# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 7 Generation of Sparse Dihedral and Trihedral Corner Reflector
However, after balancing the mass reduction and the BSCS deviation of the sparse structure compared to the original WG, we chose GEET = 25% to create the sparse structure when the incident wave changes its excitation direction. When \(\theta^{\text{inc}}=0\)-\(360^{\circ}\), \(\varphi^{\text{inc}}=0\)-\(360^{\circ}\), the dependence of mass and surface, computational cost reduction, and correlation coefficient on \(T\) is shown in Figure 16:6 Based on the correlation coefficient, it is predicted that when \(T=800\), the BSCS of the sparse CTCR still matches that of the original CTCR. The shape and BSCS of the sparse structures at the \(\theta=55^{\circ}\), \(\varphi=45^{\circ}\) planes are shown in Figure 16:7 It is observed that when \(T=800\), the characteristics of the sparse CTCR align well with the original WG (Figure 27c), while the mass reduction is 1.45 times. When \(T=900\), the mass reduction of the structure is about 1.5 times, but the BSCS of the sparse CTCR at the \(\theta=55^{\circ}\), \(\varphi=45^{\circ}\) is slightly reduced compared to the original WG (Figure 27d). Therefore, selecting the sparse CTCR with \(T=800\) is entirely reasonable in this case. Next, when the plane wave excites in the main lobe (\(\theta^{\text{inc}}=40\)-\(67^{\circ}\) and \(\varphi^{\text{inc}}=27\)-\(63^{\circ}\)), we created the sparse CTCR. Dependences of reduction in mass, surface, computational cost and correlation coefficient of BSCS for the sparse and original CTCRs on \(T\) are shown in Figure 16:8 The shapes of the sparse structures and their backscatter fields at different \(T\) values (\(T=600\), 700, and 800) are shown in Figure 16:9 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 1.44 and 1.51 times, respectively. When \(T=800\), the mass reduction is 1.6 times, but the BSCS for the sparse DCR deviates quite a lot from that for the WG. Therefore, in this case, \(T=700\) can be chosen to create a sparse CTCR structure with reasonable mass reduction and scattering properties. Figure 18.0 The obtained BSCSs for original and sparse CTCR in \(\theta=55^{\circ}\) (**a**) and \(\varphi=45^{\circ}\) (**b**) planes. Figure 18.1 \(T\) dependences of the reduction in mass, surface, computation cost for the sparse SCTCR (**a**) and of correlation coefficient of group 1 (**b**) when \(\theta^{\text{inc}}=40\)–\(67^{\circ}\) and \(\varphi^{\text{inc}}=27\)–\(63^{\circ}\). Figure 18.2 \(T\) dependences of the reduction in mass, surface, computation cost for the sparse SCTCR (**a**) and of correlation coefficient of group 1 (**b**) when \(\theta^{\text{inc}}=0\)–\(360^{\circ}\), \(\varphi^{\text{inc}}=0\)–\(360^{\circ}\). Figure 18.3 The MATLAB models of the sparse CTCR when \(\varphi^{\text{inc}}=0\)–\(360^{\circ}\) and \(\theta^{\text{inc}}=0\)–\(360^{\circ}\) at \(T=800\) (**a**), \(900\) (**b**), and the obtained BSCSs for original and sparse CTCRs in \(\theta=55^{\circ}\) (**c**) and \(\varphi=45^{\circ}\) (**d**) planes. All these observations demonstrate the effectiveness of the proposed algorithm in creating sparse DCR and CTCR structures.