## 1 Introduction  
Global navigation satellite system (GNSS) in space applications started to be investigated in the mid to late 1970s, while in 1982 the first spacecraft flew with an onboard spaceborne receiver [1]. Since then, the use of GNSS at low earth orbit (LEO) has been successfully adopted, favored by the strong signal powers and the good relative geometry that a receiver at these altitudes experiences. Moreover, the great benefits of GNSS-based navigation over conventional ground-based methods, such as increased spacecraft's autonomy and reduced operational costs, as well as the will to improve the achieved accuracy, motivated the investigation of global positioning system (GPS) at higher altitudes, leading to the first recordings beyond LEO in 1997. The eagerness to exploit GNSS signals at higher orbits has increased in recent years, keeping in mind new innovations such as improved weather prediction, exploration moon missions and beyond, formation flying, etc. Although space users showed great enthusiasm for GNSS-based navigation, they had to face important difficulties compared to earth users. Indeed, primarily intended for earth navigation, initial GPS system specifications (such as minimum received power level and availability) covered only earth users or up to 14\({}^{\circ}\) half angle of the transmitters' antenna [1]. Due to the great utility for space users above 14\({}^{\circ}\) and the significant changes between the different blocks, space users wanted formal specifications to be included. Efforts to include space service volume (SSV) did not start until the 1990s and it was in February 2000 when space requirements were officially included. However, this was not enough, and further improvements were needed. GPS III included new space requirements: (1) SSV was further subdivided in two regions, medium earth orbit space service volume (MEO SSV) (3000-8000 km) and geostationary earth orbit/high earth orbit space service volume (GEO/HEO SSV) (8000-36,000 km) and (2) specified worst case signal strength and availability. Even though it is clear that processing signals from the side lobes can significantly improve the availability (and the receiver/transmitters geometry) in GEO/HEO, so far, for many GNSS signals and GNSS satellites blocks, detailed specifications of the transmitters' side lobes have not been yet explicitly stated. As stated in [2], \"Protection of GPS Side Lobes through Specification is critically important to 'Do No Harm' to current and future users of SSV\". Under these circumstances, a GPS receiver in GEO/HEO should be able to process signals transmitted from the side lobes of the GPS antenna patterns. The lower power levels that these signals have, compared to the ones transmitted from the main lobe, affect the range accuracy with higher receiver noise. Moreover, if the receiver's sensitivity is not high enough, the availability of GNSS signals can be drastically lower, with a consequent worsening of the geometric dilution of position (GDOP), or in the worst case preventing the computation of the navigation solution, for which at least four observations are needed. In this context, in order to correctly simulate the GNSS-based navigation performance of a spaceborne receiver, the assumptions on the GNSS antenna patterns are very important and delicate, especially on the side lobes. The main lobe is well known and no assumptions are needed. Figures 1 and 2 show, respectively, the angle from the antenna boresight at which the signals are transmitted by the GPS satellites (for each pseudo random noise (PRN)) and the number of signals that have been transmitted from the main lobe or the side lobes, for a direct moon transfer orbit (MTO), presented in Section 2. As can be observed, in the case of space users operating in all SSV and up to the Moon, most of the signals would be acquired and tracked from the side lobes.