## 4 Simulation and Measurements Results
### Results for the 28 GHz Array  
The impedance matching of the simulated and measured bare and embedded version across the entire n257-band is depicted in Figure 8a. The bare and embedded minimum \(1S_{11}\)\({}^{2}\) values shifted slightly by 0.3 GHz to a lower frequency of 29.3 GHz compared to the simulations, while staying well below \(-\)10 dB. The manufactured array dimensions were measured with an optical profilometer with a measurement uncertainty below 1 \(\upmu\)m, revealing deviations of 2% from the design parameters, which are considered negligible. The frequency shift, which is often observed in similar studies, is hence associated with variations of the dielectric permittivity. The back side of the embedded patch array remained exposed to the free space as depicted in Figure 5d, and displayed almost the same resonant frequency as the bare version. The frequency variation of the axial ratio is shown in Figure 8b, achieving AR < 3 dB around f = 28 GHz for all three data sets. The embedded array exhibits a wide 3-dB axial ratio bandwidth \(\mathrm{B_{AR}}\approx 1500\) MHz. The angular variation of the axial ratio is shown in Figure 8c, indicating an elevation range from \(\Theta=-18^{\circ}\ldots+15^{\circ}\) with AR < 3 dB for the bare measured version, which slightly shifted to \(\Theta\) = \(-11^{\circ}\ldots+17^{\circ}\) for embedded version. The simulated realized gain and radiation efficiency of the array amounted to \(\mathrm{G_{UESim}}\) = 15.4 dBi and \(\mathrm{\eta_{sim}}\) = 85%, respectively. The radiation efficiency decreased to \(\mathrm{\eta_{meas}}\) = 60% for the measured bare antenna, associated with a lower gain of \(\mathrm{G_{UESES}}\) = 14 dBi. The radiation patterns are shown in Figure 8d,e for the three assembly versions. The normalized vertical cuts at \(\Phi\) = 0\({}^{\circ}\) and 90\({}^{\circ}\) of the simulated and measured antenna in its bare state agree well with each other, while the pattern measured for the embedded array displays more pronounced ripples, in agreement with the findings for the lower frequency. In addition to the impact of dielectric embedding, adverse effects may result from the transition from the coaxial feed cable to the microstrip feed line. As a consequence, the realized gain of the embedded array decreased by 0.3 dB to \(\mathrm{G_{emb}}\) = 13.7 dBi in comparison to the measured bare antenna array. Thus, the radiation efficiency is decreased to \(\mathrm{\eta_{meas}}\) = 56% for the measured embedded antenna, associated with a lower gain of \(\mathrm{G_{UESES}}\) = 13.7 dBi. The embedded array offers a 3-dB beamwidth of \(\mathrm{\Theta_{UES}}\) = \(\pm\)12\({}^{\circ}\) and an impedance bandwidth \(\mathrm{B_{emb}}\) > 4 GHz due to an increase in the overall thickness of the assembly. All simulated and measured results are summarized in Table 5. An uplink data rate of \(\mathrm{D_{UL}}\) = 7 Mbit/s is anticipated for the measured free-space n257-band 4 \(\times\) 4 circular patch antenna array. This value decreases to 6 Mbit/s for the embedded array due to the lower realized gain which, however, is still favorably suitable for the intended applications. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Bare Antenna**} & \multicolumn{2}{c}{**Embedded Antenna**} \\ \cline{2-4}  & **Simulated** & **Measured** & **Measured** \\ \hline Input reflection \(1S_{11}\)\({}^{2}\) (dB) & \(-18\) & \(-11\) & \(-9\) \\ Realized gain G (dBi) & 9 & 8.9 & 9.9 \\
6-dB bandwidth \(\mathrm{B_{-6}}\) (GHz) & 210 & 110 & 160 \\ Radiation efficiency n (\%) & 74 & 59 & 67 \\
3-dB axial ratio bandwidth & 30 & 80 & 100 \\ \(\mathrm{B_{AR}}\) (GHz) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of simulated and measured results of bare and embedded n78-band array. To address the advantages of the proposed UE antenna array, the performance comparison is tabulated in Table 6. In [21], the hybrid design of the slot and DRA is employed to realize dual-band circularly polarized function.