Preliminary simulation and analysis of the Taiji formation’s laser interference signal with phase-locked loops

Space gravitational wave detection formation of three spacecraft uses phase-locked loops to achieve weak-light amplification, Doppler frequency shift compensation, and control of the heterodyne interference beat notes. The formation's laser closed-loop control system, with the heterodyne interference phase as feedback, directly influences the detection signal and noise transfer. This study discusses various phase-locking schemes for the Taiji formation and analyzes the impact of in-loop noise limits. A phase-locked loop model is developed for the entire laser closed-loop control system using the phases of the scientific and reference interferometers as the feedback signals for the sequential inter- and intra-spacecraft phase-locking. Based on this model, the signal output models of all interferometers in the Taiji formation were obtained, and a Simulink simulation program was completed. Using the detection of a supermassive binary black hole waveform as a case study, six phase-locking schemes were evaluated. The results demonstrate that the selection of the phase-locking scheme has a negligible impact on data post-processing outcomes, provided that various noise sources comply with Taiji program requirements and the in-loop noise of the phase-locked loop remains below 0.001<i>p</i><i>m</i>/<i>H</i><i>z</i>^1/2 in the Taiji sensitivity frequency band. Additionally, the amplified in-loop noise simulation experiment shows that the limit of in-loop noise for the Taiji program is 0.1<i>p</i><i>m</i>/<i>H</i><i>z</i>^1/2. The developed entire laser closed-loop control and signal output model enhance the precision of signal simulations for space-based gravitational wave detection, providing valuable insights for optimizing system parameters and operational strategies.