## 4 Simulation and Measurements Results
### Results for the 3.5 GHz Array  
The impedance matching of the bare simulated (red curves), bare measured (blue), and embedded measured versions (green) across the entire n78-band are compared in Figure 7a. The \(\left|\,\mathrm{S}_{11}\,\right|^{2}\) data for the embedded state follow the simulated trend but with smoothened ripple due to additional conductor losses. The operational bandwidth of \(\Delta\mathrm{f}_{\mathrm{op}}\approx 100\) MHz around f = 3.5 GHz is covered with a favorable input matching of \(\left|\,\mathrm{S}_{11}\,\right|^{2}\)\(<-10\) dB for the bare simulated version, and while the matching level degraded to the still acceptable level \(\left|\,\mathrm{S}_{11}\,\right|^{2}\)\(<-6\) dB for the bare measured version in the same bandwidth. The measurement in the embedded state covered \(\left|\,\mathrm{S}_{11}\,\right|^{2}\)\(<-6\) dB over a bandwidth of 160 MHz, most likely reflecting the additional attenuation caused by the rear spoiler material. The frequency variation of the axial ratio is shown in Figure 7b, which confirms a favorable polarization symmetry with AR \(<3\) dB around f = 3.5 GHz for all three data sets. The embedded array exhibits a 3-dB axial ratio bandwidth \(\mathrm{B}_{\mathrm{AR}}\approx 100\) MHz. The angular variation of the axial ratio is shown in Figure 7c, indicating an elevation range \(\Theta\) from \(-40^{\circ}\) to \(+30^{\circ}\) where AR \(<3\) dB for the bare simulated version. These elevation ranges shifted for the measured bare and embedded versions to \(\Theta=-45^{\circ}\)\(\ldots\)\(+50^{\circ}\) and \(\Theta=-50^{\circ}\)\(\ldots\)\(+25^{\circ}\),respectively. All angular ranges cover the 3- dB beamwidth \(\Theta_{\mathrm{UE}}=\pm 30^{\circ}\) of the proposed embedded array and appear feasible for the intended applications. The simulated realized gain and the radiation efficiency of the array were found to be \(\mathrm{G}_{\mathrm{Uesim}}=9\) dBi and \(\mathrm{\eta}_{\mathrm{sim}}=74\%\), respectively. The radiation efficiency decreased slightly to \(\mathrm{\eta}_{\mathrm{meas}}=59\%\) for the measurement of the bare antenna, associated with the reduced gain of \(\mathrm{G}_{\mathrm{Uemeas}}=8.8\) dBi. The radiation patterns are displayed in Figure 7d,e for the three 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 shifted towards \(0^{\circ}\) and a side lobe developed in the direction of excitation for \(\Phi=0^{\circ}\). Upon embedding, apparently, the plastic material covering the patch elements deteriorates  
Figure 6: (**a**) Antenna measurement setup in bare condition, (**b**) measurement setup in rear spoiler. the radiation performance of the antenna array, e.g., through degrading the symmetry and affecting the phase balance between the elements. In addition, the realized gain of the embedded array increased by 1 dB to \(\mathrm{G_{emb}}\) = 9.9 dBi in comparison to the measured bare antenna array as the embedded measured directivity is 1.5 dB higher than simulated array. The embedded array offers a 3-dB beamwidth of \(\mathrm{\Theta_{UE}}=-30^{\circ}\)\(\ldots\) +15\({}^{\circ}\) and an impedance bandwidth \(\mathrm{B_{emb}}\approx\) 160 MHz due to an increase in the overall thickness of the assembly. Figure 7: (**a**) Input reflection coefficients 1S\({}_{11}\)12 for the bare simulated (red-colored curve), bare measured (blue) and embedded measured (green) antenna array, (**b**) axial ratio versus frequency along zenith, \(\mathrm{\Theta}\) = 0\({}^{\circ}\), (**c**) axial ratio versus co-elevation at f = 3.5 GHz, (**d**) vertical cut of normalized realized gain at f = 3.5 GHz for \(\mathrm{\Phi}\) = 0\({}^{\circ}\) and (**e**) for \(\mathrm{\Phi}\) = 90\({}^{\circ}\) (same color coding as in panel a). All simulated and measured results are summarized in Table 4. The data rate was calculated according to Section 2.