# 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
Figure 3: Measured (\(\bullet\bullet\bullet\)) and calculated BSCS results for the scatterer in the xOy (**a**) and yOz (**b**) plane using MoM with PBF (\(--\)) and PWS (\(--\)). Figure 2: Rectangular scattering plate (**a**) and its equivalent WG structure (**b**). The OCGA for Creating Sparse Scatterers When It Is Excited by an Incident Wave at a Specific Direction  
The results obtained in Section 3 have verified the accuracy of approximating the perfect conducting flat plate using the WG structure. However, as mentioned above, it is not necessary to use all the wires of the grid to simulate the plate. Therefore, in this section, we present an OCGA-based approach for the initial WG scattering structure when the incident wave is at a fixed direction, aiming to achieve a sparse WG structure. Since OCGA is based on the characteristics of surface current, it is essential to analyze the current distribution in the structure when it is excited by a plane wave. In this section, we assume that the incident wave has \(\theta\)-polarization perpendicular to the plate, which means that the horizontal wires are completely unaffected by the incident plane wave. As a result, the current that appears on the horizontal wires is very small compared to that on the vertical wires. Figure 4 presents the magnitude of the obtained current distribution (\(|II|\)) at the left vertical edge (AB) and along the central vertical line (EF) of the plate. It is observed that \(|II|\) along the plate at the edge (\(I_{\text{max}}^{AB}=1.23\) mA) reaches a higher value compared to that at the center line of the plate (\(I_{\text{max}}^{EF}=0.68\) mA). According to electromagnetic theory, the tangential component of an electric field must be continuous across the boundary between two media (in this case, the surface of the plate). However, the sudden changes in geometric shape at the edges of the plate caused significant variations in the electromagnetic field. Specifically, in the central region of the plate, the electromagnetic field is distributed uniformly across the surface, while at the edges, the electric field was more intensely excited. This phenomenon leads to high accumulation of electric charge at the edges, resulting in high current at these locations (edges AB and CD). In contrast, the current distribution obtained in the central region of the plate surface is lower. We developed the OCGA algorithm to create a sparse scatterer structure (Figure 5). After applying MoM with PBF based on WG to the plate, \(|II|\) was obtained for all wire segments. The obtained \(|II|\) was then normalized by its maximum value (\(|II|_{\text{max}}\)). Subsequently, the normalized current results (\(I_{\text{nor}}\)) were compared with GEET. Segments with \(I_{\text{nor}}\) values smaller than GEET were removed from the initial WG structure. As a result, the obtained sparse structure consists only of segments with \(I_{\text{nor}}\) values greater than GEET. The indices of the segments in the sparse structure were stored in a matrix denoted as \(M_{\text{s}}\), which has the size of \(1\times N_{\text{s}}\) where \(N_{\text{s}}\) is the total number of segments in the sparse structure. Figure 4: The dependences of \(|II|\) on coordinates along the AB and EF of considered structure when \(\theta_{\text{inc}}=\varphi_{\text{inc}}=90^{\circ}\). Then, we calculated the impedance matrix (\(\mathbf{Z}_{\mathrm{s}}\)) and excitation vector (\(\mathbf{v}_{\mathrm{s}}\)) for the sparse scatterer to determine the scattering characteristics of the structure. There are two approaches to achieve this. The first approach involves recalculating the elements of \(\mathbf{Z}_{\mathrm{s}}\) and \(\mathbf{v}_{\mathrm{s}}\) directly using MoM with PBF for the sparse structure. This approach is easy to implement in code. However, as mentioned earlier, actual scattering structures are electrically large (much larger than \(\lambda\)), which means that their modeling using WG requires a significant number of segments (\(N\)) (potentially reaching tens of thousands).