## 2 Mission Scenario and Requirements of the Antenna System  
The main specifications of the cellular coverage, shown in Table 1, have been established from those of current multibeam satellites in Ka-band [2; 3; 11; 12] and the Rec. ITU-R S.672-4 [13]. The coverage must be formed by around 100 spots in a triangular lattice,  
Figure 1: Example of a four-color multispot coverage. (**a**) Hexagonal service cells working in four different colors. (**b**) Hexagonal cells covered by circular beams generated in two orthogonal polarizations (P1, P2) and two frequencies (F1, F2). (**c**) Example of a European four-color coverage that would be generated by a geostationary satellite.  
generated with a four-color reuse scheme based on two different frequencies and two orthogonal CP. The four-color coverage must be simultaneously generated at Tx and Rx user frequencies in Ka-band, which comprise from 19.2 to 20.2 GHz for Tx and from 29.0 to 30.0 GHz for Rx. Thus, both Tx and Rx frequency bands must be divided into two sub-bands to provide the four-color coverage with two orthogonal CP simultaneously in Tx and Rx. Figure 2 shows a schematic representation of a multispot coverage with a four-color reuse scheme of two frequencies (F1, F2) and two polarizations (P1, P2) together with the operating scheme of the current multi-fed reflectors used onboard the satellite, where each reflector generates a lattice of non-contiguous spots in a single color, simultaneously in Tx and Rx (the interlaced beams produced by the four reflectors form the final four-color coverage of contiguous spots). The diameter of the spots is set to 0.65\({}^{\circ}\) to cover a circular area of around 300 km on the Earth. The angular separation between adjacent spots from center to center to form the appropriate triangular lattice of spots must be 0.56\({}^{\circ}\) (computed as sin(60\({}^{\circ}\))\(\cdot\)0.65\({}^{\circ}\)). The minimum end of coverage (EOC) gain of the beams is set to 45 dBi, the minimum single-entry carrier over interference ratio (C/I) at 20 dB, and the minimum co-polar over cross-polar discrimination (XPD) is also fixed to 20 dB.  
The proposed antenna configurations operate by an improved SFPB configuration, taking advantage of the ability of reflectarrays to generate independent beams at different frequencies [14] or polarizations [15] with a single feed. The proposed reflectarrays will be illuminated by a cluster of 27 feeds defined with a triangular lattice, in order to provide the required multibeam coverage with a triangular grid of spots. The feeds have been modelled considering the 54 mm Ka-band feed-chain reported in [4], thus the separation between adjacent feeds has been set to 55 mm. The radiation pattern of the feeds has been  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Requirement** \\ \hline Number of spots & 100 \\ Reuse scheme & 4 colors \\ Spot lattice & Triangular \\ Spot diameter & 0.65\({}^{\circ}\) \\ Spot separation & 0.56\({}^{\circ}\) \\ EOC gain & 45 dBi \\ Single-entry C/I & 20 dB \\ XPD & 20 dB \\ Tx frequency band & 19.2–20.2 GHz \\ Rx frequency band & 29.0–30.0 GHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Antenna system requirements.  
Figure 2: (a) Four-color multispot coverage required simultaneously in Tx and Rx. (b) Operating principle of current reflectors used onboard the satellite, operating simultaneously in Tx and Rx.  
modelled in the simulations by an ideal cos\({}^{\text{q}}(\theta)\) distribution. Figure 3 shows the proposed cluster of 27 feeds using the local coordinate system (x\({}_{\text{f}}\), y\({}_{\text{f}}\)), the origin of which matches the center of the aperture of the central feed (C3 in Figure 3). The symmetry of each antenna configuration will be used to reduce the number of feeds considered in simulations (the lines of feeds A, B, C, plotted with thicker lines, or the array of 3x5 feeds plotted with solid lines in Figure 3).