## 3 Proposed Antenna
### Measurement Results with and without the Superstrate  
The antenna was manufactured and assembled as in Figure 3a and set up in a shielded anechoic chamber, as shown in Figure 3b, for measurements. Figure 4 compares the measured and simulated S-parameters for the single element without the superstrate. Since the S-parameters of the design with the superstrate were very similar, in accordance with expectations, they were omitted for clarity. The measured \(\mid\)\(S_{22}\)\(\mid\)\({}^{2}\) (\(f\)) -curves in the DL band were shifted by 500 MHz to lower the frequencies compared to the simulations, whereas the simulated and measured \(\mid\)\(S_{11}\)\(\mid\)\({}^{2}\) (\(f\))-data follow similar trends. In general, these differences are due to the differences between the idealized and real en  
Figure 2: (a) Exploded view of the single antenna element; (b) side-view; (c) side-view of the single antenna element with the superstrate. vironments, for example, the simulations were performed in a free-space environment which did not take into account the presence of antenna probes and positioning equipment. There are also the manufacturing and assembly tolerances of the antenna's geometry and the substrate's properties. The shift in the \(\left|\,S_{22}\,\right|^{2}\left\langle f\right\rangle\) -curves does not, however, influence the measured gain to the extent that the data rate and gain bandwidth are affected. The transmission coefficient was \(\left|\,S_{12}\,\right|^{2}<-20\) dB over the entire frequency range, which is in good agreement with the numerical simulations and indicative of good port isolation. The fractional bandwidth requirements of 15 % in downlink and 4% in uplink for LEO satellite connectivity were fulfilled and validated by the measurements. From the measured gain curves in Figure 5a, it is clearly visible that the superstrate yields a \(3\ldots 6\) dB gain improvement across the entire DL-band. There is, however, a shift in the measured gain enhancement compared to the simulations. This shift is attributed to the variations in the dielectric permittivity of the inhomogeneous medium comprised of the air gap and the superstrate; as for the experiments, the superstrate was fixed using four screws above the antenna element. For the final application, these manufacturing anomalies need  
Figure 3: (**a**) Assembly of the single antenna element; (**b**) setup of the antenna for spherical far-field measurements in the shielded anechoic chamber at TU Ilmenau. to be compensated for to achieve a properly matched antenna. While the improvement in the UL-band was around 2 dB, this is still quite an acceptable performance in view of the significantly relaxed data rate requirement for uplink compared to downlink. Moving on to Figure 5b,c, the polarization purity was studied by comparing the right-hand circularly polarized (RHCP) and left-hand circularly polarized (LHCP) gain values and the axial ratio (AR) of the main beam at boresight. Over the frequency bands of interest, the RHCP gain was higher than the LHCP gain by \(8\ldots 10\) dB, and the measured axial ratio was below 5 dB. The lower axial ratio value observed in the measurements compared to the simulated data is the result of shadowing from the positioner. This leads to a weakening of the LHCP beam with respect to the RHCP beam in the boresight. Figure 4: Reflection and transmission coefficients of the single antenna element for input and output matching (top) and isolation (bottom). Figure 5: _Cont._  
In Figure 6a-d, the elevation cuts of the normalized RHCP gain are plotted for the downlink frequency \(f=11\) GHz and show very good agreement between the simulations and the measurements. The antenna performance at the uplink frequency \(f=14\) GHz is presented in Figure 7a-d.