## 3 Realization of EPP-BSA Using Planar Antenna Array Thinning  
It is possible to design a PAA with a large number of antennas packed into a tiny space on a chip to create a system for millimeter-wave applications when the size of the antenna element is very small. Consider the test case of the \(M=\) eight-element LAA with uniform element spacing \(d_{z}=0.5\)\(\lambda\) and size \(L_{h}=3.5\)\(\lambda\), where the cosine wave half period is chosen to be greater than the array size, \(H>L_{h}\) and equals \(H=4\lambda\), and \(R=3.5\)\(\lambda/4\)\(\lambda=0.875\). For cosine wave amplitude \(A_{c}\) changing from \(2\)\(\lambda\) to \(-2\)\(\lambda\) in the \(Y\)-direction, its span will be \(2A_{c}=4\)\(\lambda\). The realization of the eight-element LAA sector beam scanning using the proposed EPP-BSA approach can be implemented by constructing a PAA of dimensions \((4\)\(\lambda\)\(\times\)\(3.5\)\(\lambda)\) in the \(Y\)-direction and the \(Z\)-direction, respectively. Taking a uniform element spacing in the \(Y\)-direction to be \(d_{y}=0.1\)\(\lambda\) and a uniform element spacing in the \(Z\)-direction to be \(d_{z}=0.5\)\(\lambda\), a \((M_{y}\times M_{z})=(41\)\(\times\)\(8)\) planar antenna array (PAA) can be constructed as shown in Figure 35, where \(M_{y}\) is the number of elements in the \(Y\)-direction that can be calculated as follows:  
\[M_{y}\ =(2A_{c}\ /0.1\ \lambda)+1=(4\lambda\ /\ 0.1\lambda)+1=41\ elements \tag{31}\]  
\(M_{z}\) is the number of elements in the \(Z\)-direction that can be calculated as follows:  
\[M_{z}\ =M=8\ elements \tag{32}\]  
Rather than using a rotating motor or progressive phase shift techniques for beam scanning, the proposed PAA configuration allows for precise array thinning to select the desired active \"ON\" eight elements and turn off the other elements to configure the designed EPP pattern to achieve a specific scan angle with the desired radiation properties. However, there may be some errors due to the mismatch between the positions of the elements of the actual antenna array and the positions of the selected active eight elements on the PAA for the desired EPP pattern. So that a position qu  
Figure 34: Polar plot of the synthesized radiation pattern using the SLL/EPP-BSA approach at compression ratio \(R=0.5\) and \(A_{c}=2\)\(\lambda\). select the nearest element on the PAA that matches the corresponding element on the actual antenna array in order to eliminate these inaccuracies as much as feasible. Table 14 shows a comparison between the actual element positions in the \(Y\)-direction compared to the corresponding quantized element positions in the \(Y\)-direction at fixed element spacing in the \(Z\)-direction. The proposed PAA thinning technique is superior to utilizing progressive phase shifters to scan the main beam from the broadside to the desired direction since the proposed technique is based on modifying the EPP pattern rather than adjusting the phase shifter. This simplifies the production process while also lowering the cost of the feeding network. Furthermore, the proposed technique eliminates interference and coupling between the main beam and the back lobe at any scanning angle by maintaining a 180 spacing angle between them. However, when utilizing the progressive phase shift technique, the spacing angle between the main beam and the back lobe decreases as the scan angle increases, resulting in increased interference and coupling between them, which indeed increases the HPBW as the main beam approaches the end-fire direction. The implementation of the proposed (\(41\times 8\)) PAA configuration using the CST microwave studio is shown in Figure 36. The array is realized using the dipole antenna illustrated in Figure 22 with resonance frequency \(f_{o}=1\) GHz. Table 15 shows 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 \(R=0.875\).