## 3 Monopulse Ratio Curve Improvement
### Proposed Monopulse Rate Curve Improvement Method Based on the Presented Tile
For the antenna system presented in this paper, the estimation of the location is not performed in the elevation angle direction based on assumptions. Therefore, a is unrelated to b, and each weight can be expressed as a vector, as shown in Equations (16) and (17). \[W^{a}\;=\;[W_{0}\;^{a},\;W_{1}\;^{a},\;\cdots,\;W_{7}\;^{a}] \tag{16}\]  
\[W^{p}\;=\;[W_{0}\;^{p},\;W_{1}\;^{p},\;\cdots,\;W_{7}\;^{p}] \tag{17}\]  
The cost function for applying the VPR algorithm was defined as shown Equation (18). \[cost\;=\;1000\,std(|\frac{P_{\Delta}}{P_{\Delta}}(\phi)|)\;+\;\frac{1}{max(P_{ \Delta})},\;\;\;\;\;(0\leq\phi\leq\phi_{o}) \tag{18}\]  
where \(std()\) is the deviation calculation function, and 1000 is the deviation evaluation weighting factor coefficient for weighting the evaluation of the deviation. In this study, the VPR algorithm was set to search for the minimum cost evaluation value. Therefore, a weight with a small deviation in the monopulse ratio curve according to phi was searched. In addition, when calculating the cost function, the reciprocal of the maximum value of the sum signal was added. We took this step to induce the linear characteristics of the monopulse ratio curve and, at the same time, set the synthesized sum pattern to achieve maximum gain. The deviation weighting coefficient was applied to increase the proportion of the monopulse ratio curve compared to the sum pattern gain for calculating the cost function. Table 3 shows the parameters of the VPR algorithm for searching for optimal weighting values. The VPR algorithm parameters for amplitude weight search and phase weight search were each set in a different manner because the conditions for each weight search were different. Figure 10 shows the cost evaluation value based on the iteration of the VPR algorithm and the optimal weighting, as searched for using the VPR algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline Parameter & \(W^{a}\) & \(W^{p}\) \\ \hline \(c_{s}\) & 0.2 & 0.6 \\ \(c_{p}\) & 0.4 & 0.9 \\ \(c_{z}\) & 0.05 & 0.147 \\ \(c_{t}\) & & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: VPR algorithm main variable settings. The algorithm stop criterion was set as the cost with 2.61. The optimal amplitude and phase weighting processes were found to be Equations (19) and (20), as shown in Figure 8b. \[W^{a}\,=\,[0.29,\,1,\,1,\,1,\,1,\,1,\,1,\,0.29] \tag{19}\]  
\[W^{p}\,=\,[180,\,78.75,\,0,\,0,\,0,\,0,\,78.75,\,180] \tag{20}\]  
Figure 11 shows the radiating characteristics of the application of the optimized weights to Equations (10) and (11). Based on \(\phi_{c}=18^{\circ}\) and the sum and difference patterns shown in Figure 11, using Equation (7), \(c_{r}\) was found to be 10.268. Figure 12 shows the monopulse ratio curve with the sum and difference patterns in Figure 9 and \(c_{r}\)= 10.268. As a result of this analysis, the MAE mean was 0.01, and the MAE maximum was 0.04. Compared to the general monopulse ratio curve improvement method, the searching range and location estimation error for the communication counterpart have been improved. Figure 11: Single-tile-optimized radiation characteristics in (**a**) polar plot and (**b**) rectangular plot. Figure 10: VPR algorithm results: (**a**) best cost value according to algorithm iteration; (**b**) optimized amplitude and phase weighting. When estimating the location of a communication counterpart using the monopulse technique, the received signal strength cannot be confirmed because the monopulse ratio curve is the ratio of the sum and difference signals. Therefore, when estimating the location, the received signal strength based on the sum pattern must also be checked. As a result of the sum pattern analysis shown in Figure 11, the gain difference within the counterpart's location estimation region is approximately 6.9 dB. As the gain difference decreases, the ambiguity involved in estimating the location of the counterpart based on the received signal strength using the sum pattern decreases.