  In this paper, we present a successful implementation of a subtraction-noise
projection method into a simple, simulated data analysis pipeline of a
gravitational-wave search. We investigate the problem to reveal a weak
stochastic background signal which is covered by a strong foreground of
compact-binary coalescences. The foreground which is estimated by matched
filters, has to be subtracted from the data. Even an optimal analysis of
foreground signals will leave subtraction noise due to estimation errors of
template parameters which may corrupt the measurement of the background signal.
The subtraction noise can be removed by a noise projection. We apply our
analysis pipeline to the proposed future-generation space-borne Big Bang
Observer (BBO) mission which seeks for a stochastic background of primordial
GWs in the frequency range $\sim 0.1-1 $Hz covered by a foreground of
black-hole and neutron-star binaries. Our analysis is based on a simulation
code which provides a dynamical model of a time-delay interferometer (TDI)
network. It generates the data as time series and incorporates the analysis
pipeline together with the noise projection. Our results confirm previous ad
hoc predictions which say that BBO will be sensitive to backgrounds with
fractional energy densities below $\Omega=10^{-16}$
