## 4 Discussion  
The separation between neighboring satellites within the same orbital plane of a Walker constellation is approximately on the order of tens of thousands of kilometers, and the optical power received at the terminal is below 1 \(\mu\)W. We simulated the relationship between the ranging precision and received optical power, as well as the correlation between the received optical power and distance. For inter-satellite laser links, the optical power received at the terminal is [24]  
\[P_{\text{R}}=P_{\text{T}}G_{\text{T}}\eta_{\text{T}}L_{\text{PS}}\eta_{\text{S }}L_{\text{APT}}G_{\text{R}}\eta_{\text{R}}, \tag{11}\]  
where \(P_{\text{R}}\) is the received power; \(P_{\text{T}}\) is the transmitted power; \(G_{\text{T}}\) is the transmitter gain; \(G_{\text{T}}=(\pi\text{D}_{\text{T}}/\lambda)^{2}\) (D\({}_{\text{T}}\) is the diameter of the transmitting telescope, and \(\lambda\) is the wavelength); \(\eta_{\text{T}}\) is the optical efficiency of the transmitter (the typical value of which is \(-1.74\) dB); \(L_{\text{PS}}\) is the path loss of the inter-satellite optical link; \(L_{PS}=(\lambda/4\pi w)^{2}\) (\(w\) is the inter-satellite distance); \(\eta_{\text{S}}\) is the link attenuation caused by the channel (which is equal to 1 for ISLs); \(L_{\text{APT}}\) is the power loss caused by acquisition, pointing, and tracking (APT) misalignment, and its value of \(-0.56\) dB is obtained according to the best matching relationship where the divergence angle of the communication beam is fives times the pointing error; \(G_{\text{R}}\) is the receiver gain (the aperture of the receiving telescope is the same as that of the transmitting telescope); and \(\eta_{\text{R}}\) is the optical efficiency of the receiver, which is the same as \(\eta_{\text{T}}\) here [24]. The diameters of both the transmitting and receiving telescopes were fixed at 100 mm, the transmitted power was specified as 25 dB, and the link safety margin was set at 3 dB [24; 25; 26]. For an inter-satellite distance of 21,343 km in the BDS, the received optical power was \(P_{\text{R}}\approx 3.5\) nW. The coherent receiver uses a local oscillator to improve the signal-to-noise ratio, in which case the noise is predominantly shot noise [27]. Shot noise is modeled as a zero-mean random Gaussian process. In the shot noise limit, the SNR is expressed as [28]  
\[SNR=\gamma R_{1}P_{\text{R}}/(2 qB), \tag{12}\]  
where \(\gamma\) is the heterodyne efficiency, \(R_{1}\) is the responsivity, \(P_{\text{R}}\) is the received optical power, \(q\) is the electron charge, and \(B\) is the receiver bandwidth. A Monte Carlo simulation was  
Figure 11: Velocity measurements for the moving target. conducted to analyze the relationship between the received optical power and the ranging precision. The results are depicted as black dots in Figure 12. Additionally, the pink curve in Figure 12 shows the correlation between the received optical power and the range. Figure 12 illustrates that in the shot noise limit, the optical power decreased as the ranging precision increased with distance. The ranging precision deteriorated sharply at an optical power of 27 nW. Here, 27 nW of optical power corresponds to a distance of 8220 km, with a ranging error of 0.15 mm and a time delay error of 0.5 ps. When the received optical power was 3 nW, the corresponding distance was 24,663 km, with a ranging error of approximately 1.51 mm and a time-delay error of approximately 5.03 ps. The theoretical waveform of the pseudo-random code is a rectangular wave, its spectrum is infinite wide, its main energy is concentrated in the main lobe, and its theoretical phase discrimination model \(Z\) is a linear model, as shown in Figure 13. The bandwidth of the actual ranging system is limited, and the devices used in the system are not ideal. These factors lead to a poor matching between the theoretical phase discrimination model and the actual system. When the theoretical phase discrimination model is used in the actual system, it will bring errors.