# Taguchi Method-Based Synthesis of a Circular Antenna Array for Enhanced IoT Applications
## 2 Synthesis of Radiation Patterns of a Concentric Ring Antenna Array Using the Taguchi Method
### Design and Validation of Concentric Ring Antenna Arrays Using CST Microwave Studio
#### 2.2.3 30-Element Antenna Array (\(N_{1}=8\), \(N_{2}=10\), and \(N_{3}=12\))  
A 30-element concentric ring antenna array (see Figure 20a) is used for validation. Table 11 presents the optimal excitation values for several well-known optimization methods from the literature, such as Evolutionary Programming (EP) [26] and Firefly Algorithm (FA) [24], which are selected for comparison with the Taguchi method. Figure 20c-e show the 3D radiation patterns for these optimization methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Excitations with Different Algorithms**} \\ \hline
**CCAA** & **Number of Elements** & **Uniform** & **EP [26]** & **FA [24]** & **Taguchi** \\ \hline \multirow{5}{*}{\(N_{1}\)} & **1** & 1.0000 & 0.2242 & 0.9354 & **0.5242** \\ \cline{2-5}  & **2** & 1.0000 & 0.2886 & 0. The best results are obtained using excitations optimized by the Taguchi method. The best results are defined as those that offer the most efficient radiation pattern, not only with reduced side-lobe level (SLL) but also with the best half-power beamwidth (HPBW) of the main lobe, which is a very important parameter for antenna array synthesis. Figure 10c shows the synthesized 3D radiation patterns for a 30-element array with dimensions \(N_{1}=8\), \(N_{2}=10\), and \(N_{3}=12\), operating at a frequency of 2.45 GHz, optimized using Evolutionary Programming (EP). Figure 10d shows the excitation optimized using the Firefly Algorithm (FA), which adjusts the amplitude and phase of each antenna element to achieve the optimal radiation pattern. Figure 10e presents the 3D radiation patterns for the same array configuration, but with excitation optimized using the Taguchi method. This optimization technique aims to minimize pattern distortion by iterating through a set of carefully designed parameter combinations. Figure 10: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Excitations with Different Algorithms**} \\ \hline
**CCAA** & **Number of Elements** & **Uniform** & **EP [26]** & **FA [24]** & **Taguchi** \\ \hline \multirow{8}{*}{\(N_{3}\)} & **19** & 1.0000 & 0.2419 & 0.5044 & **0.1995** \\ \cline{2-6}  & **20** & 1.0000 & 0.1183 & 0.4125 & **0.7903** \\ \cline{2-6}  & **21** & 1.0000 & 0.1144 & 0.2457 & **1.0000** \\ \cline{2-6}  & **22** & 1.0000 & 0.4708 & 0.9673 & **0.9712** \\ \cline{2-6}  & **23** & 1.0000 & 0.1685 & 0.2516 & **0.9810** \\ \cline{2-6}  & **24** & 1.0000 & 0.2090 & 0.3827 & **0.2068** \\ \cline{2-6}  & **25** & 1.0000 & 0.2566 & 0.4854 & **0.1995** \\ \cline{2-6}  & **26** & 1.0000 & 0.2200 & 0.3444 & **0.7903** \\ \cline{2-6}  & **27** & 1.0000 & 0.1000 & 0.3209 & **1.0000** \\ \cline{2-6}  & **28** & 1.0000 & 0.4229 & 0.9734 & **0.9712** \\ \cline{2-6}  & **29** & 1.0000 & 0.1273 & 0.3290 & **0.9810** \\ \cline{2-6}  & **30** & 1.0000 & 0.1020 & 0.3651 & **0.2068** \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _Cont._  
2.4 Antenna Array with 36-Elements (\(N_{1}=6\), \(N_{2}=8\), \(N_{3}=10\), and \(N_{4}=12\))  
The structure of the concentric ring antenna array with 36-elements is presented in Figure 21a. Similarly, by applying the optimized values mentioned in Table 8 to excite the array, we obtain an analysis of the different radiation patterns: Figure 21b shows uniform excitations, while Figure 21c demonstrates excitations optimized using the Taguchi method, which provides better performance for our array. To address the concern regarding the radiation efficiency of the circular concentric ring antenna array, we have conducted a detailed analysis of this efficiency by calculating the total radiated power relative to the input power, taking into account losses due to materials, the feed network, and impedance matching. We also performed simulations using electromagnetic tools such as CST to evaluate the impact of the concentric ring structure on radiation efficiency.