Time delay interferometry with minimal null frequencies

Time delay interferometry (TDI) is a key technique employed in gravitational wave (GW) space missions to mitigate laser frequency noise by combining multiple laser links and establishing an equivalent equal arm interferometry. The null frequencies will be introduced in noise spectra and GW response when the periodical signal/noise is canceled in synthesized laser links. These frequencies are characteristic frequencies (CFs) of a TDI which related to its geometry of combination. In this work, we implement a second-generation TDI configuration referred to as hybrid Relay to perform noise suppressions and data analysis, whose CFs are only one-quarter that of the fiducial second-generation Michelson observables. We examine the performance of TDI configuration in laser noise cancellation and clock noise suppression and justify its essential capabilities. To assess its robustness for signal extraction, we simulate data containing GW signals from massive black hole binaries and perform parameter inferences with comparisons against the fiducial Michelson TDI configuration. The results demonstrate that the alternative TDI solution could be more robust than Michelson in fulfilling data analysis.