## 3 Simulation Results and Discussion  
After finalizing the design of a unit-cell comprised of a layered DIL with two sets of overlapped circular discs periodically sandwiched between the layers for suppressed OSB, a LWA containing 15-unit-cells has been designed and simulated with commercial HFSS. The full length of the proposed antenna is 6.9 \(\lambda_{0}\), where \(\lambda_{0}\) is the free-space wavelength at the broadside frequency (172 GHz). The simulated scattering parameters of the antenna including reflection loss (S\({}_{11}\)) and insertion loss (S\({}_{21}\)) for two types of unit-cells with one circular disc and two overlapped circular discs with a center-to-center spacing of \(\lambda\)g/4 are described in Figure 3a,b, respectively. It is seen from Figure 3a that the unit-cell with a single metal disc presents a high reflection loss over the frequency range of 173-181 GHz, causing no radiation and creating an OSB problem. However, the unit-cell with two overlapped discs gives a very low reflection loss, less than -18 dB at 172 GHz leading to radiation of the broadside (See Figure 3b). From this figure, it can be inferred that from 157.5 GHz to 206 GHz, the return loss S\({}_{11}\) was less than 10 dB, and the antenna was completely matched. It exhibits a relatively wide impedance bandwidth of 28.19%. Moreover, the simulated insertion loss \(S_{21}\) was less than \(-8\) dB.  
The normalized E-plane radiation patterns of the proposed antenna as a function of frequency have also been analyzed and the results are shown in Figure 4. As it can be seen in this figure, the beam continuously scans from \(-23^{\circ}\) at 157.5 GHz in the backward direction to 38\({}^{\circ}\) at 201.5 GHz in the forward direction. At approximately 172 GHz, the broadside radiation is observed. The corresponding plot of co- and cross-polar radiation patterns in the E- and H-plane is depicted in Figure 5. As can be seen, a gain of 13.6 dBi with the side lobe level (S\({}_{\rm LL}\)) of 13.2 dB was obtained.  
The simulated gain and main beam angles versus frequency is also shown in Figure 6. A precise inspection of this plot reveals that gain increased consistently with frequency, with a slight dip at the broadside radiation point. As can be seen, in the band around 172 GHz, the gain was slightly decreased due to the weaker reflection cancellation leading to a reflected wave at the incident port (OSB effect); however, it was still 13.6 dBi. Furthermore, the gain was consistently varying less than 5 dBi over the working frequency band, varying from 10.5 dBi to 15 dBi. The main beam of the proposed LWA was scanned from \(-23^{\circ}\) to \(38^{\circ}\) in a frequency range from 157.5 to 201.5 GHz. Accordingly, we were reaching a wide continuous beam scanning range of 61\({}^{\circ}\) through the broadside. The simulated radiation efficiency versus frequency is also depicted in Figure 7. As it can be seen from this figure,the proposed antenna ensures the minimum efficiency of 60% with 15 unit cells over the scan frequency range. Table 1 illustrates the comparison between the proposed LWA and previous similar works available in the literature. The proposed antenna had a small length with a relatively high gain and provides a wider beam scanning from the backward region to the forward region.  
Figure 4: Simulated radiation patterns in the E-plane at different frequencies.  
Figure 3: Frequency variation of S-parameters of the proposed antenna for two type of unit-cells; (**a**) one circular disc, (**b**) two overlapped circular discs with a center-to-center spacing of \(\lambda\)g/4.  
Figure 5: Simulated co- and cross-polar E-plane and H-plane radiation patterns at the broadside frequency of 172 GHz.  
Figure 6: Simulated main beam angles and gain versus frequency.  
Figure 7: Simulated radiation efficiency versus frequency.