# 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
Similar conclusions can also be drawn based on the data presented in Table 4. Overall, S40 provides scattering characteristics with lower accuracy compared to S35, but these can still be considered acceptable when weighing the advantages of reduced scatterer mass, surface, and computational costs for subsequent simulations. Manufacturers can choose an appropriate sparse structure depending on their specific applications and design requirements. If they need the performance that is closely aligned with the original structure, OCGA can be applied with GEET = 35% or lower. When they seek for a scatterer with reduced mass, surface, and modeling costs, OCGA with a higher GEET value (40%) may be applied to the original WG structure. Figure 9a,b demonstrates that when the incident wave is excited at \(\theta_{\text{inc}}=\varphi_{\text{inc}}=90^{\circ}\), the RCS for S35 closely matches that of the original WG structure. However, when the BSCS graphs (Figure 9c,d) illustrate that as the incident wave deviates from \(\theta_{\text{inc}}=\varphi_{\text{inc}}=90^{\circ}\), the side lobes of the S35 BSCS also exhibit greater deviation compared to those of the original WG structure. This can be attributed to the fact that the current sparse structure has only been evaluated based on the impact of the incident wave at a specific direction (\(\theta_{\text{inc}}=\varphi_{\text{inc}}=90^{\circ}\)) on the original WG structure, while the influence of excitation from other directions has not yet been considered. Additionally, it is observed that the differences in the side lobes of the BSCS for the sparse scatterer compared to the original WG structure also increase as GEET increases (in the cases of GEET = 40% and 50%). The development of sparse scatterer structures considering the influence of incident waves from various directions will be examined and analyzed in more detail in the following section. Figure 9: The obtained RCSs (**a,b**) and BSCSs (**c,d**) for original and sparse structures in xOy (**a,c**) and yOz (**b,d**) planes. The OCGA for Creating Sparse Scatterers Excited in Unknown Region Through the Scattering Plate Example  
As mentioned, in the study of scattering structures, it is essential to consider not only the case when the incident wave is perpendicular to the structure but also various excitation directions. It is important to note that when the incident wave excites the original WG structure from different directions, vector \(\mathbf{v}\) in each case will vary, while matrix \(\mathbf{Z}\) remains the same across all scenarios. As a result, the obtained vector \(\mathbf{i}\) will differ for each case. Consequently, we will consider a sparse scattering structure for each direction of the incident plane wave. In the general case, when the specific excitation region of the incident wave is not determined, it is necessary to consider the impact of all incident angles (\(\theta\) = 0-359\({}^{\circ}\) and \(\varphi\) = 0-359\({}^{\circ}\)) on the original WG structure, followed by the creation of a sparse structure. Conversely, if a specific excitation region is identified, it suffices to create the sparse scattering structure based on the angles within the effective range of the incident wave. The algorithm for generating this structure is illustrated in Figure 10. Below, we will explain the main steps involved in developing the sparse scattering structure when the specific excitation region of the incident wave is not determined in advance. For the cases when the excitation region has been identified, the process of creating the sparse scattering structure will follow a similar logic. After determining the shape of the initial structure, the next step is to identify the direction of the incident wave where the BSCS of the structure achieves its maximum magnitude (in this work, at \(\theta_{\text{inc}}\) = \(\varphi_{\text{inc}}\) = 90\({}^{\circ}\)).