# 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
### Amplitude Synthesis
Afterward, select the appropriate orthogonal experimental design, OA \((27,9,3,2)\), which helps in arranging the experiments efficiently by ensuring that all main effects and some interactions are properly tested. Then, specify the reduced function value \((rr=0.6)\), which optimizes the array by reducing unnecessary complexity and focusing on the most relevant interactions. Finally, set the convergence \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Elements**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline
**Level 1** & \(-19.79\) & \(-20.02\) & \(-17.31\) & \(-18.45\) & \(-19.77\) & \(-21.13\) \\ \hline
**Level 2** & \(-19.65\) & \(-20.04\) & \(-19.73\) & \(-19.95\) & \(-19.71\) & \(-19.60\) \\ \hline
**Level 3** & \(-19.29\) & \(-18.66\) & \(-21.68\) & \(-20.32\) & \(-19.24\) & \(-17.98\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Response table for the first iteration. Figure 11: Simulation results of a concentric ring array (\(N_{1}=2\), \(N_{2}=4\), and \(N_{3}=6\)). value to 0.01, ensuring that the optimization process stops once the desired accuracy is reached, avoiding any further unnecessary iterations. The optimization objective is achieved after 60 iterations, as indicated in Figure (b)b. The excitation weights of this optimized antenna array using the Taguchi method are mentioned in Table 5.  
1.3. _Concentric Ring Antenna Array with 24 Elements (\(N_{1}=6\), \(N_{2}=8\), and \(N_{3}=10\))  
The array factor is described by the following Equation (11):  
\[AF(\theta,\phi)=2\sum_{m=1}^{3}\sum_{n=1}^{12}w_{mn}\cos(kr_{m}(\sin(\theta) \cos(\phi-\phi_{mn})-\sin(\theta_{0})\cos(\phi_{0}-\phi_{mn}))) \tag{11}\]  
To effectively apply the Taguchi method for optimization, it is essential to follow these steps: First, determine the number of parameters, which is set to \((k=12)\), along with the number of levels, which is \((s=3)\). Next, define the strength of the orthogonal array, here chosen as \((t=2)\). Afterward, select the appropriate orthogonal experimental design, in this case, OA \((27,12,3,2)\), which dictates the arrangement of experiments. The following step is to specify the reduced function value \((rr=0.6)\), which is crucial for reducing the dimensionality of the design space. Finally, set the convergence threshold value to 0.01, ensuring that the optimization process stops once the desired level of precision is achieved. The Figure (a)a shows that we have successfully minimized the side-lobe level (SLL) down to \(-21.2004\) dB, where the gain is approximately 16.7 dB compared to the side-lobe level of the uniform concentric ring antenna array (SLL = \(-4.5\) dB). The optimization objective is achieved after 25 iterations, as indicated in Figure (b)b. The excitation weights for this optimized antenna array using the Taguchi method are presented in Table 6.  
Figure 12. Simulation results of a concentric ring array (\(N_{1}=4\), \(N_{2}=6\), and \(N_{3}=8\)). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(N_{1}\)} & \multicolumn{2}{c}{\(N_{2}\)} & \multicolumn{2}{c}{\(N_{3}\)} \\ \hline
**Elements** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline
**Weights** & 0.5417 & 0.4623 & 0.4931 & 1.0000 & 0.8540 & 0.5184 & 0.8743 & 0.5000 & 0.1893 \\ \hline \hline \end{tabular}
\end{table} 
Table 5. Optimized excitations of the array (\(N_{1}=4\), \(N_{2}=6\), and \(N_{3}=8\)). 1.4.