# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 3 Verification of the Modeling Results for Scattering Plate Using MoM with PBF Based on WG Model
The values of the Euclidean coefficient and standard deviation range from 0 to +\(\infty\), with values closer to 0 indicating greater similarity between the two vectors. These coefficients were categorized into group 2. Figure 13 illustrates the dependence of the correlation coefficients on \(T\) with a step size of \(T\) equal to 10. It can be observed that the Pearson and Cosine coefficients show a good match with each other, while the Spearman and Kendall coefficients have a similar shape but differ in value. Similarly, the Euclidean and standard deviation coefficients exhibit a similar shape but differ in magnitude (the Euclidean coefficient is significantly higher than the standard deviation). In general, Figure 13 indicates that when \(T<400\), the correlation coefficients demonstrate that the FS BSCSs are similar to the WG BSCS in the region of \(\theta=60\)-\(120^{\circ}\) and \(\varphi=60\)-\(120^{\circ}\). However, at \(T=100\) (or \(T=200\)), the Spearman and Kendall coefficients show a significant drop (or the Euclidean and standard deviation coefficients increase rapidly), indicating that the FS BSCSs at \(T=100\) (or \(T=200\)) differs from the WG BSCS more than at other \(T\) within this range. This again may be explained by the fact that the phase of \(\mathbf{i}\) on the removed wires were not considered. Overall, it can be concluded that in the case when the incoming wave excites in the region of \(\theta=60\)-\(120^{\circ}\) and \(\varphi=60\)-\(120^{\circ}\), to create a FS that  
Figure 13: The dependence of correlation coefficient of group 1 (\(\mathbf{a}\)) and group 2 (\(\mathbf{b}\)) on \(T\). achieves scattering characteristics similar to the original WG, \(T<400\) should be considered (except for \(T=100\) or \(200\)). Additionally, the dependence of the reduction in mass and computational cost on \(T\) is illustrated in Figure 14. Similarly to the GEET value, as \(T\) increased, the number of segments decreased, resulting in a reduction in mass, surface, and computational cost. When \(T=0\) (meaning no segments were removed from each structure after parsing at each direction excitation), the structure mass and surface nearly halved, indicating that in the considered region, many horizontal wire segments were not considered for creating the sparse structure. Furthermore, Figure 14 depicts that when \(T<400\), the reduction in mass and surface is almost consistent, suggesting that in this range of \(T\) values, the number of segments removed when applying different \(T\) is quite similar. To verify the observations, the FS scattering characteristics based on the correlation, we examined the FS BSCSs when \(T=50\) (FS\({}_{5}\)50), \(100\) (FS\({}_{1}\)100), \(200\) (FS\({}_{7}\)200), and \(300\) (FS\({}_{3}\)300). The shapes of the FS\({}_{5}\)50, FS\({}_{1}\)100, FS\({}_{2}\)200, and FS\({}_{7}\)300 structures are presented in Figure 15.  
Similar to Section 3, when \(T\) is small, the FS still has more segments than S40 (the sparse structure with the most segments when changing the excitation direction of the incoming wave). This can be explained by the fact that with GEET = 40%, when the  
Figure 14: \(T\) dependences of the sparse WG reduction in scatterer mass and surface, and in the time and memory on subsequent simulations after OCGA. \[corr(a,b)\ =\ \frac{\sum\limits_{i\ =\ 1}^{n}\left(X_{a,i}-\overline{X_{a}} \right)\left(Y_{b,j}-\overline{Y_{b}}\right)}{\sqrt{\sum\limits_{i\ =\ 1}^{n}\left(X_{a,i}-\overline{X_{a}}\right)^{2}\sum\limits_{i\ =\ 1}^{n}\left(Y_{b,j}-\overline{Y_{b}}\right)^{2}}} \tag{1}\]0 The MATLAB models of FS\({}_{5}\)50 (**a**), FS\({}_{1}\)100 (**b**), FS\({}_{7}\)200 (**c**), and FS\({}_{7}\)300 (**d**). incoming wave changed direction, other segments (in addition to those present in S40) were also considered.