# SIW Cavity-Backed Antenna Array Based on Double Slots for mmWave Communications
## 2 Design
Once the cavity-backed antenna was designed, we compared the performance between the use of a single slot (Figure 3a) and a double slot (Figure 3b) as follows: First, a parametric study of the cavity-backed antenna using a single slot is shown in Figure 4. The modified parameters are \(\mathrm{s_{y1}}\), \(\mathrm{  
figure, the parameter under study is modified while maintaining the rest of the parameters as indicated in the caption of Figure 3. The parameter s\({}_{\text{y1}}\) (Figure 4a) represents the movement of the radiating slots in the \(y\) direction. It can be observed that this is an important parameter for generating the operating frequency band. For s\({}_{\text{y1}}\) = 0.73 mm, a peak (resonance) in \(|S_{\text{11}}|\) appears around 35 GHz, but it has a narrow bandwidth. The length of the radiating slot l\({}_{\text{s1}}\) in Figure 4b strongly defines the existence of a frequency bandwidth, since there is only one value that produces an impedance bandwidth below -10 dB. For other values of the slot length, no impedance bandwidth is observed. Finally, for the slot width w\({}_{\text{s1}}\), we performed a sweep of values (Figure 4c). The slot width allows the fine tuning of the frequency bandwidths, providing an adjustment of the peaks depending on the target frequency ranges. In the figure, two separate peaks in \(|S_{\text{11}}|\) can be observed. So, by varying the width of the radiating slots, the center frequency can be tuned. Figure 4: _Cont._  
Figure 5 presents the parametric study of the second slot in the cavity-backed antenna with a double slot. For a fair comparison, the dimensions of the single slot are the same as the one in the results presented in Figure 4. The dimensions under study for the second slot are the displacement in the \(y\) direction (s\({}_{\text{y2}}\)), slot length (l\({}_{\text{s2}}\)), and slot width (w\({}_{\text{s2}}\)). In Figure 5a, the reflection coefficient is illustrated when s\({}_{\text{y2}}\) is modified. This parameter enables the control of the center frequencies of two narrow frequency bands. If it is modified properly, a greater impedance bandwidth can be achieved, as shown for s\({}_{\text{y2}}=1.3\) mm. The operating frequency range obtained has a bandwidth of 1.6 GHz, where most of the values are under \(-15\) dB in the reflection coefficient. Compared with the previous results using a single slot in Figure 4a, the great flexibility in the tuning of the operating frequency band(s) of the cavity-backed antenna when the double slot is introduced can be observed. The modification of the slot length l\({}_{\text{s2}}\) is displayed in Figure 5b. In this case, the slot length produces a greater modification in the resonances of the cavity-backed antenna, providing better control than that observed for the single slot case (Figure 4b). Lastly, the slot width w\({}_{\text{s2}}\) was varied. As observed for the single slot case, the slot width provides the fine tuning of the operating frequency band, as illustrated in Figure 5c. Given these results and the comparison with the single slot case, the introduction of a second slot in the cavity-backed antenna provides more degrees of freedom in the design of the desired operating frequency bands. Figure 4: Parametric study of the single slot: (**a**) sweep of parameter s\({}_{\text{y1}}\), (**b**) sweep of parameter l\({}_{\text{s1}}\), and and (**c**) sweep of parameter w\({}_{\text{s1}}\).