## 2 Scenario and Requirements: Communications On The Move (COTM)  
In the following, a COTM scenario is described. In Figure 1, an example depicting in-flight connectivity scenario is shown, with an antenna mounted on an aircraft fuselage. When dealing with COTM applications, the antenna is subjected to high scan angles. In the case of aircraft applications, when the flight route is close to the poles and GEO is used, high steering angles are needed for ensuring a stable connectivity with the satellite above the equator. However, usually the performance drops when the steering is outside the range of \(\pm 60^{\circ}\)[1].  
With respect to the sketch in Figure 1, in (a), the antenna is able to catch signals from LEO and GEO satellites. However, during the aircraft's turn, both satellites disappear from the antenna's FoV. In the case of LEO, a handover to another satellite in the FoV is required, while GEO remains outside the FoV.  
Usually, the antenna's FoV refers to the range of angles within which the carrier-to-noise-ratio \(C/N\) allows for a reliable and robust communication [30]. In this work, the FoV is computed by considering a scan loss of 3 dB and an axial ratio of \(<\)3 dB (with a tolerance of 0.5 dB). The choice to include the axial ratio in the FoV calculation is motivated by the prevalent use of circular polarization in satcom. When the axial ratio exceeds the set threshold, both the circular polarized component and the overall \(C/N\) suffer degradation. Additionally, selecting a directivity scan loss of 3 dB outperforms the conventional ideal \(\cos\theta\) roll-off, ensuring satisfactory \(C/N\) values overall.  
In the following, the definition of requirements and the reference planar array architecture are first presented.  
The requirements for the array are listed in Table 1. A directivity of 40 dBiC is desirable, with a scan range of \(\pm\)70\({}^{\circ}\). As previously stated, the FoV is computed considering a maximum directivity scan loss of 3 dB, which outperforms the traditional \(\cos\theta\) gain roll-off. Moreover, an axial ratio of \(<\)3 dB is also required, with a tolerance of 0.5 dB.  
A planar array composed of 60 \(\times\) 60 elements spaced at \(\lambda/2\) is considered as reference, achieving a directivity of 42.3 dBiC. It is presented in Section 4. To enhance the FoV of the reference planar phased array architecture, 3D geometries are explored and simplified by faceting the conformal architecture. Indeed, given a 3D surface, its total surface area \(\mathcal{S}\) can be expressed as \(\mathcal{S}=\sum_{n=1}^{N_{f}}\mathcal{F}_{n}\), where \(\mathcal{F}\) denotes the discretization of the surface via facets and \(N_{f}\) denotes the total number of facets. In an ideal hemisphere, \(N_{f}\rightarrow\infty\) and \(\mathcal{F}_{n=1,\ldots,N_{f}}\to 0\). To find a suitable 3D architecture that can be easily manufactured, a trade-off analysis is conducted, minimizing the number of facets \(N_{f}\). This way, the 3D architecture can be easily manufactured using planar PCBs (the facets).  
In the next Section, directivity and axial ratio are considered to estimate the total FoV, and their computation for different 3D array geometries is explained.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Figure of Merit** & **Value** \\ \hline Directivity, \(D(\theta,\varphi)_{max}\) & \(\approx\)40 dBC \\ \hline Axial Ratio, \(AR(\theta,\varphi)_{max}\) & \(<\)3 dB (tolerance 0.5 dB) \\ \hline Scan Range & \(>\)\(\pm\)70\({}^{\circ}\) \\ \hline Maximum Directivity Scan Loss & 3 dB \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the main requirements.  
Figure 1: Pictorial representation of a satcom terminal suffering from limited FoV in mobility applications: (**a**) the satellite is within the FoV of the satcom terminal, (**b**) the satcom terminal loses connectivity with the established satellite while in motion, requiring a handover to another satellite.