## 2 Proposed EPP-Based Beam Scanning Approaches
### Test case (3): \(R=0.7778\)
#### 2.1.3. CST Realization of the Proposed EPP-BSA  
In this section, the proposed EPP-BSA is realistically validated for actual antenna elements rather than isotropic antennas. The antenna array is created using the CST microwave studio software package utilizing a dipole element, the dimensions of which, as well as the H-plane and E-plane patterns, are shown in Figure 22. The simulated scattering parameter (reflection coefficient) \(|S_{11}|\) of the dipole antenna is illustrated in Figure 23, showing a resonance frequency \(f_{o}=1\) GHz.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Compression Ratio**} & \multirow{2}{*}{**Cosine Wave Amplitude \(A_{c}\)**} & \multicolumn{2}{c}{**Scan Angle Range with Respect to**} & \multirow{2}{*}{**SLL**} & \multirow{2}{*}{**HPBW**} \\  & & & & & **Broadside Direction** & \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{\(R=1\)} & 0 to 0.19 \(\lambda\) & From 0° to 7.01° & \(<-\)10 dB & Constant \\ \cline{3-6}  & & 0.19 \(\lambda\) to 1.5 \(\lambda\) & From 7.01° to 52.91° & \(>-\)10 dB & Decreased by 3° \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{\(R=0.875\)} & 0 to 0.25 \(\lambda\) & From 0° to 8.56° & \(<-\)10 dB & Constant \\ \cline{3-6}  & & 0.25 \(\lambda\) to 2 \(\lambda\) & From 8.5° to 51.36° & \(>-\)10 dB & Decreased by 3.6° \\ \hline \multirow{2}{*}{3} & \multirow{2}{*}{\(R=0.7778\)} & 0 to 0.3 \(\lambda\) & From (0° to 9.08° & \(<-\)10 dB & Constant \\ \cline{3-6}  & & 0.3 \(\lambda\) to 2 \(\lambda\) & From 9.08° to 48.78° & \(>-\)10 dB & Decreased by 1.38° \\ \hline \multirow{2}{*}{4} & \multirow{2}{*}{\(R=0.7\)} & 0 to 0.39 \(\lambda\) & From 0° to 10.62° & \(<-\)10 dB & Constant \\ \cline{3-6}  & & 0.39 \(\lambda\) to 2 \(\lambda\) & From 10.62° to 45.69° & \(>-\)10 dB & Increase by 1.1° \\ \hline \multirow{2}{*}{5} & \multirow{2}{*}{\(R=0.5\)} & 0 to 0.65 \(\lambda\) & From 0° to 10.83° & \(<-\)10 dB & Constant \\ \cline{3-6}  & & 0.65 \(\lambda\) to 2 \(\lambda\) & From 10.62° to 31.25° & \(>-\)10 dB & Increased by 2.83° \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison between the five test cases of compression ratio. The optimal value is in bold.  
Figure 22: (a) Dimensions of dipole antenna, (b) H-plane pattern, and (c) E-plane pattern.  
Considering the recommended test case 2 with a compression ratio \(R=0.875\), which yields the best results in terms of HPBW and scanning range, we created the synthesized eight-element antenna arrays applying the proposed EPP-BSA approach. The synthesized antenna arrays and the associated 3D radiation patterns are shown in Figure 24, while the polar plots of the synthesized radiation patterns using the CST software package are shown in Figure 25. The CST simulation results for \(A_{c}\) changing from 0 to 2 \(\lambda\) are recorded in Table 7 compared to the MATLAB simulation results indicating the resultant scan angle, SLL, and HPBW. The comparison shows a high matching between the CST and MATLAB simulation results with minimal fractal changes because the CST acts as a real environment and considers the mutual coupling between antenna elements in the synthesized array structures. This demonstrates the ability of practical validation of the proposed EPP-BSA approach.  
Figure 23: The scattering parameter (reflection coefficient) \(|S_{11}|\) against the frequency for the designed dipole antenna.  
Figure 24: _Cont._  
Figure 24: The 3D radiation pattern plots of the synthesized antenna arrays using CST software package applying the proposed EPP-BSA approach for an 8-element ULAA for \(R=0.875\) at (**a**) \(A_{c}=0\), (**b**) \(A_{c}=0.25\)\(\lambda\), (**c**) \(A_{c}=0.5\)\(\lambda\), (**d**) \(A_{c}=0.75\)\(\lambda\), (**e**) \(A_{c}=1\)\(\lambda\), (**f**) \(A_{c}=1.251\)\(\lambda\), (**g**) \(A_{c}=1.5\)\(\lambda\), (**h**) \(A_{c}=1.75\)\(\lambda\), (**i**) \(A_{c}=2\)\(\lambda\), and changing from positive to negative.