## 4 Sub-Array Demonstrator
### Experimental Results  
Two prototypes of this \(2\times 8\) array were fabricated and used to implement a total \(4\times 8\) array for the measurement setup. The prototypes were placed on a metallic plane properly shaped, and two plexiglass bars were used to secure the two prototypes on the metallic support; see Figure 12a. For that reason, two columns of radiating elements were unavailable, and the array under test was a \(4\times 6\) array. The measurement setup is shown in Figure 12b, with all the measurements performed in an anechoic chamber.  
The measured \(S_{ij}\)-parameters are shown in Figure 12c for both the V and H ports, labeled as port 1 and port 2, respectively. The measurements show a frequency shift in the resonance, that is centered to \(\tilde{f}_{0}=f_{0}-0.09f_{0}\) instead of \(f_{0}\). However, a fractional bandwidth of 10% is achieved between \(f_{\min}=f_{\min}-0.09f_{0}\) and \(\tilde{f}_{\max}=f_{\max}-0.09f_{0}\), and the isolation between ports is lower than \(-30\) dB.  
The frequency shift can be attributed to different aspects:  
Figure 11: (**a–d**) Radiation patterns for (**a,b**) horizontal polarization, and (**c,d**) vertical polarization at \(f_{0}\). In (**a–c**), co-polar component; in (**b–d**), cross-polar component.  
Figure 12: (**a**) Array demonstrator; (**b**) measurement setup. The inset in the top-right corner shows the feeding mechanism. (**c**) Measured S-parameters.  
An important PCB curvature has been observed. This is due to the manufacturing process, and at the design frequency this issue can affect the antenna gain and the \(S_{ij}\)-parameters;
2. Possible variations in the dielectric constant with respect to the one shown in the data sheet of the materials;
3. Possible interactions between the metallic support and the radiating elements. These metallic parts are very near to the radiating board, and their effect could be not negligible.  
Moreover, the expected higher-frequency resonance in the reflection coefficients for both the H and V ports is deteriorated. This effect is most likely due to the curvature of the PCB caused by the lamination process used to stack the multiple layers.  
With this setup, it is possible to evaluate the total pattern from the active reflection coefficient. As is known, the total pattern can be obtained by pattern multiplication between the array factor and the active element pattern \(G_{\text{e,act}}\), which in turn is related to the active reflection coefficient \(\Gamma_{\text{act}}\) for every scan angle \(\theta_{0},\phi_{0}\) through the relation [25]  
\[G_{\text{e,act}}(u_{0},v_{0})=\frac{4\pi\cos\theta_{0}p_{x}p_{y}}{\lambda^{2}} (1-|\Gamma_{\text{act}}(u_{0},v_{0})|^{2}) \tag{12}\]  
where \(p_{x}\) and \(p_{y}\) represent the periodicity of the array along the \(x\)- and \(y\)-axis, respectively, with \(u_{0}=\sin\theta_{0}\cos\phi_{0}\) and \(v_{0}=\sin\theta_{0}\sin\phi_{0}\).  
The results obtained with (12) from the measurement of the scattering parameters are shown in Figure 13, whereas in Figure 14 are shown the principal planes of the active element pattern for both polarizations, and the gain plot versus frequency at broadside for both polarizations. From these results it can be seen that the active element gain has a quite flat and regular shape in the \(uv\) plane and a peak value near to the theoretical expected value in the \(\tilde{f}_{\text{min}}\)-\(\tilde{f}_{\text{max}}\) band. The main reason for this behavior is due to the frequency shift reported in Figures 12b and 14, where the peak gain and the minimum of the reflection coefficient are located around \(\tilde{f}_{0}\).  
Figure 13: (a–c) Gain measurements on the \(uv\) plane for H polarization at (a) \(\tilde{f}_{\text{min}}\), (b) \(\tilde{f}_{0}\), and (c) \(\tilde{f}_{\text{max}}\), (d–f) As in (a–c) but for V polarization.