## 2 Antenna Design and Analysis  
### Single Antenna Configuration  
The single antenna was printed on a Rogers RO4003C (Rogers Corporation, Evergem, Belgium) substrate, which has a thickness of 1.52 mm, a loss tangent of 0.0027, and a relative permittivity of 3.55. Figure 1 shows the proposed antenna design. The overall dimensions of the printed monopole antenna are 25.7 \(\times\) 50 mm\({}^{2}\). The initial width and length of the printed monopole in Figure 1 are calculated by Equations (1) and (2):  
\[W=\frac{1}{2f_{r}\sqrt{\mu_{0}\epsilon_{0}}}\sqrt{\frac{2}{\epsilon_{r}+1}} \tag{1}\]  
\[L=\frac{1}{4\,f_{r}\sqrt{\epsilon_{ref}}\sqrt{\mu_{0}\epsilon_{0}}} \tag{2}\]  
The radiating element consists of a rectangular patch with five circular slots (radius = 1.5 mm) forming a rose-shaped slot at the center, along with two thin slots (1 \(\times\) 4 mm\({}^{2}\)) at the top of the patch. A 50 \(\Omega\) microstrip feedline with a width of 3.5 mm was used to feed the antenna. Impedance matching between the transmission line and the rectangular patch was accomplished by using a quarter-wavelength transformer with a characteristic impedance of 75 ohm. As displayed in Figure 1, the portion of Lf1 = 12 mm that extends 8.5 mm above the ground plane forms the microstrip transmission line. The proposed single-element antenna has a wideband behavior spanning from 2 to 7.62 GHz, which covers most of the frequency bands allocated for WiMAX, sub-6 GHz, and sub-7 GHz applications, as shown in Figure 2.  
The design procedure of the antenna can be understood from Figure 3. Different configurations were designed from step 1 to step 3 to improve the antenna's bandwidth, gain, and efficiency. As seen in Figure 3, the rose-shaped slot, along with two thin slots at the top of the monopole patch (step 3), was ultimately chosen as the most effective design for improving antenna performance. The inclusion of these slots led to increased bandwidth and gain in the higher-frequency region, as seen in Figure 3a,b, compared to the other antenna configurations (steps 1 and 2). It is also noted that the addition of these slots effectively contributed to the increase in radiation efficiency in the higher-frequency region, which is attributed to the higher gain achieved in that region, as illustrated in Figure 3c. These improvements show that these slots effectively modify the radiation characteristics of the antenna, leading to enhanced directivity and radiation efficiency at higher frequencies. Figure 1: The proposed single-element design: (**a**) front; (**b**) back. Figure 3: Evolution of the single-antenna design: (**a**) simulated reflection coefficient; (**b**) simulated realized gain; (**c**) simulated radiation efficiency. A crucial parameter that greatly influences the antenna's performance regarding return loss is the length of the ground plane (Lg). For the ground plane to fully cover both the 50 ohm and 75 ohm transmission lines and form a quarter-wave transformer, the maximum value of Lg should be Lf + Lf1 = 25.5 mm. If it exceeds this value, the structure will start to resemble a microstrip patch rather than a printed monopole. Therefore, a maximum of 25 mm was selected for Lg analysis. On the other hand, considering the frequency range of 2-7.62 GHz, the center frequency is approximately 4.8 GHz. For a 75 ohm transmission line at 4.8 GHz, the quarter wavelength is about 9.5 mm. When Lf = 13.5 mm is added to this, theoretically, Lg = 9.5 + 13.5 = 23 mm can be selected. By performing a parametric sweep around the theoretical value of 23 mm (\(\pm\)2 mm), the most optimal value of Lg was found to be 22 mm, as shown in Figure 4. This value closely aligns with the theoretical expectation. At Lg = 22 mm (proposed), the antenna demonstrates a wideband response spanning from 2 to 7.62 GHz. The adjustment in Lg improves impedance matching. This impedance matching is crucial for maximizing power transfer and, consequently, enhancing radiation efficiency and bandwidth.