## 5 Performance Evaluation
### Ranging Accuracy  
In this section, we first evaluate the ranging accuracy of DDBDM under different conditions, based on the theoretical expressions, and then verify the consistency between the theoretical and simulation results by Monte Carlo simulation. The ranging accuracy of DDBDM can be assessed based on the code tracking accuracy of the DLL, using the NELP discriminator [55]:  
\[\sigma_{\text{NELP}}^{2} =\frac{B_{L}(1-0.5B_{L}T_{coh})\int\limits_{-B_{r}/2}^{B_{r}/2} \left(1+\frac{P_{l}}{N_{0}}G_{l}(f)\right)G_{n}(f)\sin(\pi fd)^{2}\text{d}f}{( 2\pi)^{2}\frac{P_{n}}{N_{0}}\left(\int\limits_{-B_{r}/2}^{B_{r}/2}fG_{n}(f) \sin(\pi fd)\text{d}f\right)^{2}} \tag{30}\] \[\cdot\left(1+\frac{\int\limits_{-B_{r}/2}^{B_{r}/2}G_{n}(f)\cos( \pi fd)^{2}\text{d}f}{T_{coh}\frac{P_{n}}{N_{0}}\left(\int\limits_{-B_{r}/2}^{ B_{r}/2}G_{n}(f)\cos(\pi fd)\text{d}f\right)^{2}}+\frac{\int\limits_{-B_{r}/2}^{B_{ r}/2}G_{l}(f)G_{n}(f)\cos(\pi fd)^{2}\text{d}f}{T_{coh}\frac{P_{n}}{P_{l}} \left(\int\limits_{-B_{r}/2}^{B_{r}/2}G_{n}(f)\cos(\pi fd)\text{d}f\right)^{2 }}\right)\]  
where \(B_{L}\) is the equivalent noise bandwidth, \(T_{coh}\) is the coherent integration time, \(B_{r}\) is the front-end bandwidth of the receiver, and \(d\) is the early-late spacing of the correlator, \(P_{n}=\sum_{k=0}^{M_{c}-1}P_{n,k}|k_{k}|^{2}\) is the received power of the navigation signal, where \(h_{k}\) is the channel coefficient, \(N_{0}\) is the PSD of the environmental noise, \(G_{n}(f)\) is the normalized PSD of the navigation signal, and \(P_{l}\) and \(G_{l}(f)\) are the power and normalized PSD of the interference signal, respectively. The ranging accuracy of ZC-NOMA is also fairly compared using the above equation, as it has a continuous navigation signal. PN-OTFS and RP-OTFSM use a discontinuous PRN preamble or pilot for positioning, so their ranging accuracy is assessed based on the code tracking accuracy of the open-loop estimator using the NELP discriminator [55; 56]. We discuss an SNR range from \(-6\) dB to \(30\) dB. The carrier power-to-noise density ratio (\(C/N_{0}\)) of the navigation signal is \(44.8\) dB-Hz at \(\text{SNR}=-6\) dB and \(\text{CNPR}=30\) dB, which is equivalent to the power level of GNSS signals. Due to the low orbital altitude of LEO satellites, it is easier to increase the SNR of the received signal. Firstly, we analyze the effect of the number of visible satellites V on the ranging accuracy. In this case, \(V\) is set to \(4\), \(8\), and \(12\), respectively, and \(\text{CNPR}=30\) dB. The navigation signal bandwidth is \(24\) MHz for both DDBDM and TFBDM, and \(120\) MHz for ZC-NOMA, PN-OTFS, and RP-OTFSM. The tracking loop parameters are \(B_{L}=0.2\) Hz, \(T_{coh}=0.133\) ms, and \(d=0.5\) chip. Figure 7 shows the curves of ranging accuracy for the five INAC schemes as a function of the SNR. It can be seen that the ranging accuracies of ZC-NOMA, PN-OTFS, and RP-OTFSM all decrease with the number of visible satellites, and do not improve significantly with the increase in SNR. This is because the navigation signals of the three schemes are subject to interference from communication signals from other satellites in a multi-satellite scenario, and ZC-NOMA, in particular, additionally receives interference with the communication signal from the same satellite. Therefore, the more visible satellites there are, the stronger the power of the interference signals, and the increase in SNR also raises the power of the communication signals acting as interference, which limits the improvement in ranging accuracy. In contrast, the ranging accuracy of DDBDM and TFBDM is almost independent of the number of visible satellites, thanks to the separation of the navigation and communication subcarriers and the employment of CDMA between the navigation signals from different satellites. For the sake of clarity of the Figure, we no longer distinguish their ranging accuracies at different numbers of visible satellites.