# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 8 Discussion  
Being newly developed for difference scattering structures, the sparse scatterer structure generation algorithm that uses the OCGA approach has proven effective in reducing the mass and surface of the original WG structure by nearly 1.5-2 times while maintaining its scattering properties. Initial processing of the free wires can be performed by choosing a small GEET value, creating a sparse structure without free wires, which enhances the reliability of the structure. Various algorithms for connecting free wires to the WG structure after OCGA have been used for sparse antennas. As shown in Section 2, these algorithms have demonstrated their accuracy while maintaining mass reduction efficiency in both real measurements and simulations. Therefore, it is quite possible to confidently apply this algorithm to sparse scatterers in the future, especially when GEET and \(T\) are large. The comparison of the computational cost shows that the proposed algorithm allows more reduction in the cost than the existing methods. Specifically, when compared with the perforated structure (usually using holes with diameters of about \(\lambda/6\) corresponding to the cell size used for WGs), the classical method such as MoM requires computational complexity O(\(N^{3}\)) and memory O(\(N^{2}\)) when solving a system of equations with \(N\) unknowns (\(N\) basis functions). When the number of unknowns is large, this significantly increases the computational cost. However, this paper considers each wire in the WG as a segment, which significantly reduces the number of unknowns compared to the perforated structure using the RWG function for analysis. The last case uses more small triangles at the holes (where the boundary conditions change abruptly), which results in an increase in  
Figure 29: The MATLAB models of the sparse CTCR when \(\theta^{\text{inc}}=40\)–\(67^{\circ}\) and \(\varphi^{\text{inc}}=27\)–\(63^{\circ}\) at \(T=600\) (**a**), 700 (**b**), and 800 (**c**) and the obtained BSCSs for original and sparse CTCRs (**d**). the number of unknowns and requires more cost for the analysis. For the method using silver-coated textiles, MoM is often used in combination with the volume integral equation, making the problem more complicated. In addition, the number of unknowns to be solved also increases because the mesh grid is not only on the surface but also in the structure. The nature of the current distribution results for sparse structures is obtained from solving the MoM system of equations, so it can be affirmed that the obtained current results are completely accurate. Not only that, taking advantage of PBF when calculating the current for sparse structures also helps reduce the required computational resources. This is because the time to solve the MoM linear system of equations is shortened, and there is no need to recalculate the impedance matrices and excitation vectors from scratch, as mentioned in Section 4. In this paper, we have obtained sparse scatterers for complex original scatterers such as DCR and CTCR with different sizes at different frequency bands and commonly used in practice. The obtained sparse structures have demonstrated effective mass reduction and retained important scattering properties of OCGA. Meanwhile, we also have performed detailed analysis of the properties of sparse structures when GEET and the excitation direction of the incident wave are varied. This analysis is conducted on a wide range of structures, from simple to complex, in order to clarify the nature and effectiveness of the presented algorithm. The choice of the threshold value \(T\) assumes that the contribution of each sparse structure (corresponding to each incident wave direction) to the resulting final sparse structure is uniform. This simplification, as demonstrated in Sections 5-7, does not significantly affect the accuracy of the resulting sparse structure in both simple and complex structures.