## 2 Design of the Proposed RDA with the EBGs
### Mutual Coupling Reduction with the Presence of the EBGs  
Figure 2a illustrates the configuration of a single CP Koch-shaped patch antenna surrounded with EBGs. The Koch fractal shape is applied into two edges along the \(x\)-direction of a rectangular patch. This Koch-shaped patch is excited through a feeding point located at distances of \(d_{x}\) and \(d_{y}\) from the center of the patch towards the \(+x\)- and \(-y\)-axes, respectively, to realize good circular polarization. The antenna is designed and optimized to operate at a frequency of 5.2 GHz using a previously published design process [17; 18; 19; 20]. Both the patch and the EBGs are printed on the upper layer of a single Taconic dielectric substrate with a dielectric constant of 3.5, a thickness of 1.52 mm, and a loss tangent of 0.0019. Owing to the difference in the geometry of the Koch-shaped patch along \(x\)- and \(y\)-axes, two types of EBGs are used. A conventional mushroom-like EBG structure is located along the \(y\)-axis [21]. Meanwhile, a slot-loaded mushroom-like EBG structure, which has compact size to avoid overlapping of the patch, is placed along the \(x\)-axis [22]. By etching two rectangular slots on the metallic patch of the EBG cell, the series equivalent capacitance can be enlarged, resulting in a more compact EBG structure. Both of these EBGs are designed to suppress the mutual coupling at a frequency of 5.2 GHz. The proposed design is simulated and optimized using CST Microwave Studio software with conductor and dielectric losses taken into consideration. The EBGs were optimized by placing one cell in the computation domain. Two perfect electric conductor (PEC) walls and two perfect magnetic conductor (PMC) walls were used to simulate the infinite-sized periodical structure [23], as shown in Figure 3a. We calculated the reflection phases of the EBGs. Simulated reflection phases are presented in Figure 3b for both the optimized conventional and slot-loaded mushroom-like EBGs with the optimized parameters listed in the caption of Figure 2. As observed in Figure 3b, the resonance frequencies for the \(0^{\circ}\) reflection phases are approximately 5.2 GHz. A prototype of the antenna with the EBGs is fabricated using the optimized parameters, as shown in the caption; a corresponding photograph is shown in Figure 2b. The measured and simulated results of the single CP Koch-shaped patch antenna with the EBGs are depicted in Figure 4. Note that the measured results are in good agreement with the simulated results. A \(-10\) dB reflection bandwidth of 5.12-5.30 GHz was found during the measurement. The measured axial ratio (AR) value was 2.42 at the designed frequency of 5.2 GHz; meanwhile, a minimum AR value of 1.32 dB was obtained at 5.175 GHz. The measured 3 dB AR bandwidth was 5.16-5.21 GHz. An antenna without EBGs was also  
Figure 2: (**a**) Single CP Koch-shaped patch antenna with EBGs; (**b**) Photograph of the fabricated prototype. \(W_{p}=15.45\) mm, \(L_{p}=12.69\) mm, \(d_{x}=1.695\) mm, \(d_{y}=1.966\) mm, \(L_{1}=0.793\) mm, \(L_{2}=3.173\) mm, \(L_{3}=9.516\) mm, \(\theta=45^{\circ}\), \(w_{1}=8.0\) mm, \(g_{1}=0.4\) mm  
investigated, and these simulated results are included in Figure 4a,b. It can be seen that the 3 dB AR bandwidth of the proposed antenna with the EBGs was shifted slightly to a lower frequency range. Moreover, the minimum simulated AR value was reduced from 1.90 to 0.96 dB when using the EBGs, hence improving the CP purity. The radiation patterns at the designed frequency of 5.2 GHz on the two major cutting planes (the \(xz\)- and \(yz\)-planes) are shown in Figure 4c. It was found that the radiation patterns exhibit left-handed circular polarization (LHCP), in which the LHCP gain is approximately 17.1 dB higher than the right-handed circular polarization (RHCP) gain in the \(+z\)-direction. Figure 4: Measured and simulated results of the single CP Koch-shaped patch antenna with the EBGs: (**a**) reflection coefficients; (**b**) ARs; and (**c**) radiation patterns at 5.2 GHz. AR: Axial ratio.