Since the end of the 19th century, radioelectronic devices (REDs) have actively penetrated into all modern community spheres. Achievements in the fields of radio engineering and electronics, as well as computing, information, telecommunications, and other technologies, have greatly contributed to this. The main elements of REDs are antennas and microwave devices. For example, linear (wire) antennas are the basis of long-distance communication agency networks of various law enforcement agencies and departments. The manufacturing of REDs requires the regular and rapid appearance of more and more advanced types with minimal costs. At the same time, the design complexity of REDs and the tightening of EMC requirements caused by the growth of upper frequencies of useful and interfering signals, the mounting density, as well as the capabilities of generators of intentional electromagnetic impacts, together with the need to take into account inter-element, inter-unit, and inter-system interference, require more and more accurate designs of REDs. However, this becomes impossible without computer modeling, which saves the time and financial resources required for their development, as well as to evaluate the correctness of the proposed technical solutions. During the design process, as a rule, a multivariate analysis or optimization of the product is performed. In this case, methods of computational electrodynamics (one of which is the method of moments) are used. They are based on the replacement of continuous functions with their discrete analogues (construction of a grid), which reduces the problem to the solution of a system of linear algebraic equations (SLAE). The problem’s complexity depends on the complexity of the SLAE solution, which is determined by its order (which in turn is determined by the complexity of the simulated object and its surrounding area) and by the number of the required SLAE solutions for each problem (determined by the upper frequency of the signal, the number, and range of the optimized parameters). This dramatically increases the computational cost, which becomes the main constraint for the optimal design. Therefore, reducing the computational cost for the analysis and optimization of RED elements (in particular, linear antennas) is an important scientific problem. Meanwhile, finding new antenna structures that meet all the desired features (low price, required characteristics, manufacturable design with small dimensions and windage, etc.) is no less important today. One of the promise solutions for these problems is using a wire grid and sparse antennas for modeling and constructing antennas. Since the last century, a lot of research has been performed on them. The aim of this paper is to review their history and the main related aspects such as computational, acceleration, and optimization used methods, the fields of their application, and their evolution to this moment. In addition, this paper provides a possible future implementation of wire-grid and sparse antennas from the authors’ point of view by presenting a new method that is under research to obtain effective wire sparse antennas.
