## 3 Realization of EPP-BSA Using Planar Antenna Array Thinning
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cosine Wave Amplitude \(A_{c}\)**} & \multirow{2}{*}{**Element Position on \(Y\)-Direction/\(\lambda\)**} & \multicolumn{8}{c}{**Number of Antenna Element on \(Z\)-Direction**} \\ \cline{3-10}  & & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \multirow{2}{*}{0.1} & Exact position & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{2-10}  & Quantized position & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{2}{*}{0.25} & Exact position & 0.5 & 0.46 & 0.35 & 0.19 & 0 & \(-\)0.19 & \(-\)0.35 & \(-\)0.46 \\ \cline{2-10}  & Quantized position & 0.5 & 0.5 & 0.4 & 0.2 & 0 & \(-\)0.2 & \(-\)0.4 & \(-\)0.5 \\ \hline \multirow{2}{*}{\(\lambda\)} & Exact position & 1 & 0.9 & 0.7 & 0.4 & 0 & \(-\)0.4 & \(-\)0.7 & \(-\)0.9 \\ \cline{2-10}  & Quantized position & 1 & 0.9 & 0.7 & 0.4 & 0 & \(-\)0.4 & \(-\)0.7 & \(-\)0.9 \\ \hline \multirow{2}{*}{2.1} & Exact position & 2 & 1.848 & 1.414 & 0.7654 & 0 & \(-\)0.7654 & \(-\)1.414 & \(-\)1.848 \\ \cline{2-10}  & Quantized position & 2 & 1.8 & 1.4 & 0.7 & 0 & \(-\)0.7 & \(-\)1.4 & \(-\)1.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: A comparison between the actual elements’ positions in \(Y\)-direction compared to the corresponding quantized elements’ positions in \(Y\)-direction at fixed element spacing in \(Z\)-direction for the realization of EPP-BSA approach using the proposed PAA thinning. Figure 35: Element distribution of the proposed (\(41\times 8\)) PAA configuration and the element distributions of the \(M=8\) elements of the actual array using the proposed EPP-BSA approach at uniform element spacing \(d_{z}=0.5\ \lambda\) on the \(Z\)-axis and \(A_{c}\) changing from positive to negative. Figure 37 shows the CST simulated 3D radiation patterns using the PAA thinning for implementation of the proposed EPP-BSA approach for the eight-element ULAA at \(R=0.875\), \(A_{c}=0\), \(A_{c}=0.5\,\lambda\), \(A_{c}=\lambda\), \(A_{c}=2\,\lambda\), and changing from positive to negative. While the corresponding polar plots are shown in Figure 38. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**CST Simulation Results Using**} & \multicolumn{3}{c}{**CST Simulation Results Using**} & \multicolumn{3}{c}{**MATLAB Simulation Results Using**} \\ \cline{3-10} \multirow{-2}{*}{**Cosine Wave Amplitude \(A_{c}\)**} & \multicolumn{3}{c}{**PAA Thinning**} & \multicolumn{3}{c}{**Actual EPP/BSA**} & \multicolumn{3}{c}{**Actual EPP/BSA**} \\ \cline{2-10}  & \multicolumn{1}{c}{**Scan Angle**} & \multicolumn{1}{c}{**HPBW**} & \multicolumn{1}{c}{**SLL**} & \multicolumn{1}{c}{**Scan Angle**} & \multicolumn{1}{c}{**HPBW**} & \multicolumn{1}{c}{**SLL**} & \multicolumn{1}{c}{**Scan Angle**} & \multicolumn{1}{c}{**HPBW**} & \multicolumn{1}{c}{**SLL**} \\ \hline
0 & 0 & 12.6 & \(-\)13.6 dB & 0 & 12.3 & \(-\)13 dB & 0 & 12.8 & \(-\)12.8 dB \\ \hline
0.5 & 17 & 12.2 & \(-\)6.5 dB & 17 & 12 & \(-\)7.5 dB & 16.81 & 12.4 & \(-\)7.88 dB \\ \hline \(\lambda\) & 30 & 10.9 & \(-\)2.8 dB & 31 & 11.2 & \(-\)4.1 dB & 31.76 & 11.2 & \(-\)4.917 dB \\ \hline
2 & 50 & 8.7 & \(-\)1.1 dB & 51 & 9.1 & \(-\)2.1 dB & 51.36 & 9.2 & \(-\)2.668 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 15: A comparison between the CST simulation results and MATLAB simulation results of the proposed EPP/BSA approach using the proposed PAA thinning and actual EPP/BSA indicating the resultant scan angle, SLL, and HPBW at \(R=0.875\). Figure 37: CST-simulated 3D radiation patterns using the PAA thinning for implementation of the proposed EPP-BSA approach for 8-element ULAA at \(R=0.875\): (**a**) \(A_{c}=0\), (**b**) \(A_{c}=0.5\,\lambda\), (**c**) \(A_{c}=\lambda\), (**d**) \(A_{c}=2\,\lambda\), and changing from positive to negative. Figure 36: The implementation of the proposed (\(41\times 8\)) PAA configuration using CST microwave studio utilizing a dipole antenna with resonance frequency \(f_{o}=1\) GHz.