# Acquisition of Weak BDS Signal in the Lunar Environment
## 1 Introduction  
The Global Navigation Satellite System (GNSS) was originally designed to provide positioning, navigation, and timing (PVT) services to ground-based users and low-orbiting spacecraft. When a vehicle orbits at an altitude higher than that of GNSS satellites, nadir antennae can be used to receive unobscured GNSS side lobe signals from the other side of the Earth [1]. Although these signals are quite weak, as the transmitting antenna gain of the side lobe tends to be about 10-15 dB lower than the main lobe, these signals have proven to be usable [2; 3; 4; 5]. The concept of space service volume (SSV) was introduced early in this century as a standard for describing the service performance of the Global Positioning System (GPS) in space applications from 3000 to 36,000 km above the Earth's surface (geostationary orbit altitude, GEO) [6]. Moreover, a new definition of SSV for GNSS has been proposed in terms of the four parameters of minimum received power, satellite visibility, pseudorange accuracy, and geometric dilution of precision (GDOP) [2]. The first GPS experiment on the highly elliptical orbit (HEO) mission Equator-S [7] successfully tracked a GPS satellite at an altitude of about 34,000 kilometers, demonstrating that it is possible to receive signals from the sidelobes emitted by transmitter antennae. Based on data from the No.2 telecommunication technology test satellite (TJS-2), [PERSON] et al. [8] analyzed the application of GPS in determining geostationary orbits and explained some systematic errors in code observations by analyzing multipath effects. Results from the Geostationary Operational Environmental Satellite-R (GOES-R) Series and the Magnetospheric Multiscale (MMS) mission conducted by National Aeronautics and Space Administration (NASA) show that the side lobe signals constitute the bulkof the received signals and can be used effectively for spacecraft navigation [9; 10]. It is worth noting that the MMS mission broke the record for navigating a spacecraft using Global Positioning System (GPS) signals at a distance of 187,166 km from Earth, about half the distance to the Moon. With the development of multiple GNSS constellations and the continuous upgrading of existing navigation constellations, multi-constellation and multi-frequency GNSS technologies have significantly improved signal availability [2; 11]. The No.5 telecommunication technology test satellite (TJS-5) [12], launched by China in 2020, carries an upgraded, highly sensitive receiver capable of tracking single-frequency signals from GPS and second and third generation Beidou Navigation Satellite System (BDS) satellites. This is the first geosynchronous orbit mission to track the second and third generation BDS satellites since the global deployment of BDS-3. Numerous studies have been conducted on the use of GNSS signals in moon transfer orbit (MTO) or lunar orbit. [PERSON] et al. [13] studied the accessibility results using only GPS receivers in lunar near-rectilinear halo orbit (NRHO), exploring the potential use of GPS in lunar navigation. [PERSON] et al. [10] explored the tracking results of GPS signals by simulating the performance of the MMS navigation system, with a simulated trans-lunar trajectory and an NRHO, which are typically of interest in lunar exploration missions. Chinese lunar experimental mission Chang'e-5T is equipped with an onboard high-sensitivity receiver with GPS tracking capabilities, acquiring an average of 7-8 GPS satellites per epoch, with 90% of observations above 28 dB-Hz [14]. A detailed exploration of the navigation performance for GEO, HEO, and Lunar trajectory using multi-GNSS side lobe signals is suggested in the literature [5; 15]. For more related research, refer to [16; 17; 18]. However, the use of GNSS receivers in lunar missions still faces significant challenges. To cope with the problems such as ultra-low signal power due to free space loss and large rates of Doppler shift, high-sensitivity receivers were designed to achieve autonomous GNSS navigation for lunar orbiting satellites.