## 3 Full-Wave Simulation Results  
The phased antenna systems based on the 2-D phased array configurations were assessed to analyze the reduction capability in terms of the number of phase shifters and beam-scanning possibilities in the planes of elevation and azimuth. The phase values were set at the input ports in order to build the phase plane in the specified direction. The 2-D phased array architectures were assessed in the CST Microwave electromagnetic solver to include mutual coupling and the errors (of amplitude and phase) caused by each proposed 2-D array configuration. CST is a reliable electromagnetic solver based on the finite integration technique. All the simulations performed by the CST electromagnetic solver took the chosen element into account, considering the dimensions and features set in the previous section. The substrate used in the antenna element and the feeding network system was FR4. All the SMA connectors and the resistors were taken into account in the full-wave simulation. The errors of the amplitude and phase were calculated for each block of the 2-D architecture and considered at the level of the amplifiers and antenna elements of the phased array system. Each beam-scanning angle was assessed for the two proposed 2-D architectures. Each design case (for each scanning direction) showed good matching behavior and the value of the reflection coefficient was lower than \(-10\) dB for the specified bandwidth. Figure 16 illustrates the behavior of the active reflection coefficient for the cases of the worst and best performance of the two proposed 2-D architectures. The configuration 1 presented the worst case for the farthest scanning angle. Figure 15: Radiation pattern of the chosen element obtained by the simulation (blue color) in CST and experimental measurements (red color): (**a**) 5.5 GHz, (**b**) 5.75 GHz, (**c**) 6.0 GHz and (**d**) 5.75 GHz (cut at the azimuth plane). Figure 17 illustrates the 2-D phased array for the proposed antenna systems and the behavior of the 3D radiation generated using CST Microwave Studio. The cases shown in Figure 17 are as follows: (a) \(\phi_{0}=15^{\circ}\) and \(\theta_{0}=18^{\circ}\) for proposed case 2, (b) \(\phi_{0}=30^{\circ}\) and \(\theta_{0}=10^{\circ}\) for proposed case 2, (c) \(\phi_{0}=20^{\circ}\) and \(\theta_{0}=10^{\circ}\) for proposed case 1, and (d) \(\phi_{0}=40^{\circ}\) and \(\theta_{0}=18^{\circ}\) for proposed case 1. A good performance in the side lobe level was obtained for each beam-scanning angle analyzed for each proposed 2-D phased array. It reached a side lobe level performance of \(-19\) dB. Figure 16: Active reflection coefficient for the cases of the worst and best performance of the two proposed 2-D architectures. Figure 18 illustrates the losses in gain of the proposed antenna system, considering beam-steering. This case is generated by the proposed case 1 and a value of 1.5 dB of gain loss is generated for the proposed case 1. Therefore, good characteristics in terms of the gain and scanning performance are obtained for the 2-D phased array systems. Furthermore, Figure 19 illustrates the behavior of the radiation pattern at 5.5 GHz, 5.75 GHz and 6.0 GHz for \(\theta_{0}=18^{\circ}\). As observed in Figure 19, the behavior of the radiation pattern is retained if the value of frequency changes, i.e., there is no significant changes with those frequency changes. The feeding network design can operate at \(\theta_{0}=30^{\circ}\) for \(\phi_{0}=0^{\circ}\), as shown in the radiation pattern of Figure 20. However, there is a trade-off between the scanning angle and the amplification value (gain value of the amplifiers). It is feasible to reach this scanning angle, but high values of amplification are required, as shown in Tables 9 and 10. Furthermore, the side lobe level deteriorates to reach \(-17\) dB. Figure 19: Behavior of the radiation pattern at 5.5 GHz, 5.75 GHz and 6.0 GHz for \(\theta_{0}=18^{\circ}\). Figure 18: Worst case of the losses in gain of the proposed antenna system, considering beam-scanning.