## 4 NR Navigation System
### Transmitting and Reception System Block Diagram  
As illustrated in Figure 3, an NR opportunity navigation system comprises three components: an NR signal transmitter, wireless channel, and navigation receiver. We first introduce the NR transmitter, whose physical layer is similar to the OFDM system. According to NR protocol [31], the higher layer of the base station generates a reference signal and random downlink bit streams. These bit streams undergo digital modulation (e.g., QAM or 16 QAM), followed by resource grid mapping. As a result, the serial data streams are transformed to parallel modulation symbols \(c_{n,k}\). OFDM modulation is implemented via inverse fast Fourier transform (IFFT), converting parallel signals to serial waveforms to generate the useful modulated signal \(s_{u}(t)\). The cyclic prefix is subsequently appended on useful signal \(s_{u}(t)\) to form the final transmitted waveform \(s_{\text{sym}}(t)\) (the frequency up and down conversions are omitted). OFDM signals experience amplitude attenuation and time delay through the wireless propagation channel. For LEO satellite signals, additional Doppler frequency shift occurs due to relative motion between satellites and receivers. The architecture of the NR navigation receiver has an analogous process flow to conventional GNSS receivers. First, the received NR signal is mixed with a local carrier to generate an intermediate-frequency (IF) signal:  
\[s_{\text{IF}}(t)=\text{Re}\Big{(}s_{R}(t)e^{-2\pi f_{\text{local}}t}\Big{)}=[s_ {\text{RS}}(t)+s_{\text{COM}}(t)]e^{-i(2\pi f_{\text{local}}+q_{\text{c}})} \tag{11}\]  
where \(f_{\text{local}}\) denotes the local carrier frequency, and \(f_{e}\) and \(\varphi_{e}\) represent the frequency and phase offset of the IF signal, respectively. \(s_{\text{COM}}(t)\) and \(s_{RS}(t)\) denote the communication data and navigation-available reference signal, respectively. The \(s_{\text{COM}}(t)\) may influence  
Figure 3: NR navigation system block diagram. the navigation performance, and this influence should be avoided as much as possible for the navigation receiver. The NR receiver consists of two core processing loops: (1) a delay-locked loop (DLL) for code delay estimation using the non-coherent early-late processor (NELP); and (2) a frequency-locked loop (FLL) dedicated to estimating carrier frequency offset. The DLL and FLL exhibit functional complementarity in signal tracking: the DLL eliminates transmission delays by adjusting the phase of the local replica signal, while the FLL maintains carrier synchronization by compensating frequency offset. The NELP employs three parallel processing branches with relative delays \(\tau\) (prompt), \(\tau-d\) (early), and \(\tau+d\) (late), where \(d\) specifies the correlator spacing. In the early branch, the local replica reference signal \(s_{\text{RS,E}}(t)\) correlates with the received IF signal. Then, the correlation results are sent to the integrate and dump (I&D) filter and generate correlation amplitude \(V_{E}\):  
\[V_{E}=\left|\int_{0}^{T_{\text{coh}}}s_{\text{IF}}(t)s_{\text{RS,E}}^{*}(t)dt \right|=R_{E}(\tau)|\text{sinc}(f_{e}T_{\text{coh}})|+n_{\text{COR}} \tag{12}\]  
where \(T_{\text{coh}}\) represents the duration of correlation integration. \(n_{\text{COR}}\) quantifies the interference caused by the CP and inter-carrier. Compared with the traditional GNSS receiver, the CP and inter-carrier communication data significantly impact DLL accuracy. An interference elimination method is proposed in the following subsection. Similarly, the correlation amplitude \(V_{L}\) of the delayed branch can be obtained. The time delay of the received signal can be measured by utilizing \(V_{E}\) and \(V_{L}\):  
\[\tau_{\text{meas}}=K_{\text{RS}}\frac{V_{E}^{2}-V_{L}^{2}}{V_{E}^{2}+V_{L}^{2}} \tag{13}\]  
where \(K_{\text{RS}}\) denotes the normalization parameter of the time delay discriminator, derived from the S-curve [2].