# Signal Design and Compatibility Assessment for LEO Navigation Augmentation System +
## 4 Compatibility Assessment  
For compatibility evaluation between GNSS signals, the degradation of effective carrier-power-to-noise density ratio (\(C/N_{0}\)) is usually used for evaluation [20]. The degradation of effective \(C/N_{0}\) under the presence of intrasystem and intersystem interference is as follows:  
\[\left(\frac{C}{N_{0}}\right)_{eff}=\frac{C}{N_{0}+I_{\text{intra-GNSS}}+I_{ \text{inter-GNSS}}+I_{\text{inter-LEO}}} \tag{1}\]  
Among them, \(C\) is the received power of the desired GNSS signal, \(N_{0}\) is the single sideband noise power spectral density, \(I_{\text{intra-GNSS}}\) is the interference power spectral density caused by signals broadcast by other visible satellites in this GNSS system, \(I_{\text{inter-GNSS}}\) is the interference power spectral density caused by signals broadcast by visible satellites in other GNSS systems, and \(I_{\text{inter-LEO}}\) is the interference power spectral density caused by signals broadcast by visible satellites in the LEO navigation augmentation system. \[ \begin{array}{l}I_{\text{intra-GNSS}}[\text{dB}]=G_{\text{intra-GNSS}}[ \text{dB}]+P_{\text{intra-GNSS}}[\text{dB}]+SSC_{\text{intra-GNSS}}[\text{ dB}]\\ I_{\text{inter-GNSS}}[\text{dB}]=G_{\text{inter-GNSS}}[\text{dB}]+P_{\text{ inter-GNSS}}[\text{dB}]+SSC_{\text{inter-GNSS}}[\text{dB}]\\ I_{\text{inter-LEO}}[\text{dB}]=G_{\text{inter-LEO}}[\text{dB}]+P_{\text{ inter-LEO}}[\text{dB}]+SSC_{\text{inter-LEO}}[\text{dB}]\end{array}  \tag{2}\]  
where \(G_{\text{intra-GNSS}}[\text{dB}]\) is the total gain caused by the total number of visible satellites in this GNSS system, \(P_{\text{intra-GNSS}}[\text{dB}]\) is the receiving power on ground of this GNSS signal, \(SSC_{\text{intra-GNSS}}[\text{dB}]\) is the spectral separation coefficient between signals in the GNSS system, \(G_{\text{inter-GNSS}}[\text{dB}]\) is the total gain caused by the total number of visible satellites in other GNSS systems, \(P_{\text{inter-GNSS}}[\text{dB}]\) is the receiving power on ground of other GNSS signals,  
Figure 2: Schematic diagram of three multiplexing methods: (**a**) phase separation multiplexing method, (**b**) chip-by-chip time division multiplexing method, and (**c**) code period time division multiplexing method (MCSK). \(SSC_{\text{inter-GNSS}}[\text{dB}]\) is the spectral separation coefficient between other GNSS signals and this GNSS signal, \(G_{\text{inter-LEO}}[\text{dB}]\) is the total gain caused by the total number of visible satellites in the LEO navigation augmentation system, \(P_{\text{inter-LEO}}[\text{dB}]\) is the receiving power on ground of the LEO signal, and \(SSC_{\text{inter-LEO}}[\text{dB}]\) is the spectral separation coefficient between the LEO signal and GNSS signal. The spectral separation coefficient can be calculated as follows:  
\[SSC=\int_{\beta_{r}/2}^{\beta_{r}/2}G(f)G_{i}(f)df \tag{3}\]  
Among them, \(G(f)\) is the normalized power spectrum of the expected signal in the transmission bandwidth, \(G_{i}(f)\) is the normalized power spectrum of the interference signal in the transmission bandwidth, and \(\beta_{r}\) is the received bandwidth. The degradation of effective \(C/N_{0}\) caused by the introduction of LEO navigation signals is as follows:  
\[ \begin{array}{l}\frac{C}{N_{0}+I_{\text{intra-GNSS}}+I_{\text{inter-GNSS}}}[ \text{dB}]-\frac{C}{N_{0}+I_{\text{intra-GNSS}}+I_{\text{inter-GNSS}}+I_{\text {inter-LEO}}}[\text{dB}]\\ =1+\frac{I_{\text{inter-LEO}}}{N_{0}+I_{\text{intra-GNSS}}+I_{\text{inter-CNS}}}[ \text{dB}]\end{array}  \tag{4}\]  
Figure 3 shows the average number of visible satellites within 24 h for GPS, Galileo, and BeiDou-3 systems. To analyze the worst impact, the total gain caused by the number of visible satellites in the GNSS signal is calculated based on the average minimum number of visible satellites. GPS is calculated based on the number of 8 visible satellites, Galileo is calculated based on the number of 7 visible satellites, and BeiDou-3 is calculated based on the number of 7 visible satellites.