# A Novel Satellite PRN Code Assignment Method Based on Improved RLF Algorithm
On the one hand, it is difficult to design thousands of PRN codes with good autocorrelation properties and high cross correlation properties. This design requires the different PRN codes for each LEO satellite to be nearly orthogonal, which is very difficult for 1023-chip C/A-code to design hundreds or thousands of PRN codes. On the other hand, if there are thousands of PRN codes, the navigation signal receiver needs more time to search and more storage resources to store PRN codes during satellite acquisition, which is not feasible for small and medium-sized receivers. If the number of PRN codes can be reduced, the burden on the receiver and PRN code design may be greatly reduced. However, at present, scholars' research focuses on modulation methods in the LEO navigation signal field. The phase-coded linear chirp signal is designed by Harshal AR [28], which is immune to Doppler frequency offset and reduces multiple access interference. [PERSON] et al. [29] design a chip level pulse quasicontinuous navigation signal, which is compatible with GNSS. [PERSON] et al. [30] propose A universal modulation scheme based on the continuous phase modulation (CPM) family. There is little research on PRN design or assignment of LEO navigation signals. In order to reduce the number of PRN codes and burden on the navigation receiver, we propose a new method where several satellites share the same PRN code. Obviously, the new method can bring benefits to the navigation signal receiver and PRN code design. However, it may make it difficult for users to distinguish the satellite that the signal is being broadcast from. If the same user cannot simultaneously observe signals from satellites sharing the same PRN code at any time, each PRN code will be used, at most, once within the user's visual range, and users will be easily able to distinguish satellite signals. Therefore, we need to design a grouping scheme for satellites so that the same user on the ground cannot simultaneously observe the same PRN code at any time. As shown in previous studies, each LEO satellite in a constellation has a unique PRN code in a LEO-based navigation signal augmentation system. In this study, for the first time, we group the LEO satellites so that several satellites can share the same PRN code. The benefits for the acquisition of receiver are analyzed. This paper is organized as follows: In Section 2, we demonstrate the feasibility and benefits of this method and provide the mathematical model and calculation process used for the minimum shared PRN codes. To evaluate the performance of six common algorithms for this problem, we design 6 LEO constellations with different satellite numbers, orbital altitudes, and types of orbits, and group satellites using these six algorithms. We show that the RLF algorithm performs best, and this is introduced and improved in Section 3. Afterwards, in Section 4, we take the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Constellation** & **Country** & **No. Satellites** & **Altitude (km)** & **Inclination (deg)** & **Year** \\ \hline \hline Iridium [10] & USA & 66 & 781 & 86.4 & 1998 \\ \hline Globalstar [21] & USA & 48 & 1400 & 52 & 2000 \\ \hline Iridium NEXT [22] & USA & 75 & 780 & 86.4 & 2019 \\ \hline LeoSat [23] & USA & 108 & 1400 & - & 2019/2020 \\ \hline \hline SpaceX Starlink [17] & USA & 1600 & 1110 & 53.8 & \\  & & 400 & 1130 & 74 & \\  & & 1600 & 1150 & 53 & 2024 \\  & & 375 & 1275 & 81 & \\  & & 450 & 1325 & 70 & \\ \cline{2-5}  & & 7518 & 340 & - & - \\ \hline \hline Boeing [18] & USA & 1190 & & 45 & \\  & & 612 & 1200 & 55 & 2027 \\  & & 1155 & & 88 & \\ \hline OneWeb [16] & USA/UK & 648 & 1200 & 88 & 2027 \\ \hline Hongyun [24] & China & 156 & 1000 & & 2022 \\ \hline Hongyan [19] & China & 54 & 1100 & - & 2023 \\  & & 324 & - & - & - \\ \hline Telesat [25] & Canada & 72 & 1000 & 99.5 & \\  & & 45 & 1248 & 37.4 & 2021 \\ \hline Astrome Technology [26] & India & 150 & 1400 & - & - \\ \hline Samsung [27] & Korea & 4600 & 1400 & - & - \\ \hline \hline \end{tabular}
\end{table}