Correlation and Data-Analysis Distinctiveness of Time-Delay Interferometry Configurations

Time-Delay Interferometry (TDI) is essential for space-based gravitational wave (GW) missions, as it suppresses laser frequency noise and achieve the required sensitivity. Beyond the standard Michelson configuration, a variety of second-generation TDI schemes have been proposed, each utilizing different combinations of inter-spacecraft laser links. In this work, we conduct a comparative study of several representative TDI configurations with different time spans, and show that while their (quasi-)orthogonal channels are highly correlated, their performance in data analysis can differ among these schemes. In the low-frequency regime, the performance of different TDI configurations are nearly identical. Their distinctions emerge primarily at high frequencies, where the GW wavelength becomes comparable to the arm length. In this regime, shorter TDI time spans with minimal null frequencies facilitate more accurate waveform modeling and parameter recovery in frequency domain. In contrast, configurations with longer time spans and more null frequencies, such as the Michelson, are more susceptible to frequency aliasing and waveform modulation effects, which degrade inference accuracy. However, if signal modeling and analysis are performed in the time domain, the optimal science channels of these TDI configurations exhibit consistent performance in parameter inference. Considering the usability in both frequency and time domain, the short-span PD4L scheme, which exhibits minimal nulls and superior performance in high frequencies, emerges as a promising candidate for future space-based GW mission designs.