# 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
Although we have broadly outlined the characteristics and variations in the scattering field as GEET changes, the analysis thus far has focused only on RCS\({}_{\rm max}\). Consequently, we will next analyze the RCS and BSCs of the sparse structure at various GEET values. Specifically, we selected the GEET values of 35% (the point at which RCS\({}_{\rm max}\) begins to decline), 40% (the value within the decreasing range of RCS\({}_{\rm max}\)), and 50% (the value with significant reduction in RCS\({}_{\rm max}\)). The models of the sparse WG structure obtained at  
Figure 7: The GEET dependences of the sparse WG reduction in scatterer mass and surface, and in the time and memory on subsequent simulations after OCGA. 300 MHz in MATLAB R2022a, after applying OCGA with GEET values of 35% (S35), 40% (S40), and 50% (S50), are presented in Figure 8.  
It is observed that when the incident wave is perpendicular to the plate, all segments of the vertical wires will exhibit the same potential. Therefore, the obtained \(|\)_11_ of the segments on the plate surface is also symmetric, which means that the sparse structure is also symmetric. The number of wires that remained in the sparse WG structure using OCGA with GEET values of 35, 40, and 50% were 614, 484, and 174, respectively, while the original structure comprised 1250 wires. Consequently, the scatterer mass and surface were reduced by factors of 2.035, 2.583, and 7.183, while memory usage decreased by factors of 4.14, 6.67, and 51.6 times, and computation time was reduced by factors of 8.427, 17.23, and 370.6 times. It can be observed that the reductions achieved with GEET = 50% are superior to those with GEET = 40%, and the reductions with GEET = 35% were the least significant. However, the characteristics for these sparse scatterers must also be compared with those for the original WG scatterer. The far-field characteristics obtained (RCSs and BSCSs) at 300 MHz in the xOy and xOz planes for S35, S40, S50, and the original WG structure are illustrated in Figure 9. The deviations in the scattering characteristics for the sparse structures compared to those for the original scatterer at 300 MHz are summarized in Table 4.  
The data from Figure 9 demonstrate that the obtained scattering characteristics from the S50 exhibit the greatest deviation from the original WG structure, followed by S40, while S35 shows the smallest deviation. The scattered field in the main lobe direction in Figure 9 indicates that the results for the sparse structures S35 and S40 match well with those of the original structure. The side lobes of RCSs illustrate that S35 again produces results that are nearly indistinguishable from those of the original WG, while the scattering field from S40 shows a more significant deviation. For the S50 structure, both the main lobe and side lobes of the scattered field demonstrate considerable differences compared to the original WG structure. A similar conclusion is drawn regarding the bandwidth (BW) of S50, which deviates significantly more than that of S35 and S40. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Structure**} & \multicolumn{4}{c}{**Deviation**} & \multicolumn{4}{c}{**Maximum Deviation, dBsm**} \\ \cline{2-9}  & \multicolumn{2}{c}{**xOy**} & \multicolumn{2}{c}{**yOz**} & \multicolumn{2}{c}{**xOy**} & \multicolumn{2}{c}{**yOz**} \\ \cline{2-9}  & **RCS\({}_{\text{max}}\)** & **dBsm** & **BW\({}_{\text{s}}\)** & **RCS\({}_{\text{max}}\)** & **dBsm** & **BW\({}_{\text{s}}\)** & **RCS** & **BSCS** & **RCS** & **BSCS** \\ \hline S35 & 0.032 & 0 & 0.032 & 0 & 0.5 & 1.7 & 0.52 & 3.14 \\ S40 & 1.388 & 0 & 1.388 & 0 & 1.54 & 2.45 & 6.82 & 17.14 \\ S50 & 10.89 & 30 & 10.89 & 2 & 10.89 & 10.89 & 19.77 & 22.89 \\ \hline \end{tabular}
\end{table} 
Table 4: RCSs, BSCSs, and bandwidth deviations for S35, S40, and S50. Figure 8: The MATLAB models of S35 (**a**), S40 (**b**), and S50 (**c**).