  The LISA mission will likely be a signal dominated detector, such that one
challenge is the separation of the different astrophysical sources, and to
distinguish between them and the instrumental noise. One of the goals of LISA
is to probe the early Universe by detecting stochastic GW backgrounds. As
correlation with other detectors is not possible for LISA, discrimination of
such a GW background from the instrumental noise requires a good estimate of
the latter. To this purpose we have revisited Time Delay Interferometry (TDI)
to look for new TDI signal combinations that fulfill the laser frequency noise
suppression requirements. We illustrate that it is possible to do a linear
combination of these TDI channels to find special null-combinations that
suppress gravitational waves and mainly carry information about instrumental
noise. We find that there exist many null-combinations that show different
sensitivities to gravitational waves, some of which seem more suitable than the
traditional T combination for estimating test-mass acceleration noise. In an
idealised LISA configuration, they are all sensitive to a particular linear
combination of the six test-masses acceleration, similar to a rigid rotation of
the LISA triangle. In the following article, we illustrate what are the noise
properties that can be extracted by monitoring these interferometry signals and
discuss the implication of these findings for the detection of stochastic GW
backgrounds.
