  The Big Bang Observer (BBO) is a proposed space-based gravitational-wave (GW)
mission designed primarily to search for an inflation-generated GW background
in the frequency range 0.1-1 Hz. The major astrophysical foreground in this
range is gravitational radiation from inspiraling compact binaries. This
foreground is expected to be much larger than the inflation-generated
background, so to accomplish its main goal, BBO must be sensitive enough to
identify and subtract out practically all such binaries in the observable
universe. It is somewhat subtle to decide whether BBO's current baseline design
is sufficiently sensitive for this task, since, at least initially, the
dominant noise source impeding identification of any one binary is confusion
noise from all the others. Here we present a self-consistent scheme for
deciding whether BBO's baseline design is indeed adequate for subtracting out
the binary foreground. We conclude that the current baseline should be
sufficient. However if BBO's instrumental sensitivity were degraded by a factor
2-4, it could no longer perform its main mission. It is impossible to perfectly
subtract out each of the binary inspiral waveforms, so an important question is
how to deal with the "residual" errors in the post-subtraction data stream. We
sketch a strategy of "projecting out" these residual errors, at the cost of
some effective bandwidth. We also provide estimates of the sizes of various
post-Newtonian effects in the inspiral waveforms that must be accounted for in
the BBO analysis.
