## 2 The Design of the Element
### Parameters and Coupling Analysis  
Like most half-wavelength antennas, the dimensions of the proposed element (\(Dx=Dy=1.3\) mm) are roughly half the wavelength of the center frequency. During the optimization of the proposed antenna element parameters, it was found that after tuning the bandwidth to the target frequency band, the bandwidth of the element can be further optimized by fine-tuning \(L_{1}\). Figure 4 shows the S\({}_{11}\) curves corresponding to different \(L_{1}\), and it can be observed that the bandwidth is the widest when \(L_{1}\) is taken as 0.65 mm.  
Existing research indicates that the active VSWR of PAAs is closely related to the coupling between elements, and excessive coupling between elements can lead to the deterioration of the active VSWR [24; 29; 36; 37]. Therefore, to verify the decoupling effects of the decoupling surface and the metallized wall, simulations of the active VSWR with periodic boundaries are conducted. Simulations are performed on the active VSWR of periodic boundary elements with and without the decoupling surface to verify the decoupling effect of the decoupling surface. Simulations are also performed on the active VSWR of periodic boundary elements with and without the metallized wall to verify the decoupling effect of the metallized wall. As shown in Figure 5a, the simulation of the active VSWR with and without the decoupling surface in the periodic boundary indicates that the performance of the active VSWR with the decoupling surface is better than that without the decoupling surface, demonstrating that the decoupling surface achieves the decoupling effect. As shown in Figure 5b, the simulation of the active VSWR with and without the metallized wall in the periodic boundary indicates that the active VSWR with the metallized wall is far superior to that without the metallized wall, demonstrating that the metallized wall achieves a very good decoupling effect.  
For a more intuitive comparison, Figure 6 provides the distribution of the surface currents of the ground at 112 GHz. Shown in Figure 6a is the surface current distribution of the proposed element ground. Shown in Figure 6b is the surface current distribution of the ground without the decoupling surface. Shown in Figure 6c is the surface current distribution of the ground without the metallized wall. Comparing Figure 6a,b, it can be found that the surface current at the edge of the ground with the decoupling surface is very small, indicating weak coupling between elements, while the surface current without the metallized wall is very small, indicating weak coupling between elements, while the surface current without the metallized wall is very large, indicating very strong coupling between elements. By comparing Figure 6b,c, it can be found that the surface current of the ground  
Figure 4: The S\({}_{11}\) curves corresponding to different \(L_{1}\).  
without the decoupling surface is smaller than that without the metallized wall; thus, the decoupling effect of adding a metallized wall is more pronounced than that of adding a decoupling surface.  
To further confirm the decoupling effect of the decoupling surface and metallized wall designed within the unit, Figure 7 provides the S-parameter simulation results of the 2 \(\times\) 2 array. It can be seen from Figure 7 that within the bandwidth of 106.25-117.49 GHz, the worst-case port isolation is higher than 17.7 dB (i.e., \(S_{31}<-17.7\) dB), and the port isolation is higher than 19 dB in most of the operating band.  
Figure 5: The periodic boundary simulation active VSWR. (**a**) With/without decoupling surface. (**b**) With/without metallized wall.  
Figure 6: The simulation surface current distribution of the ground at 112 GHz. (**a**) The proposed element. (**b**) Without decoupling surface. (**c**) Without metallized wall.  
Figure 7: The S-parameter simulation results of the 2 \(\times\) 2 array.