# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 1 Introduction  
Antennas and scattering structures are widely used in various fields, from civil [1, 2, 3, 4, 5] to military [6, 7, 8, 9, 10]. With the continuous advancement of science, the demand for producing compact antennas and scatterers with intelligent designs is increasing [11, 12, 13, 14]. Designing those structures to achieve required properties while maintaining low production costs necessitates high-accuracy simulation software with low computational costs. Simulating structures significantly reduces production costs, allowing for the assessment and optimization of structural properties before manufacturing. Additionally, it helps avoid technical errors during production [15]. Thus, simulation becomes an essential part of the design process for antennas and scattering structures [16, 17]. However, accurate modeling may require intensive computations, especially when analyzing complex structures. In the meantime, the proper choice of numerical methods for modeling can significantly impact the cost and efficiency of the design process. One of the common methods for analyzing antenna and scatterer structures is the method of moments (MoM) [18, 19, 20, 21, 22]. MoM is based on transforming the integral equations of the electric field into a system of linear algebraic equations, and then the current distribution in the structure is determined by inverting the impedance matrix [23, 24]. MoM is considered to have a simple algorithm and low computational costs compared to other methods, while allowing for acceptable simulation results. Based on MoM, many new approaches to modeling antennas and scatterers have been developed [25, 26, 27, 28, 29]. One prominent method is the surface approximation of structures using wire grid (WG). Thisapproach simplifies the surface shape, making the implementation of modeling in source code easier. Multiple studies on modeling antenna and scattering structures have been conducted taking advantage from this approach (WG based on MoM) [30; 31; 32; 33; 34]. The reduction in antenna mass is an important factor in many engineering fields [35; 36]. Low mass and compact size not only reduce transportation costs (for example, into space [37; 38]), but also simplify installation and maintenance, and can minimize negative environmental impacts on the structure (for instance, wind and rain). Similarly, in the field of interferometric synthetic aperture radar (InSAR), corner reflectors (CRs) are a typical example of scattering structures [39; 40; 41; 42]. These structures are prominent because they are easy to fabricate and feature significant scattering capabilities over a wide range for incident plane waves. However, a clear disadvantage is that the size of CRs is often quite large (for example, a trihedral CR can have edge lengths of up to 2.5 m [43]). In addition, their weight is also relatively heavy, mainly due to the use of conductive metal materials. Therefore, reducing the mass of these structures to facilitate transportation, installation, and maintenance is an important issue that needs to be solved. Several methods have emerged to reduce the weight and size of these structures. One example is the use of silver-coated textiles [44]; however, a disadvantage of this method is that the conductive material is susceptible to environmental factors. In addition, the silver-coated technology is complex and expensive. Another method is the use of structures with a perforated plate [45]. Although this method significantly reduces the weight of the entire structure and improves drainage of accumulated rainwater [46], the perforation process complicates manufacturing and increases costs [47]. Moreover, perforation can often cause surface deformation [43]. Therefore, there is a need to develop new methods to reduce the weight of such structures. To reduce antenna mass and surface, we [38] developed a technique that uses optimal current grid approximation (OCGA) based on MoM and WG.