## 4 Simulation and Measurement Results  
By modifying the parameters such as W1, W2, L1, d1, d2 and d3 and so on of the end-fire antenna array a little up and down around their calculated values, performance of the antenna is optimized. After the optimization of the parameters of the end-fire antenna arrays, Figure 10a shows the simulation and measurement results of the S parameter of the two-element end-fire antenna array without auxiliary dipole antenna. The antenna array has a bandwidth \begin{table}
\begin{tabular}{l c c} \hline \hline  & **S11 at 24 GHz (dB)** & **Antenna Gain\_Sim (dBi)** \\ \hline
2-element end-fire antenna without auxiliary dipole antenna & \(<\)\(-\)20 & 7.7 \\
2-element end-fire antenna with 1 auxiliary dipole antenna & \(<\)\(-\)18 & 9 \\
2-element end-fire antenna with 2 auxiliary dipole antennas & \(<\)\(-\)20 & 8.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison of HFSS simulation results of end-fire antenna arrays with the same input impedance matching network. Figure 9: Top view of the two-element end-fire antenna arrays (**a**) without an auxiliary dipole antenna and (**b**) with one auxiliary dipole antenna (**c**) or with two auxiliary dipole antennas in HFSS software. (**d**) Side view of the end-fire antenna prototype without an auxiliary dipole antenna; (**e**) side view of the end-fire antenna prototype with two auxiliary dipole antennas. (S11 \(<-\)10 dB) of 0.9 GHz, extending from 23.7 to 24.6 GHz. Figure 10b,c show the simulated and measured antenna gain of two-element end-fire antenna array with no auxiliary dipole antenna. The measurement results agree with the simulation results. The antenna achieves 9.1 dBi maximum gain and a 43\({}^{\circ}\) half power width (from \(-\)16\({}^{\circ}\) to 27\({}^{\circ}\)) in the X-Y plane. In the X-Z plane, the antenna achieves 8.8 dBi maximum gain and a 59\({}^{\circ}\) half power width (from \(-\)27\({}^{\circ}\) to 32\({}^{\circ}\)). The measured cross polarization ratio is below \(-\)11 dB at 24 GHz. Figure 11a shows the simulation and measurement results of the S parameter of the two-element end-fire antenna array with 1 auxiliary dipole antenna. The antenna array has a bandwidth (S11 \(<-\)10 dB) of 1.3 GHz, extending from 23.3 to 24.6 GHz. Figure 11b,c show the simulated and measured antenna gain of the two-element end-fire antenna array with one auxiliary dipole antenna. The antenna achieves 8.8 dBi maximum gain and a 56\({}^{\circ}\) half power width (from \(-\)35\({}^{\circ}\) to 21\({}^{\circ}\)) in the X-Y plane. In the X-Z plane, the antenna achieves 8.8 dBi maximum gain and a 65\({}^{\circ}\) half power width (from \(-\)37\({}^{\circ}\) to 28\({}^{\circ}\)). The measured antenna efficiency is 0.95. The measured cross polarization ratio is about \(-\)20 dB at 24 GHz. Figure 10: _Cont._  
Figure 11: _Cont._  
Figure 10: Simulation and measurement results of the (**a**) S parameter, (**b**) gain in the X–Y plane, and (**c**) gain in the X–Z plane of the two-element end-fire antenna array with no auxiliary dipole antenna. Figure 12a shows the simulation and measurement results of the S parameter of the two-element end-fire antenna array with two auxiliary dipole antennas. The antenna array has a bandwidth (S11 \(<-\)10 dB) of 0.6 GHz, extending from 24 to 24.6 GHz. Figure 12b,c show the simulated and measured antenna gain of the two-element end-fire antenna array with two auxiliary dipole antennas. The antenna achieves 9.9 dBi maximum gain and a 52\({}^{\circ}\) half power width (from \(-\)23\({}^{\circ}\) to 29\({}^{\circ}\)) in the X-Y plane. In the X-Z plane, the antenna achieves 9.9 dBi maximum gain and a 72\({}^{\circ}\) half power width (from \(-\)37\({}^{\circ}\) to 35\({}^{\circ}\)). The measured cross polarization is about \(-\)15 dB at 24 GHz.