# Miniaturized MIMO Antenna Array with High Isolation for 5G Metal-Frame Smartphone Application
## 2 Proposed MIMO Antenna Design
### Antenna Element Design  
The planar structure and detailed dimensions of the proposed adjacent antenna elements are shown in Figure 2a. Inverted-F antennas (IFAS) are widely used in terminal antennas due to their small size. Based on the principle of transmission line, we have assumed that the entire length of L3 is close to the \(\lambda/4\) electrical length, which excites resonance and produces an impedance bandwidth. L3 is shown in Figure 2b. To verify this hypothesis, we tried to etch the inverted F-shaped folded groove on the metal frame and used the inverted L-shaped microstrip line for feeding to transfer the energy into the inverted-F groove by coupling. Plus, the resonance was successfully excited to form the impedance bandwidth required. The resonant surface currents and the reflection coefficients of the simulated antenna elements are shown in Figure 3. It is clear that the resonant surface current is mainly distributed along with the L3 slot of the IFA slot. This result is consistent with the hypothesis. In addition, the effect of the distance between the two short slots (L1 and L2) on the impedance bandwidth has been studied, as shown in Figure 2b. The result in Figure 4a shows that moving L2 to the right will lower the frequency and reduce the impedance matching. Figure 4b shows that moving L1 to the left also lowers the frequency. The two simulation results show that the resonance length of L3 can be changed by adjusting the distance of L1 and L2, and that the resonance frequency can be shifted. By comparing the simulation results, the effect is the best when the distance between L1 and L2 is shown in Figure 2a front view. The target of our proposed IFAS is to cover the 4.4-5.0 GHz operating bandwidth. Figure 1: Overall geometry and dimensions of the proposed MIMO antenna array. Next, let us discuss why L1 and L2 slots are needed for the antenna. Figure 5 shows the simulation results of reflection coefficients in four cases. The simulation results for the reflection coefficient of the antennas with L1 and without L1 and L2 are shown in Figure 5a,b. It is obvious from two results that resonance cannot be achieved in the desired frequency band in either situation. L1 and L2 are thus needed. When the relative position between the feeding line and the L3 is changed, the simulation results for the reflection coefficient of the antenna without L1 and L2 are shown in Figure 5c,d. These two findings demonstrate that resonance in the band cannot be attained. If there is simply L3, L3's length needs to be increased in order to achieve resonance in the band. This is not what we had hoped for. Figure 3: Surface current distributions of the resonance and simulates the reflection coefficient of the antenna element. Figure 2: Detailed dimensions of the antenna element. (**a**): Inverted L-shaped microstrip line and de-coupling element and (**b**): no optimized antenna element. Figure 6 shows the simulated results for the reflection coefficient of a single antenna when the relative position between the feeding line and L3 is adjusted. The simulation findings show that the relative position between the feeding line and L3 has an impact on the impedance matching to some extent. The optimized location has the best matching effect. Figure 4: Simulate reflection coefficient of the antenna element. **(a)**: With effects of L2 distance moved and **(b)**: with effects of L1 distance moved. Figure 5: Simulation results. **(a)**: Reflection coefficients without L1, **(b)**: reflection coefficients without L1 and L2, **(c)**: the reflection coefficients obtained after moving the feeding line to the left and right, respectively, and **(d)**: the reflection coefficient obtained after moving the feeding line up and down, respectively. The isolation of the arranged MIMO antenna system without any decoupling structure can reach more than 13.5 dB, as shown in Figure 7. The MIMO antenna systems are fully capable of terminal products with low isolation requirements and limited clearance.