# Taguchi Method-Based Synthesis of a Circular Antenna Array for Enhanced IoT Applications
### Design and Validation of a Circular Antenna Array with CST Microwave Studio  
An IoT antenna designed for the 2.45 GHz frequency is commonly used in a variety of wireless communication systems, particularly for Internet of Things (IoT) applications. The 2.45 GHz frequency band is one of the most widely used frequencies for wireless communication due to its balance between range, data rate, and penetration capabilities. It is used by several wireless communication standards, including Wi-Fi, Bluetooth, Zigbee, and other IoT protocols [17; 18; 19; 20; 21]. The proposed antenna is shown in Figure 3. Our antenna is printed on a plexiglass substrate with a relative permittivity of 2.5, a loss tangent of 0.02, and a thickness of 4 mm. The antenna dimensions are \(L=36\,\)mm and \(W=36\,\)mm for 2.45 GHz. The design of the circular antenna array is shown in Figure 4.  
Table 1 presents the optimal excitation values for several well-known optimization methods from the literature, such as PSO [22], GA [23], and FA [24], which are selected for comparison with the Taguchi method. The best results are obtained using the excitations optimized by the Taguchi method. The best results are defined as those that provide a radiation pattern not only with reduced SLL but also with the best half-power beamwidth (HPBW) of the main lobe, which is a crucial parameter for antenna array synthesis. The PSO (Particle Swarm Optimization), GA (Genetic Algorithm), and FA (Firefly Algorithm) are optimization techniques inspired by natural phenomena, each  
Figure 3: Geometry of the proposed antenna. Figure 2: Electronic-scanning of the space with a secondary lobe level of \(-28\) dB for a circular antenna array of 16 elements. and limitations in antenna array synthesis. PSO, based on the behavior of particle swarms, is effective for exploring large search spaces, though it can be sensitive to parameter choices and may become trapped in local minima. The Genetic Algorithm, based on natural evolution principles, is particularly suited for complex, combinatorial problems but often requires a large number of evaluations to converge to an optimal solution. The Firefly Algorithm, which mimics the behavior of fireflies based on light intensity, strikes a good balance between exploration and exploitation, offering fast convergence and a strong ability to avoid local minima. In contrast, the Taguchi method, while simpler and computationally less expensive, stands out for its effectiveness in handling relatively simple and well-defined problems. It quickly optimizes design parameters with a limited number of trials, making it highly efficient for systems where relationships between variables are linear or relatively simple. However, it is limited for more complex or high-dimensional problems, where heuristic algorithms like PSO, GA, and FA outperform its exploration capabilities. The Figure 5 illustrates the reflection coefficient and 3D radiation pattern for our test antenna at the operating frequency of 2.45 GHz. The reflection coefficient highlights the antenna's matching performance, while the 3D radiation pattern provides a detailed view of its directivity and radiation characteristics. The Figure 6a-e show the polar radiation patterns of the circular array. It has been demonstrated that the Taguchi excitations provide the maximum reduction in the side-lobe level (SLL), which is lower than that obtained by the various algorithms: PSO, GA, FA, and even with uniform excitation. Figure 4: Design and simulation of a circular antenna array with 10 elements. Figure 5: Reflection coefficient of the proposed antenna and 3D radiation pattern at 2.45 GHz. Figure 7 presents 3D radiation patterns for the different optimization methods, while the front views are depicted in Figure 7a-d. The optimized array factor obtained was compared to those obtained using other well-known numerical optimization techniques. The Taguchi method demonstrates superior performance compared to the other methods.