# 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  
The MoM is widely used for modeling different antenna designs with low computational cost and optimizing their designs to meet specific requirements. A review of the MoM-enhanced antenna modeling history and the potential of using WG to approximate the solid metallic surface of different antenna types is presented in [38]. To further reduce the antenna mass, surface, and computational cost, sparsifying WG antenna structure by using OCGA was firstly proposed in [38]. The OCGA works based on obtaining the current distribution in a WG structure. After this, the current magnitudes in each wire are normalized by their average or maximum value. Then, all wires with current magnitudes less than a certain threshold are eliminated since their contribution to the radiation is negligible. This threshold is called the grid element elimination tolerance (GEET) and can be adjusted according to each specific requirement. The result is a sparse WG structure that includes only wires with large currents. Compared with the original WG structure, the sparse WG structure has lower antenna mass and surface as well as its modeling cost. To generate sparse WG structures using OCGA, it is necessary to accurately approximate the solid metal surface of the antenna using WG. Many recommendations have been proposed in the past for approximating metal surfaces using WG. However, they are not complete and are not suitable for creating an original WG structure to which OCGA can be applied to create a sparse structure. The suitability and inadequacy of the previous recommendations are presented in detail in [52]. Therefore, new recommendations were proposed in [52] for approximating the solid surface of horn structures using WG, which can be used as an original structure for applying OCGA to create a sparse structure. An approximate comparison of antenna surface using WG with different cell types such as square and trapezoidal was carried out. Antenna surface approximation using WG and OCGA to create sparse structures was compared in different computer-aided design systems such as TUSUR.EMC [53], MMAA-GAL [54], and 4 NEC2 [55]. In addition, an optimization method based on OCGA was proposed in [56] to generate sparse WG structures that meet the given criteria. The algorithmic details of this optimization method were presented, and software with a user-friendly interface was developed based on this method. However, the WG structure obtained after OCGA encounters difficulties in fabricating unprinted antennas because it has wires that are not connected to the structure (free wires). To overcome these difficulties, a modification of OCGA to create a sparse WG structure with connected current paths was proposed in [38]. This modified approach is referred to as \"Connecting\" OCGA (COCGA), and its main idea is to recover radial wires to create a current path between the free wires and the structure, since for radial structures these wires usually carry large currents. The algorithm details of the OCGA and COCGA approaches were presented in detail in [38]. The OCGA and COCGA approaches have been applied to a reflector antenna (5.1-5.9 GHz), a horn antenna at 8 GHz, perforated X-band horn antenna (8-12 GHz), and a conical horn antenna at 8 GHz. A comparative analysis of the sparse structures obtained after applying OCGA and COCGA to these types of antennas was presented in [57] in detail. The comparative analysis shows that COCGA generally results in antenna characteristics closer to the original structure, demonstrating higher accuracy in preserving the original characteristics, while OCGA also demonstrates the possibility of reducing the antenna mass and surface as well as the time and memory requirements for subsequent modeling. In addition, [58] presented details on the classification of hidden antenna types and the possibility of using sparse WG structures to design hidden antennas that meet specific requirements.