# A Dual-Polarized and Broadband Multiple-Antenna System for 5G Cellular Communications
## 2 Characteristics of the Dual-Polarized CPW-Fed Antenna  
This section discusses the critical characteristics of the single-element antenna. The antenna schematic is depicted in Figure 1, featuring two closely positioned trapezoidal slot antennas equipped with L-shaped radiating stubs. The antenna is designed on a substrate made of 1.6 mm FR4 material. This substrate has a permittivity (also known as relative permittivity or \(\epsilon_{\mathrm{r}}\)) of 4.3 and a loss tangent (\(\tan\delta\)) of 0.023. These material properties are crucial in determining the electrical properties and overall performance of the antenna. The choice of the dielectric material influences the antenna's impedance, radiation efficiency, and bandwidth, among other factors. FR4 is a popular low-cost material commonly used in designing RF and microwave circuits and antennas. The specific dimensions and parameter values of the single and the MIMO antenna designs are outlined in Table 1.  
Figure 1: (**a**) Side and (**b**) front views of the introduced antenna design. The S-parameters of the antenna are shown in Figure 2. Notably, the dual-polarized single antenna pair exhibits a wide operational bandwidth from 3.2 GHz to 6 GHz, with an S\({}_{\text{nn}}\)\(-\)10 dB. Moreover, the designed CPW-fed antenna demonstrates high isolation, particularly at the center frequency. Figure 3 showcases the antenna's S-parameters (S\({}_{11}\)/S\({}_{21}\)) with varying L\({}_{1}\), a specific parameter in the antenna design. During the simulation, L\({}_{1}\) is adjusted while all other parameters remain constant, as listed in Table 1. The plot demonstrates that different values of L\({}_{1}\) have a substantial effect on the matching and mutual coupling characteristics between the feeding ports. Notably, for L\({}_{1}\) = 14.25 mm, the antenna achieves its optimal performance, indicating the best impedance matching and mutual coupling properties among the investigated values of L\({}_{1}\). As illustrated in Figure 3a, adjusting the value of L\({}_{1}\) has improved the antenna's impedance bandwidth, particularly at higher frequencies. Additionally, as shown in Figure 3a, when L\({}_{1}\) is set to 11.75, the mutual coupling between the elements at the lower frequency (3 GHz) and higher frequency (6 GHz) is approximately \(-\)16 dB and \(-\)11 dB, respectively. Increasing L\({}_{1}\) to 14.25 further improves the mutual coupling, reducing it to about \(-\)20 dB at 3 GHz and \(-\)13 dB at 6 GHz. These demonstrate that adjustments to the L\({}_{1}\) parameter can influence and reduce mutual coupling within the desired operating band. \begin{table}
\begin{tabular}{c c c c} \hline
**Param.** & **mm** & **Param.** & **mm** \\ \hline W & 23 & W\({}_{2}\) & 1.8 \\ L & 23 & L\({}_{2}\) & 10.2 \\ W\({}_{\text{S}}\) & 150 & W\({}_{3}\) & 4.5 \\ L\({}_{\text{S}}\) & 75 & L\({}_{3}\) & 0.25 \\ W\({}_{1}\) & 2.4 & W\({}_{4}\) & 2.9 \\ L\({}_{1}\) & 14.25 & L\({}_{4}\) & 1 \\ \hline \end{tabular}
\end{table} 
Table 1: Design values of the antenna parameters. Figure 2: S-parameters of the suggested antenna design. To better understand the broadband and multi-resonant behavior of the proposed antenna design, Figure 4 presents the surface current densities at 3.2 GHz, 4.7 GHz, and 5.5 GHz. The same maximum scale is applied across all plots for consistency. A detailed examination reveals that significant resonance activity occurs in several key areas as follows: the L-shaped radiation stub, as well as both the inner and outer regions of the trapezoidal slot antenna. These combined contributions from multiple components of the antenna are crucial in achieving the wide bandwidth performance observed. This synergy between the design elements highlights the antenna's effectiveness in generating broad-spectrum resonances [41; 42]. Figure 5 presents the efficiency characteristics of the dual-polarized antenna, including both the radiation efficiency (R.E.) and total efficiency (T.E.).