## 5 Application of IWOA in the Array Antenna Pattern Synthesis
### Result Analysis  
The array element adopts the traditional single-layer microstrip antenna and uses the coaxial feeding mode. The radiation patch is nearly square with a half wavelength in length. As shown in Figure 6, the patch is symmetrically chamfered in the center to ensure that the antenna radiates circularly polarized waves. Simulation results show that the gain of the antenna at the center frequency is 7.5 dBi and the axial ratio is 0.3 dB. It has favorable circularly polarized radiation characteristics and meets the performance requirements of array element antenna. The radiation pattern of the array element is shown in Figure 7.  
For the 64-element planar array antenna shown in Figure 8, the frequency is set to 30 GHz, and the unit patterns of all elements are imported through the simulation software  
Figure 6: Microstrip antenna model. Figure 7: Radiation pattern of array element. HFSS. We control the range of amplitude variation within 20 dB. In the actual engineering project, we design a two-stage amplitude-phase control chip. A 6-bit digital attenuator is used to achieve a 20 dB amplitude control, and the beamformer sends instructions through the wave control interface. The chip is integrated with 6-bit phase shifter, 6-bit attenuator, gain module, power divider, serial-parallel converter, and power modulation circuits. The block diagram of the chip is shown in Figure 9.  
Subsequently, the GA, PSO, DE, IWO, MOA, standard WOA, and IWOA are carried out for sidelobe suppression optimization. The parameter design of each algorithm is shown in Table 2. Each algorithm iterated 2000 times and repeated 20 times independently to ensure the reliability of the experiment. To compare the performance of these algorithms more intuitively, the average convergence results of 20 independent experiments are provided in Figure 10. It can be seen that the convergence speed of IWOA is significantly faster than other algorithms, and the final solution is also better than the others. Figure 8: A 64-element planar phased array antenna. Figure 9: Block diagram of the amplitude-phase control chip. Owing to the requirement of engineering implementation, the range of amplitude excitation is limited in the algorithm. The amplitude attenuation is controlled between 0 to 20 dB. Since the minimum amplitude attenuation step in our chip can only reach 0.5 dB, we carried out a quantization process before obtaining the result of each iteration of the algorithm. Then, the result obtained after quantization is used as the required solution and the optimal solution is obtained after continuous iterations. In terms of engineering implementation, we take the optimal solution of the proposed algorithm as input and use a 6-bit digital attenuator to achieve the amplitude control. Corresponding instructions are sent by the beamformer through the wave control interface. The arrangement of the 64-element planar array antenna is shown in the following Figure 11, and the optimal solution obtained through the proposed algorithm is shown in Table 4.  
Figure 11: Positions of the 64-element planar phased array antenna. Figure 6:0 Convergence rates of the 64-element planar phased array. The optimal solution of the above seven algorithms for sidelobe level suppression problem is determined, and the corresponding 2D antenna pattern diagrams are shown in Figure 12, where the maximum sidelobe of the conventional pattern is \(-11.05\) dB without adjusting the amplitude, while the maximum sidelobe obtained by IWOA optimization is \(-22.87\) dB, illustrating the great performance of IWOA for sidelobe suppression. Figure 13 portrays the 3D antenna pattern diagram synthesized by IWOA. The optimal value, average value, and variance of 20 independent experiments are shown in Figure 6:1 After IWOA optimization, the optimal MSLL reaches \(-23.09\) dB, the worst MSLL is \(-22.53\) dB, and the standard deviation of 20 experiments is 0.25.