# 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
Additionally, some horizontal segments were present in the final structure because when the incoming wave is deflected away from the yOz and xOy planes, its polarization may no longer be perpendicular to the horizontal wires, leading to a greater current appearing on them. However, this phenomenon only occurred with the horizontal wires at the edge of the plate, not in the middle. Furthermore, it is observed that both FS\({}_{\text{r}}\)50 and FS\({}_{\text{r}}\)100 contained horizontal segments, while FS\({}_{\text{r}}\)200 and FS\({}_{\text{r}}\)300 did not. This is likely because horizontal segments are still less affected by the incoming wave compared to vertical segments, even at different angles of excitation. The obtained BSCSs for S40, FS\({}_{\text{r}}\)50, FS\({}_{\text{r}}\)100, FS\({}_{\text{r}}\)200, and FS\({}_{\text{r}}\)300 were then compared with the WG BSCS in the region of \(\theta\) = 60-120\({}^{\circ}\) and \(\varphi\) = 60-120\({}^{\circ}\), as well as in the xOy and yOz planes. In the region of \(\theta\) = 60-120\({}^{\circ}\) and \(\varphi\) = 60-120\({}^{\circ}\), comparing the 3D graph (representing the obtained BSCS) for the structures is quite challenging; therefore, we converted it into a 2D plot to make the comparison easier. In this graph, the vertical axis represents the BSCS magnitude in dBsm, while the horizontal axis combines the \(\theta\) and \(\varphi\) values (with a total of 3721 values). Specifically, 0-61\({}^{\circ}\) corresponds to \(\theta\) = 0\({}^{\circ}\) and \(\varphi\) = 60-120\({}^{\circ}\); 62-123\({}^{\circ}\) corresponds to \(\theta\) = 1\({}^{\circ}\) and \(\varphi\) = 60-120\({}^{\circ}\); \(\ldots\); 3660-3721\({}^{\circ}\) corresponds to \(\theta\) = 120\({}^{\circ}\) and \(\varphi\) = 60-120\({}^{\circ}\). However, accurate comparison of the BSCS values is quite difficult due to the abrupt variations in the graph, so we used the function \"smooth\" in MATLAB to smooth the obtained BSCS magnitudes, making it easier to observe (Figure 16). Additionally, the discrepancies in BSCSs for S40, FS\({}_{\text{r}}\)50, FS\({}_{\text{r}}\)100, FS\({}_{\text{r}}\)200, and FS\({}_{\text{r}}\)300 in the region of \(\theta\) = 60-120\({}^{\circ}\) and \(\varphi\) = 60-120\({}^{\circ}\) (actual values, not smoothed) and in the xOy and yOz planes compared to the WG structure are presented in \[corr(a,b)\ =\ \frac{\sum\limits_{i\ =\ 1}^{n}\left(X_{a,i}-\overline{X_{a}} \right)\left(Y_{b,j}-\overline{Y_{b}}\right)}{\sqrt{\sum\limits_{i\ =\ 1}^{n}\left(X_{a,i}-\overline{X_{a}}\right)^{2}\sum\limits_{i\ =\ 1}^{n}\left(Y_{b,j}-\overline{Y_{b}}\right)^{2}}} \tag{1}\]1  
From Figure 16a, it can be seen that the obtained BSCS for FS\({}_{\text{r}}\)50 matches best with that of the WG scatterer, followed by FS\({}_{\text{r}}\)300 and FS\({}_{\text{r}}\)200. The FS\({}_{\text{r}}\)100 BSCS deviates more compared to the other FS structures, indicating that the use of the Spearman, Kendall, Euclidean, and standard deviation coefficients accurately predicted the similarity of the BSCS for the sparse structure with that of the WG. This also explains why the FS\({}_{\text{r}}\)300 BSCS is slightly better than the FS\({}_{\text{r}}\)200 BSCS. The maximum FS BSCS values deviate more as \(T\) increases. Additionally, it is observed that S40 has a much greater BSCS deviation compared to the other sparse structures. From Figure 16a, when \(\theta\) approaches 60\({}^{\circ}\) or 120\({}^{\circ}\), which are the boundaries of the excitation region (represented in the graph as approximately 0-700 and 3000-3721), the BSCSs of the resulting FS structures show significant differences from the WG. This may be explained by the fact that as \(\theta\) nears the boundary values of the excitation region, the \(\theta\)-polarization significantly affects the horizontal wires, leading to higher currents on these wires at these angles.