*3.4. Application Scenario*

An application scenario of the presented antenna held in dual-hand mode (DHM) is studied to identify the robustness and practicability of the proposed MIMO antenna array. Figure 6 plots the simulated S-parameters in DHM and the −10 dB bandwidth of Ant. 5, with Ant. 8 not being able cover two target bands. The −10 dB impedance matched bandwidth of Ant. 2, Ant. 3, Ant. 6, and Ant. 7 can contain 5G 3.6–3.8 GHz and 4.8–5 GHz frequency bands. The simulated S11 and S44 can still wholly cover the two desired bands. Figure 6b provides the total radiated power (TRP) of the proposed antenna when Ant. 1, Ant. 2, Ant. 5, and Ant. 6 are separately excited with 1 W input power. The radiating ability of four inner elements (Ant. 2, Ant. 3, Ant. 6, and Ant. 7) are generally better than the other four elements constructed in the corners of the system substrate, which have the closest distance to the hand tissue compared with the inner four elements. Figure 7 presents the proposed antenna's simulated three-dimension (3D) and two-dimension (2D) radiation patterns when Ant. 8 and Ant. 7 are independently excited at 3.5 GHz and 4.9 GHz, respectively. The simulated specific absorption rate (SAR) distribution when Ant. 8 and Ant. 7 are separately excited with 100 mW input power at two resonant modes, as shown in Figure 8. A maximum SAR value of 1.45 W/kg and 1.22 W/kg is acquired at 3.5 GHz and 4.9 GHz, respectively. Both SAR values are lower than the European and American requirements of 2.0 W/kg and 1.6 W/kg.

**Figure 6.** Simulated (**a**) S-parameters and (**b**) TRPs for the presented antenna held in DHM.

**Figure 7.** Simulated 3D and 2D patterns when (**a**) Ant. 8 excited at 3.5 GHz and (**b**) Ant. 7 excited at 4.9 GHz.

**Figure 8.** SAR field distribution.

#### **4. Experimental Results**

A prototype of the explored antenna was printed and measured to validate the simulated results. Figure 9 presents the photograph of the prototype and test scenarios using a vector network analyzer (VNA: N5224A) and anechoic chamber. In Figure 9a, when Ant. 2 and Ant. 3 are excited, two distinctly resonant modes around 3.5 GHz and 4.9 GHz can be obtained, and excellent uniformity between S22 and S33 can be observed. Little

frequency offset occurs because of the soldering process of the SMA connectors. Figure 9b illustrates the measuring environment of the 2D radiating patterns. Figure 10a,b compare the simulated and measured S-parameters (Sii and Sij, respectively). A slight frequency shift exists between the simulated and measured results, but the measurement can still completely cover the target bands. Measured worst isolation (14.5 dB) of S23 appears at around 3.5 GHz. Figure 10c,d present the measured S-parameters of the proposed antenna. All the tested input return loss curves of eight ports can contain the desired bands, and the measured mutual coupling is separately larger than 14.5 dB and 15 dB at 3.5 GHz and 4.9 GHz. Figure 11 provides the simulated and measured gain and radiating efficiency of Ant. 1 and Ant. 2. As shown in Figure 11a, maximum gains of 5 dBi and 4.8 dBi are achieved during the former and latter operating bands, respectively. Radiating efficiency of approximately 60% and 70% is obtained separately at 3.5 GHz and 4.9 GHz, as shown in Figure 11b. The measured and simulated 2D radiating patterns of the proposed antenna are illustrated in Figure 12. The discrepancies between the simulated and measured curves are caused by the soldering process and the installation angle of the antenna when it is tested in the anechoic chamber.

**Figure 9.** Photograph of the manufactured model of the proposed antenna and the experimental environment (**a**) measured by the VNA and (**b**) measured in the anechoic chamber.

Numerous indicators, including ECC, DG, TARC, and ME, were computed to assess the MIMO performance of the designed MIMO antenna. Figure 13 . The largest measured ECCs of 0.004 and 0.008 are realized across the former and the latter operating modes, respectively. The ECCs are computed from the radiating results based on Formula (1) [18]. The computed DGs, calculated from Formula (2) [19], are better than 9.99 dB and 9.978 dB within the two target bands, respectively. TARC is the definition of the square root of the ratio of total reflected radio-frequency (RF) power to the total incident power. As shown in Figure 14, the TARC curves are calculated by Equation (3) [20], which are well below the −10 dB level within the two desired bands. ME is defined as the power loss of a realistic antenna in achieving a given power capacity compared with an ideal antenna with total percentage radiation efficiency. ME can be expressed by Equation (4) [21]. Figure 15 compares the simulated and measured ME results between Ant. 1 and Ant. 2, and between Ant. 2 and Ant. 3, respectively. Measured ME values of approximately 70% and 75% are obtained at 3.5 GHz and 4.9 GHz, respectively. Remarkable consistency between the simulated and measured ME curves was observed.

$$\text{ECC} = \frac{\left| \mathbf{S}\_{\text{ii}}^{\ast} \mathbf{S}\_{\text{ij}} + \mathbf{S}\_{\text{ji}}^{\ast} \mathbf{S}\_{\text{jl}} \right|^{2}}{(1 - \left| \mathbf{S}\_{\text{ii}} \right|^{2} - \left| \mathbf{S}\_{\text{ji}} \right|^{2})(1 - \left| \mathbf{S}\_{\text{jj}} \right|^{2} - \left| \mathbf{S}\_{\text{ij}} \right|^{2})} \tag{1}$$

$$\text{DG} = 10 \times \sqrt{1 - \text{ECC}^2} \tag{2}$$

$$\text{TARC} = \sqrt{\frac{(\text{S}\_{11} + \text{S}\_{12})^2 + (\text{S}\_{22} + \text{S}\_{21})^2}{2}} \tag{3}$$

$$\text{ME} = \sqrt{\eta\_1 \eta\_2 (1 - \text{ECC}\_{12}^2)} \tag{4}$$

where η<sup>1</sup> and η<sup>2</sup> represent the total efficiency of Ant. 1 and Ant. 2, respectively.

**Figure 10.** Simulated and measured S-parameters (**a**) Sii, (**b**) Sij, (**c**) measured Sii, and (**d**) measured Sij.

**Figure 11.** Simulated and measured (**a**) gain and (**b**) radiating efficiency of Ant. 1 and Ant. 2.

**Figure 12.** Measured and simulated 2D radiating patterns. (**a**) Ant. 1 is excited at 3.5 GHz, XOY plane, (**b**) Ant. 1 is excited at 3.5 GHz, XOZ plane, (**c**) Ant. 2 is excited at 4.9 GHz, XOY plane, (**d**) Ant. 2 is excited at 4.9 GHz, XOZ plane.

**Figure 13.** Simulated and measured ECCs and DGs.

**Figure 14.** Simulated and measured TARCs.

**Figure 15.** Simulated and measured MEs.

Table 2 presents a performance contrast between the presented antenna and other 5G smartphone antennas exploited in recent years. The primary highlights of the proposed antenna are the lowest lateral sideboard, superior isolation performance, and lower ECCs.

