# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 2 Review of Approaches for Reducing Mass and Surface of Various Antenna Structures Using the OCGA
Since the current distribution on the obtained WG structure is different at different frequencies in the operating frequency range, the effect of frequency selection on the obtained sparse structure after OCGA and COCGA application on the horn antenna X-band (8-12 GHz) was analyzed in [59]. The analysis results show that the sparse structures obtained based on the current distribution at the lowest frequency in the operating frequency range provide antenna characteristics closer to those of the original antenna and less dependent on the GEET value, compared to the other structures. In addition, at the highest frequency in the operating frequency range, the sparse structures obtained after COCGA provide results with minimal differences compared to the original structure. The sparse structure obtained after COCGA has antenna characteristics close to those obtained for the original structure. However, it recovers a large number of radial wires to maintain the current paths in the structure and its continuity, which leads to a nonoptimal reduction in mass and simulation cost. Therefore, OCGA modifications were proposed in [60] to create a sparse WG structure with all wires interconnected. These approaches were referred to as \"Eliminating\" OCGA (EOCGA) and \"Near-Connecting\" OCGA (NCOCGA). To provide a current path in the sparse WG structure, EOCGA eliminates all free wires in the sparse WG structure obtained after OCGA, while NCOCGA restores only those wires that are necessary to connect these free wires to the structure. The algorithms of these approaches were discussed in detail, and their performance was verified on different types of antennas. However, the algorithms of these approaches were based on the geometric position of the wires in the grid, which limits their accuracy. Furthermore, they are only applicable to radial WG designs such as antenna reflectors and conical horn antennas. Therefore, new algorithms were proposed in [61] to improve the OCGA and its modifications. Its aim is to use the start and end coordinates of the wires in combination with an algorithm for finding free wires and determining the shortest path to connect them. The results obtained after applying the modernized algorithms were compared with the results of the previous algorithm. The comparison results showed that these new algorithms had higher accuracy, efficiency, and flexibility and could be applied to many different types of WG structures. The OCGA, EOCGA, and NCOGA with the modernized algorithms have shown to be effective in creating sparse structures on various types of antennas operating at various frequency bands. A series of prototypes, original WG and sparse WG structures obtained after applying various approaches on various types of antennas are presented in Table 1. The improvements in antenna mass and surface, memory and time cost in subsequent modeling for various sparse structures were obtained after applying different approaches to different types of antennas compiled from different works and presented in Table 2. Moreover, Table 2 also summarizes the maximum differences in characteristics of these sparse antennas compared to the original antenna in the operating frequency range. Then, comparative analyses were performed to analyze the effect of frequency selection on the sparse structure generated after applying different approaches.