## 3 Simulated and Measured Results Discussion  
The photo of the proposed antenna is shown in Figure 14. The distance between the metal plate and antenna is 8 mm. The reflection coefficient curve and gain of the proposed antenna is presented in Figure 15. The proposed antenna has good impedance matching from 5.7 GHz to 7.7 GHz with \(|\)S11\(|<-10\) dB. The measured results have the same trend with the simulated results. Over the band of 5.7-7.7 GHz, the simulated gain of the tilted antenna is from 12.1 dBi to 13.8 dBi, including 1-dB gain variation in the band of 5.7-7.0 GHz and 1.7-dB gain variation in the band of 7.0-7.7 GHz. The measured gains over the band of 5.7 -7 GHz are slightly lower than the simulated gains from 11.6 diBi-12.3 di because of the manufactured tolerance and tested tolerance. The radiation patterns of the proposed antenna are illustrated in Figure 16. Over the band from 5.7 GHz to 7.0 GHz, the radiation patterns keep stable, and the beam angle is fixed at \(-38^{\circ}\). The co-polarization of the proposed antenna is along the x-axis. Additionally, the cross-polarization level is less than \(-17\) dB. The measured results are in coincidence with the simulated results. Over the band of 7.0 GHz-7.7 GHz, the radiation beams vary from \(-37^{\circ}\) to \(-53^{\circ}\), the sidelobe levels increase obviously, and the simulated gain is in the range of 11.3 dBi -12.5 dBi at \(-38^{\circ}\), as shown in Figure 17.  
Figure 14: Photos of the proposed antenna. (**a**) top and bottom surfaces, (**b**) full view. Figure 15: Reflective coefficients and gain of the proposed antenna. All of the previous designs in Table 1 tilt beams by loading the metamaterial plate on the antenna. These designs radiate tilted beams with various angles over a certain frequency band because of the narrow frequency band of the metamaterial retaining the desired refractive index. However, the proposed antenna can radiate fixed tilted beams over 5.7 GHz-7.0 GHz. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multirow{2}{*}{
\begin{tabular}{c} **Bandwidth** \\ **(GHz)** \\ \end{tabular} } & \multirow{2}{*}{**Height**} & \multicolumn{2}{c}{**Gain Enhancement**} & \multicolumn{1}{c}{**Tilting Angle**} & \multicolumn{1}{c}{**Possible Tilting**} \\  & & & **hancement** & **Angle** & **Range** \\ \hline
[5] & null & \(1\lambda_{0}\) & \(8\,\mathrm{dB}\) & \(20^{\circ}\) & null \\ \hline
[7] & \begin{tabular}{c} 26 \\ 28 \\ 29 \\ \end{tabular} & \begin{tabular}{c} 0.37\(\lambda_{0}\) \\ 2 layers \\ \end{tabular} & \begin{tabular}{c} 30\(\lambda\) \\ 30 dB \\ 36\({}^{\circ}\) \\ 5.2 dB \\ \end{tabular} & \
\begin{tabular}{c} 30\({}^{\circ}\) \\ 38\({}^{\circ}\) \\ 35\({}^{\circ}\) (4 layers) \\ \end{tabular} &
\begin{tabular}{c} 0-55\({}^{\circ}\); \\ 55\({}^{\circ}\) (4 layers) \\ \end{tabular} \\ \hline
[8] & \begin{tabular}{c} 3.4 \\ 3.5 \\ 3.6 \\ \end{tabular} & \begin{tabular}{c} 0.32\(\lambda_{0}\) \\ 5 layers \\ \end{tabular} & \begin{tabular}{c} 4.7 dB \\ 5.1 dB \\ 5.2 dB \\ \end{tabular} & \
\begin{tabular}{c} 30\({}^{\circ}\) \\ 33\({}^{\circ}\) \\ 35\({}^{\circ}\) \\ 35\({}^{\circ}\) \\ \end{tabular} &
\begin{tabular}{c} Port1: \(-32\)-0\({}^{\circ}\); \\ Port2: 0-32\({}^{\circ}\) \\ \end{tabular} \\ \hline
[9] & \begin{tabular}{c} 5.1-5.3 \\ 4 layers \\ \end{tabular} & \begin{tabular}{c} 0.6\(\lambda_{0}\) \\ 4 layers \\ \end{tabular} & \begin{tabular}{c} 0.75 dB \\ 0.75 dB \\ \end{tabular} & \begin{tabular}{c} Port1: \(-38^{\circ}\) \\ Port2: 38\({}^{\circ}\) \\ 36\({}^{\circ}\) \\ \end{tabular} & \begin{tabular}{c} Port1: \(-38^{\circ}\) \\ Port2: 0-38\({}^{\circ}\) \\ 36\({}^{\circ}\) \\ \end{tabular} \\ \hline Pro. & \begin{tabular}{c} 5.7-7.0 \\ (20\%) \\ \end{tabular} & \begin{tabular}{c} 0.17\(\lambda_{0}\) \\ \end{tabular} & \begin{tabular}{c} 3 dB \\ \end{tabular} & \
\begin{tabular}{c} 52\({}^{\circ}\) \\ \end{tabular} &
\begin{tabular}{c} 0\({}^{\circ}\)-60\({}^{\circ}\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}