# Wire-Grid and Sparse MoM Antennas: Past Evolution, Present Implementation, and Future Possibilities
## 5 Wire-Grid Sparse Antennas
### OCGA Method: Explanation  
The method proposed here is named the Optimal Current Grid Approximation (OCGA) and is aimed at improving the development of radiators and scatterers of the electromagnetic field through the optimal approximation of the wire grid. Unlike well-known solutions, this can be achieved not by complicating but by simplifying the structures and by modeling without doing too much. This section outlines how this is achieved. This method can be used for manufacturing a wire-grid antenna. The main idea is to avoid using those wires with low currents in the antenna grid, since their contribution to radiation is small. This can be achieved by excluding from the grid those wires in which the current modulus is less than a given threshold. This in turn will make it possible to reduce the mass, windage,and dimensions of the antenna with controlled accuracy of its characteristics. This method can also be used for accelerated modeling of the electromagnetic field of a conducting surface with a sparse wire grid. The main idea is to avoid using wires with low currents in each simulation of the electromagnetic field of the wire-grid structure in a range of parameters, since their contribution to the total radiation is small. This can be achieved by adding a number of actions to the regular modeling process to identify these wires after the first modeling of the original (full) grid, and for any further simulation, only the resulting sparse grid with a smaller number of wires in a given range of parameters should be used. This will require less memory and time spent on the modeling, with controlled accuracy. Such an approach can be applied to obtain fast estimates of antenna characteristics. As a result, the same idea of identifying and eliminating essentially unnecessary wires can be used both in developing and modeling antennas and scatterers. The proposed method is based on MoM and consists of the following steps:  
1. Obtain an integral equation for a given structure from [PERSON]'s equations;
2. Describe (input or import) the task geometry;
3. Specify the required frequency range;
4. Select the required characteristics to be calculated;
5. Select the excitation source;
6. Construct the grid (divide the boundaries of the structure into \(N\) subdomains, select the type of basis functions, and approximate the desired function in each subdomain by the corresponding basis function);
7. Select the type of test functions and test the approximated desired function by MoM;
8. Calculate the entries of impedance matrix \(\mathbf{Z}\) of order \(N\) and the entries of the SLAE right-hand side voltage matrix \(\mathbf{V}\);
9. Solve the obtained SLAE \(\mathbf{ZI}=\mathbf{V}\) to find the matrix of surface currents \(\mathbf{I}\);
10. Calculate the required characteristics of the antenna from matrix \(\mathbf{I}\). What follows is the explanation and the algorithm of the proposed OCGA. This method is proposed as a method of modeling based on MoM, as mentioned above. The OCGA algorithm consists of the following. It begins with the construction of a geometric model of a real surface in the form of a wire grid. After that, an excitation with its parameters is set. Then, the wire-grid segmentation is performed. After calculating the entries of matrix \(\mathbf{Z}\) that characterize the grid of the structure and the entries of matrix \(\mathbf{V}\) that characterize the excitation, the SLAE \(\mathbf{ZI}=\mathbf{V}\) can be solved. From the calculated elements of the matrix of currents \(\mathbf{I}\) in the grid segments, the required antenna characteristics are calculated. Further, the previous steps are repeated when the parameters change in a given range. However, according to OCGA, before repeating the previous steps, the current vector element modules should be normalized with respect to their maximum. The choice of the normalizing criterium depends on the structure.