# MAOA: A Swift and Effective Optimization Algorithm for Linear Antenna Array Design
## 4 Results and Discussion
### Antenna Current Amplitude Optimization
#### 4.2.4 Design 9: Side Lobe Average Power Minimization Along with Null Placement of a 20-Element LAA  
The SLL average power minimization with deep placement of the nulls is considered in this design by adjusting the current amplitude of the antenna elements. The fitness function applicable for this design is illustrated above in Equation (28), in which the first part deals with SLL average power minimization, and the second is responsible for placing the deeper nulls at appropriate locations as defined by \(\theta_{k}\). Here, the region of the side lobes is decided as [0\({}^{\circ}\), 82\({}^{\circ}\)] and [98\({}^{\circ}\), 180\({}^{\circ}\)], and the nulls are required at \(64^{\circ},76^{\circ},104^{\circ}\), and 116\({}^{\circ}\). The MAOA, ALO, AOA, and STO algorithms are used here to optimize the current amplitude of the LAA, and the values thus obtained are mentioned in Table 12. Using these values of the current amplitude, the array pattern is drawn as mentioned in Figure 16. Comparison of the null depth and FNBW is outlined in Table 13. Consistent null depths are obtained at the four required locations by MAOA, whereas other algorithms provide better null depth at some locations but worse at the other locations of the required nulls. Figure 17 depicts the convergence profile of different algorithms, and the graph shows that the proposed algorithm presents comparable results in comparison to other algorithms.  
4.2.5 Design 10: Side Lobe Average Power Minimization Along with FNBW Constraint of a 20-Element LAA  
In this design, SLL reduction of a 20-element LAA is performed with the condition that the beamwidth remains unchanged. To handle these two objectives simultaneously, the fitness function is formulated and mentioned above in Equation (29). The current amplitude is then optimized for the reduction of SLL in the region \([0^{\circ},82^{\circ}]\) and \([98^{\circ},180^{\circ}]\). The normalized current amplitude and FNBW obtained after simulation of the fitness function by various optimization algorithms are outlined in Table 14, and the array pattern is illustrated in Figure 18. The outcome reveals that MAOA not only minimizes the average power of the SLL but also maintains the constant beamwidth of the antenna array taken into consideration. The FNBW offered by ULA is 11.40 degrees, while by MAOA, it is 10.80 degrees; hence, almost constant beamwidth is offered by the proposed optimization algorithm. Figure 19 presents the convergence profile of different algorithms, and the profile shows that the proposed algorithm presents comparable results. Therefore, the MAOA algorithm is superior to other applied optimization algorithms in optimizing the current amplitude and improving the antenna array radiation performance.  
Figure 17: Convergence profile of design 9.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Required Nulls at** & \(\mathbf{64^{\circ}}\) & \(\mathbf{76^{\circ}}\) & \(\mathbf{104^{\circ}}\) & \(\mathbf{116^{\circ}}\) & \\ \hline \multicolumn{5}{c}{**Method**} & \multicolumn{5}{c}{**Null Depth (dB)**} & \multicolumn{1}{c}{**FNBW (Degree)**} \\ \hline ULA & - & - & - & - & 11.40 \\ \hline ALO & \(-67.00\) & \(-81.00\) & \(-81.00\) & \(-67.00\) & 16.40 \\ \hline AOA & \(-93.00\) & \(-60.00\) & \(-60.00\) & \(-93.00\) & 15.00 \\ \hline STO & \(-62.00\) & \(-65.00\) & \(-65.00\) & \(-62.00\) & 15.40 \\ \hline MAOA & \(-76.01\) & \(-77.61\) & \(-77.61\) & \(-76.01\) & 17.60 \\ \hline \end{tabular}
\end{table}
Table 13: Null depth and FNBW of design 9.