## 1 Introduction
[29], the data-transmission rate reached 78.125 kbps with a BER of less than \(10^{-4}\), and the inter-satellite ranging resolution improved to 3.75 m. Similarly, with a modulation index of 0.1 rad, in experimental research by [PERSON] [23], a data-transmission rate of 78.125 kbps or 80 kbps was achieved, with a BER lower than \(10^{-6}\) and an inter-satellite ranging resolution of 3.75 m. For the Taiji mission, in optical experimental studies by [PERSON] et al. [30], using a modulation index of 0.1 rad, a data-transmission rate of 19.5 kbps with a BER of less than \(10^{-6}\) and an inter-satellite ranging resolution of 3.75 m were achieved. Regarding the TianQin mission, [PERSON] conducted bidirectional laser ranging experiments [31], achieving an inter-satellite ranging resolution of 3 m.  
From the existing published literature, in the area of inter-satellite laser communication and ranging for space-based gravitational wave detection, LISA has provided the requirement of communication data transmission and the mark of BER, proposed inter-satellite communication solutions based on ranging and conducted systematic experimental validation. Taiji has also proposed inter-satellite laser ranging and communication solutions and validated the optical systems. However, TianQin has only provided the requirement of data transmission and analyzed the performance of inter-satellite ranging. Whether TianQin's inter-satellite communication performance can meet the requirements under different inter-satellite laser interferometric measurement parameters, compared to LISA, still needs to be analyzed. In the LISA constellation, the proposed inter-satellite communication solution requires a communication rate of no less than 15 kbps [29]. In the TianQin constellation, based on the optimized orbital design [32; 33], the inter-satellite communication rate is required to exceed 41.54 kbps [34]. Meanwhile, for the LISA program, the target BER is less than \(10^{-6}\)[23]. In response to these requirements, this paper will conduct an in-depth analysis of how to achieve high-reliability data transmission using lower power in gravitational wave-detection links, in order to meet the inter-satellite data transmission needs for space-based gravitational wave detection. The paper will focus on modeling and simulation of inter-satellite laser communication for space-based gravitational wave detection, and will also perform performance analysis of inter-satellite communication from a simulation perspective, based on the laser interferometry parameters of the TianQin constellation. Section 2 of this paper introduces the basic principles and operational processes of inter-satellite laser communication for space-based gravitational wave detection. Section 3 outlines the simulation requirements, including the selection of PRN codes, the signal scheme design and the development of the mathematical models for signal transmission. Based on these requirements, a simulation model for inter-satellite laser communication is constructed using Simulink(R2023a). Section 4 validates the simulation model's functionalities, including spreading, phase modulation, noise addition, phase demodulation and despreading. Additionally, it examines the system's BER under various modulation indices, confirming that the simulation model meets the data-transmission requirements for inter-satellite laser communication in space-based gravitational wave detection.