## 2 Design and Optimization
### Optimization of the Multi-Element AVA Design  
To meet the high-gain requirements of the 5G antennas operating in the mm wave frequency bands, the single element AVA (type-C in Figure 1) is converted into a two, four and eight element AVA array, as shown in Figure 3. The inter-element spacing between the individual antenna elements is set to 6 mm in order to obtain a broadside radiation pattern. The individual elements of the array antennas are excited by carefully designing a power-dividing network. The simulated S11, gain vs. frequency plots and the radiation patterns of the single and multi-element antennas are compared and illustrated in Figure 4, Figure 5, and Figure 6, respectively. The simulations are performed in CST MWS vs. 2018. The dimensions of the proposed 8-element array antenna are outlined in Table 1. The S\({}_{11}\) of the antennas (Figure 4) shows that minimal variations in the deriving-point impedance bandwidth (S\({}_{11}<-10\) dB) of the single and multi-element antennas is observed. However it is worth-mentioning that as the number of radiating elements is increased from one to eight, the absolute gain of the antenna is significantly increased, for example, 3.6 to 12 dBi at f = 28 GHz. The radiation patterns of the antennas in the two principal planes, that is, E-plane (\(\phi\) = 90\({}^{\circ}\)) and H-plane (\(\phi\) = 0\({}^{\circ}\)) are compared in Figure 6, which shows that the gain of the main lobe is increased as the number of elements in the antenna array is increased, however, due to the mutual coupling between the neighboring elements, the direction of the main-lobe is slightly shifted. The mutual coupling between elements can be calculated when all elements of eight element AVA are fed by separate ports instead of single port as shown in Figure 7. The mutual coupling between elements of eight elements AVA is shown in Figure 8. It can be observed that mutual coupling between neighboring elements seems greater at lower frequencies than higher frequencies. This is due to spacing requirement, as lower frequency required greater spacing compared to higher frequencies. Therefore, while designing multiband array antenna, the spacing should be adjusted in keeping lower frequencies in mind to avoid mutual coupling. The spacing distance is adjusted at 6 mm (less than \(\lambda_{o}/2\)) which is calculated at 24 GHz. The summary of the main lobe magnitude (MLM), main lobe direction (MLD), half power beamwidth (HPBW), and side lobe level (SLL) is presented in Table 2. It is evident that as the gain of the antenna is increased, the HPBW is reduced [36; 37]. It is also evident that beam steering along the main lobe direction occurs in the multi-element antennas, relative to the single element reference antenna. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Parameter & L & L\({}_{1}\) & L\({}_{2}\) & L\({}_{3}\) & L\({}_{4}\) & L\({}_{5}\) & L\({}_{6}\) \\ \hline Value (mm) & 33.31 & 7 & 12 & 2.2 & 1.69 & 12.4 & 1.6 \\ \hline Parameter & L\({}_{7}\) & L\({}_{8}\) & L\({}_{9}\) & L\({}_{v}\) & L\({}_{d}\) & L\({}_{g1}\) & L\({}_{g2}\) \\ \hline Value (mm) & 1.653 & 6.4 & 6.405 & 2.2 & 6 & 18.748 & 1.4 \\ \hline Parameter & L\({}_{g3}\) & L\({}_{g4}\) & W & W\({}_{1}\) & W\({}_{o}\) & W\({}_{2}\) & W\({}_{3}\) \\ \hline Value (mm) & 5 & 2.252 & 54.96 & 2.43 & 0.4 & 1.371 & 0.811 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the 8-element AVA. Figure 4: S\({}_{11}\) comparison of single and multi-element antennas. Figure 3: Geometry of multi-element array antennas. (a) 2-element array. (b) 4-element array. (c) 8-element array. Figure 5: Gain comparison of the single and multi-element AVA antennas as function of frequency. Figure 6: Comparison of radiation pattern in the E- and H-planes. Based on the aforementioned analysis, the eight-element antenna offers higher gain in the designated frequency bands, as compared to the rest of the candidate antennas and is considered as the proposed antenna for the 5G and Ku-band radar applications.