). \[\text{CCL}=-\log_{2}[\text{det}(\Psi)],\ \Psi=\left[ \begin{array}{cc}\text{P}_{11} &\text{P}_{12}\\ \text{P}_{21}&\text{P}_{22}\end{array} \right] \tag{4}\]  
\[\text{P}_{ii}=1-|\text{S}_{ii}|^{2}-|\text{S}_{\bar{ij}}|^{2},\ \text{P}_{\bar{ij}}=-( \text{S}_{ii}\text{S}_{\bar{ij}}+\text{S}_{\bar{ij}}\text{*}\text{S}_{\bar{ij}} )\ ;\ \text{for i, j}=1\ \text{or 2} \tag{5}\]  
The calculated CCL of the proposed MIMO antenna system is shown in Figure 11. The values of CCL in the operating frequency bands are smaller than 0.5. The total active reflection coefficient (TARC) is calculated from S-parameters in Equation (6). \[\text{TARC}=\sqrt{\frac{(\text{S}_{11}+\text{S}_{21}\text{*})^{2}+(\text{S}_{2 1}+\text{S}_{22}\text{*})^{2}}{2}} \tag{6}\]  
The calculated TARC of the proposed MIMO antenna system is shown in Figure 12. The values of TARC in the operating frequency bands are smaller than \(-10\ \text{dB}\). Figure 11: Calculated DG. Figure 10: Calculated ME. The radiation patterns of the proposed antenna element at 3.5 GHz, 4.9 GHz, and 5.5 GHz are shown in Figure 13. The measured co-pol and cross-pol are represented by solid and dashed lines, respectively. The cross-pol of all antennas is smaller than the co-pol. The co-pol and cross-pol of the same antenna are different at disparate frequency points. Since Ant.1 and Ant.2 have the same shape and different positions, radiation patterns are slightly similar, but not identical. Figure 12: Calculated TARC.