# LCNS Positioning of a Lunar Surface Rover Using a DEM-Based Altitude Constraint
## 3 Moonlight and LCNS
### Rover LCNS Receiver  
In line with previous works [29; 32], the lunar surface rover will be equipped with a LCNS receiver, which can be modelled similarly to a space-borne GNSS receiver. Such a receiver is comprised of a radio frequency front-end (RFFE) and digital parts for signal processing. The main difference with respect to a GNSS receiver will be the change of carrier frequency from the L-band to S-band; the rest will be almost identical. The carrier-to-noise-density ratio (\(C/N_{0}\)) as seen by the receiver is modelled using Equation (1) [35]. The \(EIRP\) is defined above and set to 15.02 dBW at boresight, \(L_{p}\) represents the free space loss, \(L_{q}\) the atmospheric losses (which should be negligible in case of the Moon), \(g_{r}\) represents the receiver gain (as shown in Figure 5), \(k\) represents Boltzmann's constant and \(T_{eq}\) represents the equivalent noise temperature (which is defined in Table 3). \[C/N_{0}=\frac{(EIRP)L_{p}L_{a}g_{r}}{kT_{eq}} \tag{1}\]  
The receiver is expected to rely on state-of-the-art tracking techniques using a DLL (delay locked loop) and PLL (phase locked loop). Within the simulation environment used in this contribution. a hard acquisition and a \(C/N_{0}\) (carrier-to-noise density ratio) tracking threshold at 30 dB-Hz was selected (in line with [29]). Any signal with a \(C/N_{0}\) below this threshold was considered not acquired nor tracked. This is an arbitrary decision that will be revisited as part of Phase A/B1 and that drives the overall link budget and \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element** & **Parameter** & **Value** \\ \hline Signal Carrier & Carrier Frequency (\(f_{S}\)) & 2491.005 MHz \\  & Carrier Wavelength (\(\lambda_{S}\)) & 12.04 cm \\ \hline Signal Modulation & Chipping Frequency (\(f_{C}\)) & BPSK(5) \\  & Chip Length (\(\lambda_{C}\)) & 58.61 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of the proposed LCNS signal. Figure 4: Antenna pattern of the LCNS satellites. payload EIRP. For the scope of this publication, the threshold is considered achievable with current state-of-the-art technology at the user level assuming the receiver implements high-sensitivity techniques to allow the tracking of a BPSK(5)-like signal below 32 dB-Hz [36]. This assumption is expected to have limited impact on the attainable positioning accuracy, as the measurement accuracy is mostly driven by the orbit determination and time synchronization (ODTS) accuracy. However, it may impact the number of satellites that are available for positioning. Furthermore, the RFFE noise figure has been set to 1 dB, which should be in line with state-of-the-art products for space applications [29]. Finally, the noise temperature is set to 113 K (based on an internal ESA assessment; this value will be re-assessed in future publications) and the LNA (low noise amplifier) gain to 30 dB. All receiver parameters are summarized in Table 3.  
The antenna of the rover is assumed to be pointing in the zenith direction (i.e., upwards). This assumes an ideal case when the rover moves on a flat surface. In reality, the direction the antenna points will vary with the slope of the local terrain. The impact of this assumption, however, is considered small (i.e., note a gain variation of 1 dB in Figure 5 between the zenith and an off-boresight angle of 20 degrees). The receiver antenna is assumed to be symmetric in the azimuth, and the elevation pattern is visualized in Figure 5, which is considered representative of what is currently available on the market for space-borne GNSS antennas. Similar performances are achievable in the S-band. No elevation mask is implemented; however, lunar terrain in the vicinity of the traverse (refer to Section 2) was considered to evaluate the impact of the local topography on the visibility between the rover and the LCNS satellites. The navigation system of the LCNS receiver will be complemented by an inertial measurement unit (IMU).