## 3 Signal Model
### PSD of NR Reference Signal  
The PSD of navigation signals enables the quantitative analysis of tracking accuracy and anti-jamming capability, serving as a critical tool for navigation performance evaluation [74]. According to the NR signal model, reference signals are distributed across subcarriers and are part of the NR signal. ZPC ensures orthogonality between reference signals on different subcarriers while eliminating interference caused by the CP and inter-carrier. Therefore, when the correlation integration period is sufficiently long, the PSD of the NR reference signal can be expressed as the summation of the PSDs of all individual subcarrier reference signals:  
\[G_{\text{RS}}(f)=\frac{1}{N_{\text{RS}}}\sum_{(n,k)\in\Omega}G_{n,k}(f) \tag{6}\]  
where \(N_{\text{RS}}\) and \(\Omega\) denotes the total number and location set of the reference signal in an OFDM resource grid, respectively. \(G_{n,k}(f)\) represents the PSD of the subcarrier reference signal at the \(n\)-th symbol and \(k\)-th subcarrier. Its corresponding time-domain signal \(s_{n,k}(t)\) comprises the modulation symbol \(c_{n,k}\) multiplied by a complex exponential (subcarrier waveform):  
\[s_{n,k}(t)=c_{n,k}e^{j2\pi k\Delta f}u_{T}(t)=c_{n,k}p_{k}(t) \tag{7}\]  
where \(p_{k}(t)\) denotes the pulse shaping waveform of the \(k\)-th subcarrier.  
For the subcarrier reference signal, its PSD \(G_{n,k}(f)\) can be derived from the PSD \(G_{\text{PRN}}(f)\) of the modulation symbol \(c_{n,k}\) and the spectrum \(P_{k}(f)\) of the subcarrier waveform [75]:  
\[G_{k}(f)=\frac{1}{T_{u}}|P_{k}(f)|^{2}G_{\text{PRN}}(f) \tag{8}\]  
where \(P_{k}(f)\) is the Fourier transform of the subcarrier's pulse shaping waveform:  
\[P_{k}(f)=FT[p_{k}(t)]=T_{u}\,e^{-j\pi(f-f_{k})T_{u}}\,\text{sinc}[(f-f_{k})T_{ u}] \tag{9}\]  
where \(f_{k}=k\Delta f\) represents the \(k\)-th subcarrier frequency.  
The modulation symbol \(c_{n,k}\) of the reference signal can be regarded as an ideal pseudo-random sequence (PRN), and its PSD remains constant at unity:  
\[G_{\text{PRN}}(f)=1 \tag{10}\]  
This paper uses a default NR and receiver configuration as listed in Table 1. Its PSD curve is illustrated in Figure 2. The PSD of the NR reference signal exhibits multiple spectral peaks at corresponding frequencies. Between these peaks, spectral notches appear due to the absence of a subcarrier reference signal. NR parameters can adjust the number and location of PSD peaks. Hence, the NR parameters determine its tracking performance.  
\begin{table}
\begin{tabular}{l l c} \hline \hline  & **Parameter** & **Value** \\ \hline \multirow{8}{*}{NR Basic} & FFT Length & 1024 \\  & Subcarrier Spacing (kHz) & 15 \\  & Sampling Rate (MHz) & 15.36 \\  & Period (ms) & 10 \\  & Slot Number Per Period & 5 \\  & Symbol Length Per Slot & 8 \\  & Used BandWidth (MHz) & 1.8 \\  & Resource Block Number & 10 \\  & Subcarrier Number & 240 \\ \hline \multirow{8}{*}{PDSCH} & Modulation & QPSK \\  & DMRS Mapping & Type A \\  & DMRS-TypeA-Position & 2 \\  & DMRSLength & 1 \\  & DMRS-Additional-Position & 0 \\  & DMRS-Configuration-Type & 2 \\  & DMRS proportion \(\alpha\) & 3.50\% \\ \hline \multirow{4}{*}{Delay-locked loop (DLL)} & \(B_{L}\) (Hz) & 20 \\  & Damping Coefficient & 0.707 \\  & Integration Time (ms) & 10 \\  & Early–Late Spacing \(\Delta\) (Sampling Time) & 2 \\ \hline \multirow{8}{*}{Delay-locked loop} & Transmit Power (W) & 10 \\  & Proportion of Reference Signal in NR signal & 19.44\% \\ \cline{1-1}  & Receiver Front-end Bandwidth (MHz) & 15.36 \\ \cline{1-1}  & Sampling Rate (MHz) & 15.36 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Default configurations in LEO NR navigation.  
Figure 2: Power spectral density (PSD) of NR. The unit of horizontal axis is \(\Delta f\).