# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 3 Verification of the Modeling Results for Scattering Plate Using MoM with PBF Based on WG Model  
Section 2 demonstrated the effectiveness of using OCGA and its modifications in generating sparse antenna structures. Therefore, it is reasonable to apply this approach to develop algorithms for generating sparse scattering structures. However, first, to verify the accuracy of using MoM with PBF based on WG in scatterer analysis, we verify the scattering field results obtained for a flat plate scattering structure. The shape of the rectangular perfect electrically conductive plate scatterer from [65] is illustrated in Figure 2a. The plate is positioned in the xOz plane and is orthogonal to the O\(y\)-axis. The origin of the coordinate system coincides with the center of the plate. The structure has a length of \(H=3\lambda\) and a width of \(W=2\lambda\). Figure 2b depicts the plate from Figure 2a, approximated using a WG in this study. The WG structure consists of the same square cells: 30 cells along the \(H\) edge and 20 cells along the \(W\) edge, while \(\Delta\) represents the edge length of all the WG cells, which is equal to the length of each cell wire. Each of the four wires forming the WG cells is represented by a single segment. This approach simplifies the construction of the structure and complies with the recommendations that no basis function passes through the intersection points of the segments. In the process of modeling the rectangular plate scatterer, the segment length (\(\Delta=\lambda/10\)) and the wire radius (\(a=\Delta/2\pi\)) were calculated based on the findings of previous publications. Specifically, at the excitation frequency \(f=300\) MHz, the dimensions of the plate were \(H=3\) m, \(W=2\) m, \(\Delta=0.1\) m, and \(a=0.016\) m. A plane wave \(\overrightarrow{E^{\mathrm{inc}}}\) with \(\theta\)-polarization was utilized for excitation at the incident angles \(\theta_{\mathrm{inc}}\), \(\varphi_{\mathrm{inc}}\). When calculating the backscattering cross section (BSCS), the scattered field \(\overrightarrow{E^{scat}}\) was considered at the angles \(\theta_{\mathrm{scat}}=\theta_{\mathrm{inc}}\), \(\varphi_{\mathrm{scat}}=\varphi_{\mathrm{inc}}\). Figure 1: Setup for sparse antenna measurement (**a**), the frequency dependence of the measured \(\mid\)S\({}_{11}\mid\) (**b**) and measured RPs in the \(E\) planes at 0.915 GHz (**c**) for the original and sparse WG antennas [63]. In this work, the BSCS of the structure was calculated using MoM with PBF based on WG and compared with numerical simulation results using MoM with piecewise-sinusoidal (PWS) basis functions, as well as with experimental results from [65] (Figure 3). The obtained results coincided well with each other. In fact, the BSCS results using MoM with PBF based on WG matched even more closely with the measured results than those obtained with MoM using PWS, particularly when the direction of the incident wave changes in the xOy plane. Observing Figure 3, it can be seen that there are differences in the results in the side lobes, possibly due to the measurement conditions and imperfections of the flat plate surface. However, the results in the main lobe of BSCS generally agree well with each other with a deviation at maximum magnitude BSCS of 0.55 dB. Additionally, when the incident wave was perpendicular to the surface of the plate, the scattered field reached its maximum; specifically, the BSCS magnitude at \(\theta=90^{\circ}\), \(\varphi=90^{\circ}\) were 26.8 dBm (MoM with PBF based on WG) and 26.25 dBm (experimentally and MoM with PWS). Note that the width of the main lobe (-3 dBsm from the maximum BSCS level) obtained in the xOy plane (12\({}^{\circ}\)) was larger than that in the yOz plane (8\({}^{\circ}\)), which was consistent with the fact that the width of the plate (\(W=2\) m) was smaller than its length (\(H=3\) m). These findings demonstrate the accuracy of using MoM-based WG with PBF for analyzing scattering plate structures.