## 5 Application of IWOA in the Array Antenna Pattern Synthesis
### Result Analysis
It can be seen that the IWOA algorithm performs better in optimization results and robustness through the comparison with other algorithms in Figure 6:2  
Figure 6:3 3D beam patterns of 64\(-\)element planar phased array. In the simulation model mentioned above, the coupling among the array elements is not considered. Therefore, EM simulations must be performed to determine whether the proposed technique can successfully optimize the maximal sidelobe in the presence of coupling. The electromagnetic simulations are performed using ANSYS electromagnetics. The amplitude excitation obtained through algorithm optimization in MATLAB is input into the 64-element planar array antenna model designed by HFSS software to verify the feasibility of the optimization algorithm in practical engineering. Figure 14a shows the comparison of 2D beam optimization effects of each algorithm obtained through EM simulation, depicting the 2D EM simulation results in 0\({}^{\circ}\) planes. The first sidelobe optimized by the IWAO is \(-18.03\) dB, and the second sidelobe level is \(-22.2\) dB. Figure 14b is the 2D EM simulation results in 90\({}^{\circ}\) planes. The first sidelobe optimized by the IWAO is \(-18.71\) dB, and the second sidelobe level is \(-19.5\) dB. Obviously, IWOA has the best sidelobe suppression performance compared with other algorithms. The sidelobe suppression performance of HFSS simulation results has deteriorated to a certain extent after the addition of coupling, yet both simulations still prove the effectiveness of the IWOA. Since the primary consideration in engineering is to solve the problem of interference avoidance, sidelobe suppression is the first optimization goal. Meanwhile, the beam width will also be broadened to some extent when performing sidelobe suppression. Through simulation analysis, the beam broadening after sidelobe suppression is within the acceptable range of the engineering as well. Table 6 shows the maximum SLL and beamwidth of the compared algorithms. Figure 15a and Figure 15b, respectively, show the 3D waveform diagrams of 64 array elements before and after optimization. The color of the maximum sidelobe becomes lighter, indicating that the value is significantly smaller, which proves that the maximum SLLs have been significantly optimized. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithms** & **Maximum SLL (dB)** & **3 dB Beamwidth (Degree)** \\ \hline Uniform Array & \(-10.92\) & \(13.46\) \\ GA & \(-14.83\) & \(13.94\) \\ PSO & \(-15.16\) & \(14.11\) \\ DE & \(-19.25\) & \(15.58\) \\ IWO & \(-20.01\) & \(16.11\) \\ MOA & \(-19.62\) & \(15.83\) \\ WOA & \(-18.46\) & \(15.01\) \\ IWOA & \(-22.85\) & \(16.92\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The maximum SLL and beamwidth of the compared algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **Best MSLL (dB)** & **Worst MSLL (dB)** & **Average MSLL (dB)** & **Standard Deviation** \\ \hline Uniform Array & \(-10.92\) & \(-10.92\) & \(-10.92\) & \(0\) \\ GA & \(-15.03\) & \(-13.95\) & \(-14.52\) & \(0.77\) \\ PSO & \(-15.31\) & \(-13.66\) & \(-14.36\) & \(0.86\) \\ DE & \(-19.77\) & \(-18.63\) & \(-19.02\) & \(0.41\) \\ IWO & \(-20.68\) & \(-18.98\) & \(-19.53\) & \(0.56\) \\ MOA & \(-20.52\) & \(-17.65\) & \(-18.68\) & \(1.54\) \\ WOA & \(-18.52\) & \(-17.38\) & \(-17.95\) & \(0.43\) \\ IWOA & \(-23.09\) & \(-22.53\) & \(-22.86\) & \(0.25\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results obtained by IWOA and other optimization algorithms. Figure 14: The 2D EM simulation results.