## 4 Reduce the Coupling of GAF MIMO Antenna Array  
We propose two ways to reduce the coupling between MIMO antenna elements. One way is to use GAF FSS to isolate spatial electromagnetic waves, and the other is to set two GAF isolation strips (ISs) between antenna elements to suppress the influence of surface electromagnetic waves. The isolation of the antenna elements can be effectively improved by adjusting the width and the spacing of the two GAF ISs. The optimized width of the GAF IS is 0.5 mm, and the length is consistent with the length of the dielectric substrate. The gap between the two GAFS is 3 mm. In addition, the GAF FSS is placed in the middle of two ISs. The substrate of GAF FSS is PET film with a thickness of 0.06 mm, dielectric constant of 3.5 and loss tangent of 0.003. The dimension of the GAF FSS element is 16 mm \(\times\) 16 mm. The width and total length are 0.5 mm and 39.8 mm, respectively, as shown in Figure 5. In practice, FSS can be integrated into the device by means of a card slot. Additionally, for high-power devices, the hollow structure is more benefiting to heat dissipate management.  
Figure 4: The simulated radiation patterns of GAF MIMO antenna array. (**a,b**) The E-plane and H-plane radiation patterns of Antenna 1, respectively, (**c,d**) The E-plane and H-plane radiation patterns of Antenna 2, respectively.  
Figure 6 shows the isolation between Antenna 1/Antenna 2 and adjacent antenna elements in the four cases of no decoupling structure, only GAF IS, only FAF FSS, and both GAF IS and FSS. It can be clearly seen from the results that both GAF IS and FSS have significant benefits in improving isolation, and both can be increased to more than 20 dB. The dual decoupling structure of GAF IS and FSS is the superposition of the effects when the two structures exist separately.  
As shown in Figure 7a,b, the isolation between GAF MIMO antenna elements is significantly improved, after adding an isolation structure of GAF FSSs and isolation strips. When Antenna 1 is used as a radiation source, the transmission coefficients between Antenna 1  
Figure 5: The geometry structure of GAF MIMO antenna array with GAF frequency selective surface (FSS) and isolation strips (ISs).  
and each antenna are \(|\text{S}_{21}\,|\,=-28.82\) dB, \(|\text{S}_{31}\,|\,=-44.86\) dB, \(|\text{S}_{41}\,|\,=-51.83\) dB. When Antenna 2 is used as a radiation source, the isolation from each antenna is \(|\text{S}_{12}\,|\,=-28.57\) dB, \(|\text{S}_{32}\,|\,=-25.41\) dB, \(|\text{S}_{42}\,|\,=-43.95\) dB. Compared with the initial GAF MIMO antenna array, the isolation is improved by more than 10 dB.  
The surface current can deeply analyze the working mode of the antenna. Figure 7c-f show the surface current of the entire MIMO antenna array when Antenna 1 and Antenna 2 are used as radiation sources, respectively. When Antenna 1 is used as a radiation source and no decoupling structure is added, there are strongly induced surface currents on Antenna 2, Antenna 3 and Antenna 4, which are caused by the coupling field, as shown in Figure 7c. On the other hand, when GAF FSS and IS are added, there is almost no induced current on the non-radiating antenna, which proves that the decoupling structure suppresses the coupling effect, as shown in Figure 7d. Analogous to the Antenna 2 as the radiation source, the decoupling structure also suppresses the coupling between the antenna elements, as shown in Figure 7e,f.  
Compared with the initial MIMO antenna array, the radiation patterns of the GAF MIMO antenna array with the decoupling structure is modified to normal phase radiation, as shown in Figure 8.  
Figure 7: (**a,b**) The simulated S-parameters of GAF MIMO antenna array with GAF FSS and IS. (**a**) Antenna 1, (**b**) Antenna 2, (**c,d**) electric field distribution comparison of Antenna 1 without (**c**)/with (**d**) GAF FSS and IS; (**e,f**) surface current distribution comparison of Antenna 2 without (**e**)/with (**f**) GAF FSS and IS.