## 2 Proposed Antenna with SIW Feeding Network  
A conventional pulsed radar system usually excites a pulse to measure a spatial distance or direction of a target using the elapsed time for receiving the reflected signal. For the range detection, the pulse width and period are important parameters for the range resolution of the radar system. The antennas in such radar systems require specific operating frequency bandwidths in terms of the radar applications due to the range resolution [28; 29]. For the angle detection, the amplitude comparison is one of well-known methods that can find the direction of the target using the ratio of the difference/sum patterns. Thus, according to the applications, the antennas need adequate difference/sum radiation pattern beam widths and density of pattern measurement points, which can decide the angle resolution and the angle detection range [30; 31]. From this background, we design the monopulse antenna system considering the difference/sum patterns for the spatial angle detection range and resolution. Figure 1 shows the geometry of the proposed monopulse antenna using a single patch radiator with a simple multi-mode SIW feeder. The antenna structure is divided into three subsections of a microstrip patch, a TE\({}_{10}\) mode SIW, and a TE\({}_{20}\) mode SIW. All three parts are printed on thin FR4-substrates (\(\varepsilon_{r}\) = 3.8, tan \(\delta\) = 0.018) with thicknesses of \(h_{1}\) and \(h_{2}\). Figure 2 depicts the flow chart of a design methodology for the proposed antenna. First, the radiating patch is placed on the substrate with a width of \(p_{1}\), and the patch width is adjusted by the parameter \(p_{2}\). Second, we design the multi-mode feeding network consisting of two SIWs with different modes, which are excited by the microstrip lines. The two SIW feeders are spaced apart by a gap of \(g\), and they have a low profile with a simple structure for fabrication compared to conventional complicated waveguide comparators. The SIW in Figure 1d has a width of \(w_{1}\) and a length of \(l_{\text{f1}}\). Via holes with a diameter of \(d_{1}\) are arranged by a separation distance of \(s_{1}\) to generate the TE\({}_{10}\) mode that results in the sum pattern. These essential SIW parameters are determined using a conventional SIW equation in [32]. The SIW is then connected to a subminiature version A (SMA) connector through the microstrip line with a length of \(l_{u1}\) and a width of \(w_{u1}\) to excite the TE\({}_{10}\) mode at 4.85 GHz. Similarly, the SIW for the TE\({}_{20}\) in Figure 1e has the design parameters of \(w_{2}\), \(l_{\text{f2}}\), \(d_{2}\), and \(s_{2}\). However, different from Figure 1d, a microstrip line (\(w_{b}\), \(l_{b}\), \(l_{u2}\), and \(w_{u2}\)), along with a slot (\(l_{s1}\), \(l_{s2}\), \(w_{s1}\), and \(w_{s2}\)), is used to effectively generate the TE\({}_{20}\) mode at the same frequency, where the triangular slot is designed to obtain the impedance matching using  
microstrip to slot feeding transition technique [33; 34; 35]. Note that the SIWs have physically larger sizes than the patch radiator, since the patch radiator is excited through the rectangular coupling aperture constructed by the cross section of the SIW and the bottom of the substrate. It is because that the electric fields inside the substrate of the rectangular patch antenna need to be distributed with TM\({}_{\text{mn}}\) mode based on the cavity model [36; 37; 38]. Then, all sections are combined by vertically inserting the SIW feeding parts into the patch antenna. For detailed tuning, all parameters are optimized using a genetic algorithm (GA), and the best result is chosen from the final generation to fabricate the proposed structure.