## 5 Performance Evaluation
### Data Transmission Reliability  
The reliability of data transmission not only affects the quality of service for broadband communication, but is also crucial for quickly receiving navigation messages and high-precision correction parameters in PNT applications. It is usually evaluated by the BER. Therefore, we compare the BER performance of different signals under the same received SNR and the amount of transmitted data. The BER performance depends on the SNR with the determined modulation and coding scheme. The actual SNR of the communication signal of satellite \(i\) is calculated as follows:  
\[\text{SNR}_{\text{com}}^{i}=\frac{\sum\limits_{k=0}^{M_{k}-1}P_{c,k}\left|h_{ k}^{i}\right|^{2}}{N_{0}M_{c}\Delta f+\sum\limits_{v=0,v\
eq i}^{V-1}\sum \limits_{k=0}^{M_{c}-1}P_{c,k}\left|h_{k}^{i}\right|^{2}} \tag{31}\]  
where \(h_{k}^{i}\) denotes the channel coefficient on the \(k\)-th subcarrier from satellite \(i\) to the UE link, including antenna gain, free space propagation loss, shadow fading, and other effects. Channel estimation and signal detection algorithms are not the focus of this work, so ideal channel estimation is used here, and a linear minimum mean square error (LMMSE) detector is employed [57]. Meanwhile, the number of visible satellites discussed here is V = 1, as the communication receivers could mitigate the impact of signals from other satellites using SIC. Due to the Doppler frequency of the Ka-band signal caused by the dynamic of the satellite far exceeding the subcarrier spacing, the satellite side compensated Doppler frequency shift scenario recommended by 3 GPP is adopted, with a residual Doppler frequency of 0.91 ppm [54]. The parameters of the TDL-C channel model used in the simulation are provided in Table 3. For each SNR and subcarrier point, the BER simulation exceeds \(10^{4}\) frames. Figure 11 shows the BER curves for the five schemes as a function of the SNR. It can be observed that DDBDM has the lowest BER for the same CNPR, which is attributed to the good orthogonality maintained by the DD basis functions in high-mobility multipath channels. ZC-NOMA has the highest BER, followed by TFBDM, as the OFDM-based design introduces ICI in high-mobility scenarios, adversely affecting data demodulation. Additionally, the navigation signal from ZC-NOMA interferes with the communication signal, resulting in a higher BER than that of TFBDM, which is also based on OFDM. The difference in BER performance between the two becomes especially more significant as the CNPR decreases. The BER of RP-OTFSM is slightly higher than that of DDBDM, due to its larger noise bandwidth. The BER performance of PN-OTFS falls between that of RP-OTFSM and TFBDM. Although it employs OTFS modulation for data transmission, the overlay of navigation messages on the communication data constellation increases the BER during the demodulation process. This effect is especially noticeable under low-CNPR conditions, leading to a special case where its BER is even higher than that of OFDM-based TFBDM, at CNPR = 0 dB. Figure 12 shows the BER curves varying with different numbers of communication subcarriers \(M_{c}\), where SNR = 10 dB and CNPR = 20 dB. It can be seen that the BER performance of DDBDM and TFBDM deteriorates as the bandwidth of the communication signal increases. This is because an increase in the noise bandwidth leads to a decrease in the effective SNR defined in (31), while the power of the communication signal remains constant. However, DDBDM still has the lowest BER compared to all other schemes. Moreover, the BER performance of PN-OTFS is almost the same as that of RP-OTFSM in this case, since the former allocates little power to the navigational message, and has little effect on the communication constellation diagram. Finally, we summarize the performance of DDBDM signals under different CNPR and bandwidth (subcarriers) conditions. The primary function of LEO constellations is to  
Figure 11: BER vs. SNR with different CNPRs. Figure 12: BER vs. \(M_{c}\), with SNR = 10 dB and CNPR = 20 dB.