  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.
