## 2 Antenna Array Specifications Based on Link Budget for LEO Connectivity  
The aim of this study is to design an antenna capable of delivering broadband internet access which, according to the U.S. Federal Communication Commission (FCC)'s definition, is \(DR_{DL}\) = 25 Mbps for download and \(DR_{UL}\) \(\geq\) 3 Mbps for upload [12]. The antenna gain \(G\) needed to meet this target is derived from the carrier-to-noise ratio (C/N) at the receiver input. The C/N is represented by Equation (1) [13] and depends on the chosen modulation and coding scheme, channel bandwidth (\(CBW\)), and the desired data rate (\(DR\)). \[\left[\frac{C}{N}\right]_{dB}=\frac{E_{b}}{N_{0}}+CBW-DR \tag{1}\]  
Typical satellite communications use digital video broadcast (DVB-S2) standards for broadcast, and this is assumed as the communication standard for LEO connectivity in this section. There are several modulation and coding schemes available for DVB-S2 systems, and the most common, 16 APSK 2/3, is considered based on the specifications of existing modems available for the application [14; 15; 16]. This scheme requires an energy per bit of \(E_{b}\)/\(N_{0}\) = 4.76 dB [17]. The channel bandwidth is taken to be \(CBW\) = 10 MHz. Substituting these values into Equation (1), we obtain C/N = 8.74 dB. This C/N value can be used to calculate the required antenna quality factor \(G\)/\(T\) as per the link budget in Equation (2) [17]. \[\left[\frac{G}{T}\right]_{dB}=FSPL+L_{atm}+K+RBW-EIRP-\frac{C}{N} \tag{2}\]  
Table 1 lists the parameters involved in the calculation of the link budget. The dominant contribution is the free-space path loss (\(FSPL\)), which depends on the orbital distance \(d\) and the frequency \(f\) of the signal. The values for \(d\) and the satellite's effective isotropic radiated power (\(EIRP\)) in Table 1 are derived from the specifications of the three major LEO  
constellations, namely SpaceX, OneWeb, and Telesat [16]. Further significant contributions result from atmospheric losses (\(L_{atm}\)) and the system's noise temperature (\(T_{sys}\)). As the Ku-band frequencies are in a range at \(f>\) 10 GHz, they are subject to attenuation due to atmospheric effects like cloud, rain, fog, and atmospheric gases, which are accumulated in \(L_{atm}\)[17]. The link should be established even under heavy-rain conditions; in other words, at 99.99% availability. Accordingly, a value of \(L_{atm}\) = 5 dB [18] was chosen. For an antenna looking at a cold sky during satellite reception, the antenna noise temperature was set to \(T_{att}\) = 20 K [19]. The other contributions are calculated from the noise figure of the RF chain based on typical frontend IC specifications [20]. For a noise figure of \(F\) = 3 dB, the effective noise temperature, as per Equation (3), [18] results in \(T_{FE}\) = 294 K.  
\[T_{FE}=295\cdot\left(10^{\frac{F}{10}}-1\right) \tag{3}\]  
Combining these temperatures as per Equation (4) [18] results in \(T_{sys}\) = 314 K as the system noise temperature. \[T_{sys}=T_{att}+T_{FE} \tag{4}\]  
Substituting this value in Equation (2) and additionally taking into account the scan loss through the roll-off factor\(f_{ro}\) = 0.1 [16] yields the required realized gain, \(G\) = 27.4 dBi. The downlink gain and data rate scale with the number of antenna elements, as summarized in Figure 1, assuming that a single patch antenna provides a realized gain of \(G_{SE}\) = 6 dBi. In a dual-band (uplink + downlink) antenna design, the number of antenna elements needed in an array is determined by the higher of the uplink/downlink data rate requirements. As \(DR_{DL}\) = 25 Mbps is needed in the downlink but only \(DR_{UL}\) = 3 Mbps is needed in the uplink, fulfilling the downlink data rate requirement would automatically satisfy the uplink requirements. This, however, corresponds to an array with 12 \(\times\) 12 = 144 antenna elements and for the half-wavelength element distance, a footprint of 6 \(\lambda\) \(\times\) 6 \(\lambda\) = 36 \(\lambda^{2}\), which would be too large for automotive applications.