Time delay interferometry with minimal null frequencies and shortened time span

Abstract

Time-delay interferometry (TDI) is essential for suppressing laser frequency noise in space-based gravitational wave (GW) observatories such as LISA. However, current second-generation TDI schemes often exhibit undesirable null frequencies and require long delay spans, which can impair data analysis performance. In this work, we introduce an alternative TDI configuration PD4L designed to minimize null frequencies and operate with a shorter effective time span. Constructed by synthesizing two distinct first-generation TDI schemes, PD4L achieves a delay span of 4$L$ (where $L$ is the arm length), half that of the standard Michelson and hybrid Relay configurations. We assess PD4L's performance by evaluating the spectral stability of instrumental noise via arm-length derivatives, simulating chirping GW signals from coalescing massive black hole binaries, and comparing waveform responses. Parameter estimation is performed in the frequency domain, and noise characterization is examined under realistic orbital dynamics. As demonstrated by the comparisons, the compact structure of PD4L offers several advantages: (1) reduced data margins at segment boundaries, (2) mitigated aliasing effects in the high-frequency regime, and (3) shortened signal tails arising from extended delay spans. Additionally, PD4L's null channels exhibit the same minimal null frequencies as its science channels, while maintaining greater spectral stability than other null streams. Overall, PD4L improves parameter estimation accuracy at high frequencies and supports reliable noise characterization over observation periods of up to four months. These results highlight PD4L as a compact and effective alternative for future TDI implementations, especially in high-frequency GW data analysis for LISA-like missions.