## 1 Introduction
In contrast, the TianQin mission requires the laser frequency noise to be suppressed to below 10 Hz/Hz\({}^{1/2}\) after PDH stabilization and further reduced to the \(10^{-5}\) Hz/Hz\({}^{1/2}\) level via TDI, satisfying the requirements for both measurement noise and relative arm length variations [24]. The fundamental principle of TDI is to reconstruct an equivalent interferometer with equal arm lengths by applying appropriate time delays and linear combinations to the measured phase data. This approach achieves common-mode suppression of laser frequency noise [25; 26]. Therefore, the implementation of TDI requires precise measurement of the absolute distances between satellites to accurately reconstruct the equivalent interferometer. Additionally, the influence of clock noise in phase measurements necessitates data communication between satellites for clock noise elimination and onboard clock synchronization [27]. From a data-transmission perspective, space-based gravitational wave-detection missions are characterized by extended durations, with only one satellite in the constellation equipped to communicate directly with the ground. Consequently, the vast amount of data acquired through laser interferometry must first be transmitted bidirectionally across inter-satellite communication links and backed up by multiple satellites. At designated intervals, these consolidated data are transmitted to the ground by the designated satellite. This strategy minimizes the need for frequent antenna adjustments, thereby reducing disruptions to the gravitational wave-detection mission. It also provides a flexible and efficient solution for handling large-scale data transmission. Moreover, during the scientific measurement phase, a real-time inter-satellite communication link is essential within the constellation. This link enables the sharing of position and attitude data, facilitating the coordinated operation of all three satellites. Such synchronization ensures the collaborative control of satellite orbits and attitudes, which is critical for maintaining the precision and stability required for the successful execution of the gravitational wave-detection mission. Inter-satellite laser communication for space-based gravitational wave detection presents unique challenges. The transmitting satellite employs Direct Sequence Spread Spectrum (DS/SS) technology to superimpose communication and ranging codes onto the laser link used for gravitational wave detection. This operation is constrained by the power distribution of the laser link, as only a small fraction of the total optical power can be allocated for communication and ranging to avoid interfering with gravitational wave detection. As a result, low-depth Binary Phase-Shift Keying (BPSK) modulation is adopted instead of the conventional BPSK modulation typically used in traditional inter-satellite laser communication. In space-based gravitational wave-detection missions, the optical power used for communication and ranging must be designed to not exceed 1% of the total optical power, meaning that the modulation depth should not exceed 0.1 rad [28]. Currently, in the research on inter-satellite communication and ranging for space-based gravitational wave detection, for the LISA mission, [PERSON] et al. have conducted studies on weak-light laser ranging and data communication using fiber optics and FPGA [28]. Under a modulation index of 0.1 rad, they achieved a data-transmission rate of 24.4 kbps with a BER of less than \(10^{-3}\), along with an inter-satellite ranging resolution of 6 m. Considering the same modulation index, in hardware implementations by [PERSON] et al.