## 4 Discussion
Figure 14a simulates the relationship between the phase discrimination model and the bandwidth. When the bandwidth becomes small, the phase discrimination model moves away from the theoretical phase discrimination model, and when the bandwidth becomes large, the phase discrimination model approaches the theoretical model. When the system bandwidth is infinitely wide, the phase discrimination model is equal to the theoretical model. As shown in Figure 14a, there is a difference between the phase discrimination model of the band-limited system and the theoretical model. When the theoretical model is applied to a system with limited bandwidth, it results in a decrease in the ranging accuracy. Figure 14a also illustrates the theoretical relationship between the ranging accuracy and ranging range in the traditional method. The phase discrimination range of the pseudo-random code is \((-T_{\text{C}}/2,T_{\text{C}}/2)\), corresponding to a chip width, which leads to the ranging accuracy periodically improving and deteriorating as the ranging range increases. When the system bandwidth is equal to one times the chip rate, the ranging accuracy of traditional method becomes very poor within the period, and as the system bandwidth continues to increase, the ranging accuracy of traditional method will gradually improve within the period. Figure 14b simulates the relationship between ranging accuracy, bandwidth, and SNR. In [PERSON]'s article, the SNR for ranging is greater than 21 dB [19]. For comparison, we simulated the variations in ranging accuracy when the SNR is greater than 20 dB. The main energy of the pseudo-random code is concentrated within  
Figure 12: Relationship between the received optical power and the ranging precision (or distance). the main lobe. As the system bandwidth increases, the discrimination model approaches the theoretical discrimination model, improving the ranging accuracy. However, the SNR decreases, leading to a deterioration in the ranging precision, as shown in Figure 14b. This issue is inherent in the traditional method, where the accuracy and precision of the distance measurement are mutually restrictive. This also explains the ranging precision of 0.33 mm and the ranging accuracy of 6 mm mentioned in [PERSON]'s article. The method proposed in this paper reduces the system bandwidth, ensures a high SNR, and improves the ranging accuracy using a discriminator with calibrated characteristic parameters so that the ranging accuracy does not show periodic variations as the ranging range increases. By employing a data-shifting method, the consistency of the discriminator in ranging is maintained. Compared with the traditional method, the proposed method improves the ranging accuracy and ensures a high ranging precision, which solves the situation that the ranging accuracy and ranging precision constrain each other. This is the difference between the proposed method in this paper and the method in [PERSON]'s paper. The symbols involved in this section are summarized in Table A3 in Appendix A.  
Figure 14: Relationship between the early–late discrimination model and bandwidth and relationship between ranging precision and bandwidth and SNR. **(a)** Relationship between the early–late discrimination model and bandwidth. **(b)** Relationship between ranging precision and bandwidth and SNR. Figure 13: Time domain and frequency domain plots of pseudo-random code and theoretical early–late discrimination model. **(a)** Time-domain plot. **(b)** Frequency-domain plot. **(c)** Theoretical early–late discrimination model.