  Armstrong et al. have recently presented new ways of combining signals to
precisely cancel laser frequency noise in spaceborne interferometric
gravitational wave detectors such as LISA. One of these combinations, the
symmetrized Sagnac observable, is much less sensitive to external signals at
low frequencies than other combinations, and thus can be used to determine the
instrumental noise level. We note here that this calibration of the
instrumental noise permits smoothed versions of the power spectral density of
stochastic gravitational wave backgrounds to be determined with considerably
higher accuracy than earlier estimates, at frequencies where one type of noise
strongly dominates and is not substantially correlated between the six main
signals generated by the antenna. We illustrate this technique by analyzing
simple estimators of gravitational wave background power, and show that the
instrumental sensitivity to broad-band backgrounds at some frequencies can be
improved by more than an order of magnitude over the standard method,
comparable to that which would be achieved by cross-correlating two separate
antennas. The applications of this approach to studies of astrophysical
gravitational wave backgrounds generated after recombination and to searches
for a possible primordial background are discussed.

Astrophysics