## 2 Proposed Antenna Design
### Verification of the Proposed Antenna  
To verify the feasibility of the proposed antenna, a unit-cell is fabricated and measured in a full anechoic chamber. Figure 5a,b present the top views of the fabricated S-band and X-band layers. The S-band element has a mesh structure, as shown in Figure 5a, and the E-shaped antenna in the X-band has extended via cavities, as shown in Figure 5b. The S-band and X-band layers are tightly attached using a glue-type adhesive. The measurement setup in the full anechoic chamber is shown in Figure 5c, where the antenna under test (AUT) in the yellow rectangle is fixed with a zig and taping. The reflection and active element patterns for the 10 elements are fully measured in the S-band and X-band.  
Figure 6 presents the reflection coefficient and bore-sight gain of the fabricated S-band element and the central X-band element. For the reflection coefficient measurement, 800 sample points are used. For the bore-sight gain measurement, 11 sample points (S-band) and 7 sample points (X-band) are used. The 'X' mark, solid line, dashed line, and dotted line indicate the measured bore-sight gain, the measured reflection coefficient, the simulated bore-sight gain, and the simulated reflection coefficient, respectively. The average gains (from 2.5 GHz to 3.5 GHz) of the S-band antenna are 5 dBi by simulation and 5.5 dBi by measurement. The simulated reflection coefficient of the S-band element is under \(-10\) dB from 2.70 GHz to 3.456 GHz (a bandwidth of 756 MHz), which is in good agreement with the measurement. The average gains (from 9 GHz to 12 GHz) of the X-band center element are 4.5 dBi by simulation and 4.7 dBi by measurement. The reflection coefficient of the X-band center element is under \(-10\) dB from 8.76 GHz and 10.72 GHz (a bandwidth of 1.96 GHz).  
Figure 7a,b show the simulated and measured two-dimensional (2D) radiation patterns of the S-band antenna at 3 GHz. A half-power beam width (HPBW) of around 80\({}^{\circ}\) is examined for the co-polarization.  
Figure 8a,b show the 2D radiation patterns of the center X-band antenna at 10 GHz. The co-polarization pattern shows a bore-sight gain of 6 dBi, while exhibiting a low level of cross polarization. A measured half-power beam width (HPBW) of 44.1\({}^{\circ}\) is observed for the co-polarization beam pattern.  
Figure 5: _Cont._Figure 5: Photographs of the fabricated antenna and measurement setup: (**a**) top view of the S-band layer; (**b**) top view of the X-band layer; (**c**) measurement setup.  
Figure 6: _Cont._  
Figure 8: Simulated and measured 2D radiation patterns of the X-band antenna: (**a**) co-polarization; (**b**) cross-polarization.  
Figure 6: Simulated and measured reflection coefficients and bore-sight gains of the antenna: (**a**) S-band; (**b**) X-band.  
Figure 7: Simulated and measured 2D radiation patterns of the S-band antenna: (**a**) co-polarization; (**b**) cross-polarization.  
In order to verify the beam forming characteristics, the active element patterns of all nine elements of the X-band antenna are measured, and then the array pattern is achieved using the following equation [28; 29]:  
\[G_{array}(\theta,\phi)=\frac{\sum\limits_{i=1}^{N}\overline{w}_{i}\overline{g}_{ i}(\theta,\phi)}{\sqrt{\sum\limits_{i=1}^{N}|\overline{w}_{i}|^{2}}}, \tag{2}\]  
where \(g_{i}\) and \(w_{i}\) are the active element pattern and weight vector of the \(i\)-th element, respectively. Figure 9 shows the simulated and measured 2D array patterns of the nine X-band elements at 10 GHz. The bore-sight gains at 10 GHz for the simulated and measured beam patterns are 13.6 dBi and 13.2 dBi, respectively.