# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 7 Generation of Sparse Dihedral and Trihedral Corner Reflector
Therefore, when \(\varphi\)inc = 0-360\({}^{\circ}\) and \(\theta\)inc = 0-360\({}^{\circ}\), \(T\) = 500 can be chosen to balance the mass and surface reduction and the scattering properties of the sparse structure. Next, we created the sparse DCR when \(\theta\)inc = 84-96\({}^{\circ}\) and \(\varphi\)inc = -40-40\({}^{\circ}\) (BSCS main lobe of DCR). The dependence of reduction in mass, surface, computational cost, and correlation coefficient of BSCS for the sparse and original DCRs on \(T\) is shown in Figure 22. It can be seen that when \(T\) = 600, 700, the BSCS for the sparse structure still agrees quite well with the original WG, while the mass reduction is 1.92 and 2.27 times, respectively. When \(T\) = 800, although the mass reduction is high (5.44 times), the BSCS for the sparse DCR deviates quite a lot from that for the WG. Figure 19: \(T\) dependences of the reduction in mass and surface, in the time and memory for the sparse DCR. Figure 16:0 The MATLAB models of the sparse DCR when \(\varphi\)inc = 0–360\({}^{\circ}\), \(\theta\)inc = 0–360\({}^{\circ}\) at \(T\) = 0 (**a**), 500 (**b**), 600 (**c**), and 700 (**d**). The shapes of the sparse structures and their backscatter fields at different \(T\) values (\(T\) = 600, 700, and 800) are shown in Figure 16:1 Consistent with the values of the correlation coefficients, when \(T\) = 600 and 700, the BSCS of the sparse DCR agrees quite well with the original WG. When \(T\) = 800, the backscatter field deviates significantly from the original WG. Figure 16:2 The obtained BSCs for the original DCR [83] and sparse DCR in \(\theta\) = 90\({}^{\circ}\) (**a**) and \(\varphi\) = 0\({}^{\circ}\) (**b**) planes when \(\varphi^{\text{inc}}\) = 0–360\({}^{\circ}\) and \(\theta^{\text{inc}}\) = 0–360\({}^{\circ}\). Figure 16:3 \(T\) dependences of the reduction in mass, surface, computation cost for the sparse DCR (**a**) and of correlation coefficient of group \(1\) (**b**). In some civil and military maritime applications, TCR and their variants are commonly used [84; 85; 86; 87; 88]. One of the popular types of TCR is the circular TCR (CTCR), which is formed by orthogonally joining quarter circular faces [89; 90; 91]. To further assess the effectiveness of the proposed algorithm, we applied OCGA to a CTCR with orthogonal edge lengths of 0.2 m at the X-band \(f\) = 9 GHz [44]. The BSCS results obtained in the \(\theta\) = 90\({}^{\circ}\) plane using the WG model are compared with those obtained using CST and measured in [44] (Figure 24). In the WG structure, the CTCR is divided into 2178 cells with the side length equal 0.17\(\lambda\). The BSCS results show a good agreement between the methods. Figure 16:4 BSCS for CTCR in \(\theta\) = 90\({}^{\circ}\) plane. From Figure 24, the difference between the average BSCS obtained from the WG-model and the measured results is 0.3 dB, while the average difference between the CST and the measured results is 1.5 dB. It can be seen that the simulation results using the WG-model match well with the measured results. A slight difference between these results due to manufacturing imperfections in the structure, include non-ideal orthogonal surfaces and surfaces that are not perfectly smooth [44]. For the TCR, the maximum BSCS is obtained at \(\theta=55^{\circ}\), \(\varphi=45^{\circ}\). Therefore, when the incident wave excites at \(\theta=55^{\circ}\), \(\varphi=45^{\circ}\), we calculate the BSCS in the \(\theta=55^{\circ}\), \(\varphi=45^{\circ}\) planes while varying the GEET. The shape of the sparse CTCR and the corresponding BSCS results are shown in Figure 16:5 The mass reduction for GEET values of 15%, 25%, and 35% are 1.06, 1.15, and 1.3, respectively. It is observed that when GEET = 15%, the BSCS of the sparse CTCR matches quite well with that of the WG. As GEET increases, the BSCS of the sparse CTCR deviates more from the WG.