## 5 Performance Evaluation
### Ranging Accuracy
The navigation signals of DDBDM and TFBDM have similar PSDs, so their ranging accuracies are the same, and are always higher than those of PN-OTFS and RP-OTFSM. The ranging accuracy of DDBDM surpasses that of the ZC-NOMA, with a larger bandwidth if the SNR exceeds 10 dB. This indicates that DDBDM has low MI, making it easier to improve the ranging accuracy. Secondly, we evaluate the ranging accuracy of the five schemes with different received navigation signal bandwidths. The number of navigation subcarriers \(M_{n}\) is set to 200, 600, and 1000, with the corresponding navigation signal bandwidth determined based on \(B_{r}=M_{n}\Delta f\). V = 8, CNPR = 30 dB, and the other parameters remain unchanged. Figure 8 shows the curves of ranging accuracy as a function of the SNR under different navigation signal bandwidths. The results indicate that DDBDM and TFBDM have the highest ranging accuracy with the same bandwidth. Even when \(M_{n}\) = 200, the ranging accuracy of DDBDM is still significantly higher than that of PN-OTFS and RP-OTFSM with \(M_{n}\) = 1000, and it also exceeds that of ZC-NOMA when the SNR is greater than 7 dB, a condition that is  
Figure 7: Ranging accuracy vs. SNR for various numbers of visible satellites. CNPR = 30 dB; bandwidth is 24 MHz for both DDBDM and TFBDM, and 120 MHz for ZC-NOMA, PN-OTFS, and RP-OTFSM. easily met in LEO scenarios. The results imply that to achieve the same or higher ranging accuracy, the navigation signal bandwidth of DDBDM can be reduced by 80% compared to ZC-NOMA, PN-OTFS, and RP-OTFSM, mitigating the signal processing burden on the navigation receiver. This is supported by the fact that DDBDM has both a dedicated broadcast signal, allowing continuous tracking of the signal, and a very low MI. In addition, the ranging accuracy of RP-OTFSM is slightly higher than that of PN-OTFS, thanks to the fact that the pilot used for ranging in RP-OTFSM has a larger mean square bandwidth than that of the time-domain PN preamble [8; 42]. Since PN-OTFS and RP-OTFSM do not have a dedicated broadcast signal component, the ranging accuracy of their open-loop estimators is significantly lower than that of DDBDM, TFBDM, and ZC-NOMA. Subsequently, we discuss the impact of different power allocations on ranging accuracy. With V = 8 and SNR = 20 dB, the remaining parameters are consistent with those in Figure 7. Figure 9 illustrates that as the CNPR increases, the ranging accuracy of all signals decreases, because the power is used more for communication rather than for navigation. Under the condition of a fixed SNR, the ranging accuracy curves for the five schemes do not intersect. DDBDM and TFBDM always have the highest ranging accuracy, while RP-OTFSM and PN-OTFS are worse because they are unable to perform continuous tracking. This is consistent with the previous results. Figure 8: Ranging accuracy vs. SNR for various navigation signal bandwidths. CNPR = 30 dB, V = 8. Finally, we verify the consistency of the theoretical analysis with the simulation. The Monte Carlo simulation uses the tracking loop given in Figure 6, with the loop parameters \(B_{L}=0.2\) Hz, \(T_{\text{c}th}=0.133\) ms, and \(d=0.5\) chip. The tracking loop conforms to the generalized structure specified in [55], and thus allows for evaluation with the theoretical results given in (30). The number of navigation subcarriers of DDBDM is set to 200 and 600, the CNPR is set to 20 and 30, and each point corresponds to \(10^{4}\) periods of signal processing. The ranging accuracy is statistically derived as shown in Figure 10. THE and SIM in the Figure represent the theoretical and simulation results for the given conditions, respectively. It can be observed that under different navigation signal bandwidths and power allocation conditions, the ranging accuracy of the simulation agrees well with the theoretical results in general, which suggests that the assessment of the ranging accuracy using (30) is justified. Figure 10: Comparison of theoretical and simulation results of DDBDM. Figure 9: Ranging accuracy vs. CNPR.