Space-based gravitational wave detection relies on laser interferometry to measure picometer-level displacements over 105–106 km baselines. To integrate ranging and communication within the same optical link without degrading the primary scientific measurement, a low modulation index of 0.1 rad is required, resulting in extremely weak signals and challenging acquisition conditions. This study developed mathematical models for signal acquisition, identifying and analyzing key performance-limiting factors for both Binary Phase Shift Keying (BPSK) and Binary Offset Carrier (BOC) schemes. These factors include spreading factor, acquisition step, modulation index, and carrier-to-noise ratio (CNR). Particularly, the acquisition threshold can be directly calculated from these parameters and applied to the acquisition process of communication and ranging signals. Numerical simulations and evaluations, conducted with TianQin mission parameters, demonstrate that, for a data rate of 62.5 kbps and modulation indices of 0.081 rad (BPSK) or 0.036 rad (BOC), respectively, acquisition (probability ≈ 1) is achieved when the CNR is ≥104 dB·Hz under a false alarm rate of 10−6. These results provide critical theoretical support and practical guidance for optimizing the inter-satellite communication and ranging system design for the space-based gravitational wave detection missions.
Ling et al. (Wed,) studied this question.