## 2 Single-Patch Multi-Beam Antenna  
To increase the amount of training data available for DNN-based direction finding, a multi-beam antenna was designed starting with a basic microstrip patch antenna operating at 2.4 GHz, as shown in Figure 2a. The size of the patch is 29.5 mm \(\times\) 29.5 mm. The height and dielectric constant of the substrate are 1 mm and 4.3, respectively. The electric field is strongly distributed on the upper and lower edges of the basic patch as shown in Figure 2b. In addition, the radiation pattern has directivity in the +z direction, as shown in Figure 2c. The realized gain of the antenna is 6 dB. Figure 1: Method for increasing training data for DNN-based direction finding. To generate the coupled mode, the basic patch is divided into two sectors using the metallic vias, as shown in Figure 3a. The radius of the metal via is 0.5 mm, and the spacing between the vias is 1.75 mm. As studied in [24], the two-divided antenna structure operates in a coupled mode in the superposed form of the even and odd modes, and the field distributions at the edge of the upper and lower sectors are asymmetrical, as shown in Figure 3b. Due to the asymmetry of the field distribution at the patch edge, the radiation pattern is inclined in the -y direction. The realized gain of the antenna is 5.96 dB. In order to utilize the additional coupled mode, metal vias are inserted in the y-axis direction. Due to the four-divided patch structure, the feeding point is shifted by 5 mm in the \(-\)x-axis direction, considering actual coaxial probe feeding. The adjustment of the feeding point caused the coupled mode to occur at 3.5 GHz in the higher-order mode. Therefore, the patch size is slightly increased to 42 mm \(\times\) 42 mm to resonate at 2.4 GHz while maintaining an additional coupled mode, as shown in Figure 4. Then, the feeding point is adjusted from \(-\)6 mm to \(-\)17 mm in the y-axis direction for matching the four-divided antenna. Figure 5a illustrates the structure of the patch that has increased in size. The electric field distribution and radiation pattern are shown in Figure 5b,c, respectively. The realized gain of the antenna is 2.56 dB in single feeding and 2.73 dB in dual feeding. The gain the of antenna is reduced due to the split field distribution of patch edges due to coupled mode and higher-order mode operation. This type of antenna has multiple beams depending on the divided field distribution and combination of excitation and has been studied with a similar structure in [25,26]. Figure 3: Configuration of the (**a**) modified patch antenna divided by two sectors, (**b**) electric field distribution, and (**c**) radiation pattern. Figure 2: Configuration of the (**a**) basic patch antenna, (**b**) electric field distribution, (**c**) and radiation pattern. The electric field distribution and radiation pattern by the excitation port are shown in Table 1 and Figure 6, respectively. Figure 4: Return loss of the four-divided patch with and without size increase. Figure 5: Configuration of the (**a**) modified patch antenna divided by four sectors, (**b**) electric field distribution, and (**c**) radiation pattern. However, when a single port is used for excitation, the wide beamwidth of the radiation pattern can cause ambiguity in signal level resolution between patterns, as previously studied in [27]. In the amplitude comparison method, the distinction between the received power values for each pattern should be clear because ambiguity occurs in areas where patterns overlap due to the wide beamwidth. These issues are directly related to the quality of the training data. To address this issue, slight modifications were made to the patch structure. In order to reduce the beamwidth, the field distribution of the aperture of the antenna must be increased.