## 4 Simulation Results  
The particle swarm algorithm was coded in MATLAB under a computer with four Xeon processors (model E5-2640) and 256 GB of memory (RAM). The configuration of the PSO was set as follows: number of iterations \(i_{max}=1800\), number of agents \(p_{size}=50\), inertial weight \(w\) varies downward in the range of [0.95-0.4], and acceleration constants \(c_{1}=c_{2}=2\). This configuration has been tested with good results in antenna array optimization [37]. We established the FDVA with N = 6, 9, and 12 antenna elements. We performed cases with symmetry and no symmetry of the locations and frequency offsets around the origin. We summarize the results of the optimization in Table 1, which contains numerical values of the optimization variables \(x_{n}\) and \(f_{n}\). In addition, Table 1 shows the values of the side lobe levels in a normalized magnitude. The cases with symmetry obtained better SLL reductions than those with no symmetry. Figure 4 shows the fitness function values during the optimization process for the cases with no symmetry. The PSO converges at the optimum solution. Figure 5 depicts the optimization variables' distributions. Using symmetrical distributions would decrease the hardware complexity of the antenna array. The symmetrical random distributions are better than the traditional Hamming distributions regarding SLL reductions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**N**} & \multirow{2}{*}{**Symmetry**} & \multirow{2}{*}{**Normalized**} & \multirow{2}{*}{**Directivity**} & \multicolumn{2}{c}{**Locations \(x_{n}\)**} & \multirow{2}{*}{**Frequencies \(f_{n}\) (KHz)**} \\  & & & & & **(A)** & \\ \hline \multirow{2}{*}{6} & \multirow{2}{*}{Yes} & \multirow{2}{*}{0.7706} & \multirow{2}{*}{6.56 dB} & 0, 1.7652, 4.4652, 7.0634, 9.7634, & 16.248, 12.135, 2.388, 2.388, 12.135, \\  & & & & 11.5286 & 16.248 \\ \hline \multirow{2}{*}{9} & \multirow{2}{*}{Yes} & \multirow{2}{*}{0.5828} & \multirow{2}{*}{8.49 dB} & 0, 2.6582, 5.3208, 7.1053, 8.8719, & 19.744, 15.234, 12.436, 1.624, 4.664, \\  & & & 10.6385, 12.4230, 15.0856, 17.7438 & 1.624, 12.436, 15.234, 19.744 \\ \hline \multirow{2}{*}{12} & \multirow{2}{*}{Yes} & \multirow{2}{*}{0.5192} & \multirow{2}{*}{9.05 dB} & 0, 2.6613, 5.1533, 7.4415, 9.1495, & 10.57043, 19.94567, 17.6699, 1, 1.3293, \\  & & & 10.8621, 13.5126, 15.2525, 16.9332, & 9.02219, 39.02219, 1.3293, 1, 17.6699 \\  & & & 19.2214, 21.7134, 24.3747 & 19.94567, 10.57043 \\ \hline \multirow{2}{*}{6} & \multirow{2}{*}{No} & \multirow{2}{*}{0.7121} & \multirow{2}{*}{6.95 dB} & 0, 2.6412, 4.5123, 6.3544, 8.1316, 9.8321 & 14.3043, 19.217, 1, 1.7049, 11.1150, \\  & & & & 2.5609 & 2.5609 \\ \hline \multirow{2}{*}{9} & \multirow{2}{*}{No} & \multirow{2}{*}{0.5904} & \multirow{2}{*}{8.43 dB} & 0, 2.6994, 5.3944, 8.0934, 9.8727, & 4.466, 3.308, 19.106, 0.1304, 1, 11.775, \\  & & & 12.5459, 14.3622, 16.0889, 17.8965 & 1.171, 07.367, 18.245 \\ \hline \multirow{2}{*}{12} & \multirow{2}{*}{No} & \multirow{2}{*}{0.5386} & \multirow{2}{*}{9.19 dB} & 0, 2.6986, 4.3989, 7.0827, 9.1845, & 3.697, 19.408, 3.252, 6.969, 20.000, \\  & & & 11.2371, 13.7306, 15.7537, 17.4566 & 13.671, 1, 19.997, 6.018, 17.358, 19.680, \\  & & & 19.1796, 20.9382, 23.6236 & 12.929 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimization variables and fitness function values. Now, these distributions generate the radiation patterns shown in Figures 6-8 for the cases with different numbers of antennas. Firstly, observe the radiation generated by the Hamming distribution in the three figures. These patterns contain grating lobes due to the spacing of the antennas at greater than \(\lambda/2\). Nevertheless, it is impossible to use \(\lambda/2\) as the spacing because this collides with the drones. In this case, the Hamming distributions are not suitable for this application. The random distributions obtain radiation with no grating lobes, as depicted in the three figures. One can infer that these distributions are better solutions for the FDVA.