# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 7 Generation of Sparse Dihedral and Trihedral Corner Reflector  
In this section, to increase the versatility of our algorithm, we applied it to the dihedral (DCR) and trihedral (TCR) corner reflector as a practical scattering structure commonly used in the calibration and validation of the SAR system [79; 80; 81; 82]. The shape of the DCR and its WG model in MATLAB are shown in Figure 17. The DCR is composed of two orthogonal square plates with the sides of 5.6088A and operates at 9.4 GHz (Figure 17b) [83]. Figure 16: The obtained BSCSs for original (smoothing value) and sparse structures in region \(\theta\) = 60–120\({}^{\circ}\), \(\varphi\) = 60–120\({}^{\circ}\) (**a**), xOy (**b**), and yOz (**c**) plane. In the WG structure, the DCR is divided into 2178 square cells with the side length equal to the segment length of 0.16\(\lambda\), and the wire radius is determined by equal area rule. For the DCR as in Figure 17b, BSCS achieves the magnitude maximum at \(\theta\) = 90\({}^{\circ}\), \(\varphi\) = 0\({}^{\circ}\). The dependence of RCS\({}^{\max}\), as well as the reduction in mass, surface, and required computational cost, on GEET is shown in Figure 18. It is seen that when GEET = 20%, the RCS\({}^{\max}\) of the structure does not change much compared to the original WG, while the mass was reduced by about 1.9 times. Therefore, we choose GEET = 20% to create sparse DCR when the direction of the incident wave changes. Now the DCR is sparsed when the excitation wave is at \(\varphi_{\mathrm{inc}}\) = 0-360\({}^{\circ}\) and \(\theta_{\mathrm{inc}}\) = 0-360\({}^{\circ}\). The reduction in mass, surface, and computation cost depending on \(T\) for this sparse DCR is shown in Figure 19. As mentioned, when \(T\) increases, the number of remaining wires of the sparse structure decreases, so the mass, surface, and computation cost also decrease. From Figure 19, it can be seen that when \(T\leq\) 600, the mass and surface of the structure decrease by less than 2.1 times, when \(T>\) 600, the mass and surface decrease faster. To analyze the influence of mass and surface reduction on the scattering properties of the DCR, we consider the BSCS for the sparse DCR at \(T\) = 0, 500, 600, and 700 (the mass and surface reduction compared to the original WG are 1.16, 1.9, 2.1, and 6.18, respectively). The shapes of the sparse DCR are presented in Figure 20.  
Figure 17: The actual DCR structure [79] (**a**) and its equivalent WG MATLAB model (**b**). Figure 18: The GEET dependence of RCS\({}_{\max}\) when \(\theta_{\mathrm{inc}}\) = 90\({}^{\circ}\), \(\varphi_{\mathrm{inc}}\) = 0\({}^{\circ}\) (**a**) and the sparse DCR reduction in mass, surface, and computation cost (**b**). The characteristics of sparse DCRs are shown in Figure 21. The WG and sparse structures in the region \(\theta\) = 90\({}^{\circ}\) and \(\varphi\) = 0-55\({}^{\circ}\) have almost no difference with the measurement results. In the region \(\theta\) = 90\({}^{\circ}\) and \(\varphi\) = 55-90\({}^{\circ}\), this deviation increases more with an average deviation of about 0.2 dB (for the results using WG-model and measurement results). As in the case of flat plate, this deviation can be due to errors in the structure fabrication and measurement conditions. In addition, at high frequencies, this deviation also increases. It can be seen that when \(T\) = 0, the BSCS is in very good agreement with the WG DCR and solid DCR in both \(\theta\) = 90\({}^{\circ}\) and \(\varphi\) = 0\({}^{\circ}\) planes. When \(T\) = 500, 600, the BSCS in \(\theta\) = 90\({}^{\circ}\) plane is still in good agreement with it for WG; however, in \(\varphi\) = 0\({}^{\circ}\) plane, the side lobes of the BSCS are more deviated than those of the WG. This deviation increases as \(T\) increases. When \(T\) = 700, the BSCS for sparse DCR is completely inconsistent with the BSCS for the original WG.