## 3 Simulation and Experimental Results  
Simulated vs. measured S\({}_{11}\) response of the proposed antenna is shown in Figure 5a. Sharp resonance was achieved at 6 GHz, and impedance bandwidth (\(-\)10 dB) is 443 MHz (7.26%). Gain vs. frequency plot of the proposed antenna is also shown in Figure 5a. At operating frequency, peak gain achieved is \(\sim\)9.4 dB. Gain bandwidth (3 dB) is from 5.82 GHz to 6.08 GHz (4.37%). A satisfactory agreement exists between simulated and measured results, establishing the accuracy of simulation and fabrication. Figure 5b illustrates the S\({}_{11}\) and gain vs. frequency response of the reference antenna (antenna without the superstrate assembly). It can be seen that \(-\)10 dB resonance of the reference antenna is slightly right-shifted as compared to the resonance of the proposed antenna. This frequency shifting is attributed to the input impedance variation when the dielectric superstrate is absent. Meanwhile, the gain of the proposed antenna is 6.4 dB at operating frequency, and is increased by 3 dB in the presence of the superstrate assembly. Figure 6a illustrates the far field H-plane radiation pattern at 6 GHz. Off-broadside radiation at an angle of \(-\)38\({}^{\circ}\) was achieved, deflected in the elevation plane, with side lobe levels (SLLs) \(\sim\)10 dB below the maximum. Deflection angle is aligned to the axis in which the increase of aperture size (gradient) is implemented. E-plane pattern is shown in Figure 6b. Manufacturing tolerances as well as positioning errors during measurements can be the cause of difference between simulated and measured patterns. The far field H-plane and E-plane radiation patterns of the reference antenna are shown in Figure 6c,d, respectively. It can be witnessed that without the superstrate, the antenna radiates towards broadside. The radiation pattern plotted at various frequencies is shown in Figure 7. The pattern is satisfactorily uniform over a bandwidth of 50 MHz, although a little deterioration of the SLLs occurs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathrm{AP_{L}}\) (mm) & 2.4 & 3.5 & 5.1 & 5.5 & 5.8 & 6.2 & 6.6 \\ \hline Reflection Phases & 97.72\({}^{\circ}\) & 86.24\({}^{\circ}\) & 10.56\({}^{\circ}\) & \(-\)23.89\({}^{\circ}\) & \(-\)38.38\({}^{\circ}\) & \(-\)63.91\({}^{\circ}\) & \(-\)81.57\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Gradient aperture lengths (\(\mathrm{AP_{L}}\)) and corresponding reflection phases. Figure 4: Proposed antenna. (**a**) Simulated model (cutout view). (**b**) Fabricated prototype. (h = 13 mm, L = 12 mm, W = 14 mm). Figure 5: Reflection coefficient and gain frequency response. (**a**) Proposed antenna. (**b**) Reference antenna. Figure 6: Radiation patterns of the proposed antenna, (**a**) H-plane. (**b**) E-plane. Radiation patterns of the reference antenna, (**c**) H-plane. (**d**) E-plane. The reference antenna's radiation efficiency at operating frequency is 95%; however, the proposed antenna's efficiency diminishes to 60%. The primary reason for this efficiency reduction can be deduced from Figure 2b, where the S\({}_{21}\) transmission is shown. It notes that since the unit cell/superstrate is a passive structure, its S\({}_{12}\) transmission response would also be exactly identical to Figure 2b. Thus, at operating frequency, the transmission magnitude is \(-6\) dB for the AP\({}_{\text{L}}\) value of 6.6 mm (the largest aperture dimension listed in Table 1), and the transmission magnitude reduces with the decreasing aperture values. This means that the loss of energy of the radiated wave occurs within the superstrate structure, and thus diminishes the radiation efficiency. To validate the antenna's scattering performance, simulated monostatic RCS plotted against frequency for normal illumination of the incident wave is shown in Figure 8. Vertically polarized (VP) and horizontally polarized (HP) incident wave cases are respectively given in Figure 8a,b.