## 3 Proposed Antenna
### Measurement Results with and without the Superstrate
The normalized cuts of the measured and simulated RHCP patterns are comparable for the case without the superstrate, while the measurement with the superstrate deviates from the simulation, as seen in Figure 7b, especially the appearance of the null, which is not observed in the simulations. This null in the measurements can be attributed to the artifacts in the measurement setup and requires further investigation. Figure 5: (**a**) Comparison of RHCP gain over frequency in measurements (solid curves) and simulation (dashed curves) without superstrate (blue colour) and with superstrate (orange colour). (**b**) Comparison of RHCP (blue colour) and LHCP gains (orange colour) in simulations (dashed curves) and measurements (solid curves) without superstrate (top) and with superstrate (bottom). (**c**) Comparison of axial ratio over frequency in simulations (dashed curves) and measurements (solid curves) without superstrate (top) and with superstrate (bottom). Such a null in the application can be detrimental for reception quality; however, in the phased array design, the null can be compensated for using adaptive weighting algorithms. Without Superstrate  
Figure 6: Normalized elevation cuts for the single element at 11 GHz in the measurements (solid curves) and simulation (dashed curves) without the superstrate (left) and with the superstrate (right) for **(a)** Elevation cut \(\Phi=0^{\circ}\), **(b)** Elevation cut \(\Phi=0^{\circ}\), **(c)** Elevation cut \(\Phi=90^{\circ}\), and **(d)** Elevation cut \(\Phi=90^{\circ}\). Figure 7: _Cont._  
The key parameters corresponding to Figures 6 and 7 are presented in Table 2. The total efficiency (\(\eta\)) for each frequency was calculated by substituting the values of the maximum RHCP realized gain \(G_{max}(\theta,\Phi)\) and the respective maximum directivity \(D_{max}(\theta,\Phi)\) in Equation (5) [30]. At 14 GHz, the measured efficiency with the superstrate was around 40% lower than the simulated efficiency as the measured directivity was approximately 3 dB higher for similar realized gains in the simulations and measurements. \[\eta=\frac{G_{max}(\theta,\Phi)}{D_{max}(\theta,\Phi)} \tag{5}\]  
The value of \(D_{max}(\theta,\Phi)\) in Equation (5) was obtained by taking the ratio of the maximum radiated power of the antenna to the power averaged at all azimuth (\(\Phi\)) and elevation (\(\theta\)) angles around the antenna at that particular frequency, as shown in Equation (6) [29]. \[D_{max}(\theta,\Phi)=\frac{4\pi\ P_{max}(\theta,\Phi)}{\Sigma P_{max}(\theta, \Phi)} \tag{6}\]  
The front-to-back ratio (\(FBR\)) mentioned in Table 2 is based on the power ratio of the beam from \(\theta=0^{\circ}\) to \(\theta=180^{\circ}\), and the half-power beamwidth (\(HPBW\)) is based on the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{4}{c}{\(11\) GHz} \\ \cline{2-5}  & \multicolumn{2}{c}{**Without Superstrate**} & \multicolumn{2}{c}{**With Superstrate**} \\ \cline{2-5}  & **Simulated** & **Measured** & **Simulated** & **Measured** \\ \hline \(Gmax(\theta,\Phi)\) (dBic) & 5.6 & 6.3 & 9 & 11.8 \\ \(\eta\) (\%) & 77 & 85 & 89 & 97 \\ FBR (dB) & 29 & 42 & 34 & 37 \\ HPBW, \(\Phi=0^{\circ}\) (\({}^{\circ}\)) & 77 & 63 & 47 & 42 \\ HPBW, \(\Phi=90^{\circ}\) (\({}^{\circ}\)) & 77 & 50 & 48 & 42 \\  & & 14 GHz & & \\ \(Gmax(\theta,\Phi)\) (dBic) & 5.28 & 6.8 & 10.35 & 9.4 \\ \(\eta\) (\%) & 88 & 76 & 89 & 55 \\ FBR (dB) & 26 & 40 & 27 & 25 \\ HPBW, \(\Phi=0^{\circ}\) (\({}^{\circ}\)) & 112 & 114 & 33 & 20 \\ HPBW, \(\Phi=90^{\circ}\) (\({}^{\circ}\)) & 94 & 80 & 32 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulated and measured antenna characteristics with and without the superstrate at 11 and 14 GHz.