# A Compact Ultra-Thin 4 \(\times\) 4 Multiple-Input Multiple-Output Antenna
## 4 Measured Results and Discussion  
### Measured Results  
A prototype of this designed antenna was manufactured. Figure 11 shows the printed model's photograph and the testing scene by a Vector Network Analyzer (VNA: N5224A) and the anechoic chamber. In Figure 11, Ant. 1 and Ant. 2 are all excited; one can see that the proposed AP precisely resonated at 3.5 GHz, and the \(-10\) dB impedance-matched band completely covered the target band. A slight difference between these two measured curves occurred due to the soldering procedure of the SMA connectors. Figure 12 makes a comparison between the simulated and measured S-parameters. The estimated \(-10\) dB bandwidth was 290 MHz (3.36-3.65 GHz). The worst isolation performance of 17 dB appeared between Ant. 1 and Ant. 2. A general uniformity was achieved among the simulated and experimental curves. The measured gain and radiating efficiency when Ant. 1 and Ant. 2 were separately excited are portrayed in Figure 13. The maximum gain and peak radiating efficiency of the proposed AP within the target band were 5 dBi and 73%, respectively.  
ECCs, DGs, TARCs, and MEs were computed to assess the diversity performance of the proposed design. As a vital parameter to evaluate the MIMO performance of the MIMO system, ECC was calculated by Equation (1) to obtain a precise observation of the independent level of two antenna elements [19]. As illustrated in Figure 14, the worst ECC between Ant. 1 and Ant. 2 (Ant. 3 and Ant. 4) within the operational band was 0.012, while ECC\({}_{13}\) and ECC\({}_{14}\) were lower than 0.009 and 0.007, respectively. Figure 14 also presents the calculated DGs by formula (2) [18], and a 10 dB DG was realized in the target operating band, explaining that the reported AP is qualified to be applied to smartphones.  
\[ECC=\frac{\left|S_{ii}^{*}S_{ij}+S_{ji}^{*}S_{jj}\right|^{2}}{\left(1-\left|S_{ ii}\right|^{2}-\left|S_{ji}\right|^{2}\right)\left(1-\left|S_{jj}\right|^{2}- \left|S_{ij}\right|^{2}\right)} \tag{1}\]  
\[DG=10\times\sqrt{1-ECC^{2}} \tag{2}\]antenna in attaining a given power capacity, compared with an ideal antenna with one hundred percent radiating efficiency and zero correlation between antenna elements. ME can be expressed [23] under the assumption of high SNR. The calculated MEs are depicted in Figure 15. Figure 16 displays the measured 2D radiating patterns of the proposed AP when Ant. 1 and Ant. 2 are separately excited.  
\[TARC=\sqrt{\frac{\left(S_{11}+S_{12}\right)^{2}+\left(S_{22}+S_{21}\right)^{2}} {2}} \tag{3}\]  
\[ME=\sqrt{\eta_{1}\eta_{2}(1-ECC_{12}^{2})} \tag{4}\]  
Table 1 compares the designed device and other reported similar MIMO AP systems for the 5G n78 band. One can see from the table that the primary highlights of our work are the lower side board height (5 mm), shorter distance (1 mm) between two elements of the AP, and smaller area of the AP. Otherwise, a simple T-shaped slot on the ground plane effectively promotes the device's MIMO performance. The measured outcomes showed that the proposed APs system can yet be regarded as an outstanding contender for ultra-thin smartphones.  
Figure 16: Measured 2D radiating pattern; (**a**) 3.5 GHz xoy plane. (**b**) 3.5 GHz xoz plane.  
Figure 15: Computed TARC and ME.