  The improved sensitivity of third generation gravitational wave detectors
opens the possibility of detecting the primordial cosmological stochastic
gravitational wave background (SGWB). Detection of the cosmological SGWB is
facing a novel challenge: it will likely be masked by the foreground generated
by a large number of coalescences of compact binary systems consisting of black
holes and/or neutron stars. In this paper, we investigate the possibility of
reducing this foreground by removing (notching) the individually resolved
compact binary signals in time-frequency space. We establish that such an
approach could be used to reach the SGWB sensitivity floor defined by the
unresolved part of the compact binaries foreground, which we find to be between
$\Omega_{\rm GW} \sim (9.1 \times10^{-12} - 8.6\times10^{-11})$ for a frequency
independent energy density spectrum and depending on the rate of coalescing
binary neutron star systems. Since third-generation gravitational wave
detectors will not be able to resolve all compact binaries, the unresolvable
component of the compact binaries foreground may limit the SGWB searches with
these detectors.
