## 3 Dual-Band Nested Antenna Array Design  
### Antenna Array for 3.5 GHz  
The geometry of the proposed CP single-element square patch antenna covering the n78-band consists of a multilayer structure utilizing an aperture-coupled feeding technique. The radiating patch is placed on Isola Astra(r) MT77 substrate with a thickness of h = 0.51 mm, a dielectric constant \(\varepsilon_{\mathrm{r}}\) = 3 (stable up to W-band frequencies), and a loss tangent tan(\(\delta\)) = 0.0017 [16]. The microstrip transmission line is fed at the bottom side of a Rogers RT 6010 LM substrate with a thickness of h = 0.64 mm, dielectric constant \(\varepsilon_{\mathrm{r}}\) = 10.2, and a loss tangent tan(\(\delta\)) = 0.0023 at 10 GHz [17]. The patch is excited via a rectangular slot placed in the ground, sandwiched between the two substrates. The maximum amount of power coupled from the rectangular slot to the patch element is determined by the higher-permittivity feed substrate and the positioning of the rectangular slot. The circular polarization was generated by introducing slots and cuts at 45\({}^{\circ}\) exciting two orthogonal modes with equal magnitude and 90\({}^{\circ}\) phase shift. The patch design offering an axial ratio AR \(<\) 3 dB at f = 3.5 GHz is shown in Figure 1. The proposed dimensions indicated in this figure were optimized with respect to the simulated \(-\)10 dB impedance bandwidth B\({}_{\mathrm{match}}\) = 62 MHz and the axial ratio AR = 1.4 dB at f = 3.5 GHz, as can be seen in Figure 2.  
For the 2 \(\times\) 2 CP antenna array, a sequentially rotated phase feeding configuration was employed as shown in Figure 3a, in order to achieve a good CP performance across the desired frequency range. Port #1 marks the feed input, while ports #2 to #5 represent the power-balanced antenna feeds with incremental phase delay of 90\({}^{\circ}\), connected to respective patch elements. The elements L\({}_{1}\) to L\({}_{7}\) represent quarter-wave impedance transformers in which L\({}_{2}\), L\({}_{4}\), and L\({}_{6}\) provide the impedance transformation between the junction points of the circular section of the phase feed. Figure 3b depicts the simulated S-parameters where the \(\left|S_{11}\right|^{2}\) values stay well below \(-\)10 dB over the entire n78-band. Moreover, the optimal transmission parameters \(\left|S_{11}\right|^{2}\) (i = 2, 3, 4, 5) are close to \(-\)6 dB, ensuring that the input power is evenly distributed to each port. Figure 3c confirms the progressive phase difference of approximately 90\({}^{\circ}\) between the adjacent ports. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **NTN** & **Unit** \\ \hline Frequency band \(\Delta\)f & n78 (3.3 \(\ldots\) 3.8) & n257 (26.5 \(\ldots\) 29.5) & GHz \\ Frequency f & 3.5 & 28 & GHz \\ Operational bandwidth B\({}_{\mathrm{op}}\) & 100 & 400 & MHz \\ Polarization purity & \multicolumn{2}{c}{AR \(<\) 3} & dB \\ Co-elevation coverage \(\Theta_{\mathrm{UE}}\) & \multicolumn{2}{c}{\(-\)30 \(\ldots\) +30} & \({}^{\circ}\) \\ Azimuth coverage \(\Phi_{\mathrm{UE}}\) & \multicolumn{2}{c}{0 \(\ldots\) 360} & \({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: UE antenna performance requirements. Figure 1: Single CP square patch antenna element. The single element was then extended to a low-profile, easy-to-integrate \(2\times 2\) aperture-coupled array as visualized in Figure 4a. The radiating patch is placed on the Isola Astra\({}^{\circ}\) MT77 substrate and the phase feed is printed on the bottom of the Rogers RT 6010 LM substrate. The rectangular coupling apertures from the feed (port 2... 4) to the patch  
Figure 3: (**a**) Sequentially rotated phase feed network topology, (**b**) simulated S-parameters \(|\,\mathrm{S_{11}}\,|^{2}\) (i = 1... 5), (**c**) phase difference in signals between consecutive output ports. Figure 2: (**a**) Simulated frequency dependence of the input reflection coefficient \(|\,\mathrm{S_{11}}(\mathrm{f})\,|^{2}\), (**b**) simulated axial ratio AR(f) versus frequency.