  One of the primary targets of third-generation (3G) ground-based
gravitational wave (GW) detectors is detecting the stochastic GW background
(SGWB) from early universe processes. The astrophysical foreground from compact
binary mergers will be a major contamination to the background, which must be
reduced to high precision to enable the detection of primordial background. In
this work, we revisit the limit of foreground reduction computed in previous
studies, point out potential problems in previous foreground cleaning methods
and propose a novel cleaning method subtracting the approximate signal strain
and removing the average residual power. With this method, the binary black
hole foreground is reduced with fractional residual energy density below
$10^{-4}$ for frequency $f\in (10, 10^2)$ Hz, below $10^{-3}$ for frequency
$f\in (10^2, 10^3)$ Hz and below the detector sensitivity limit for all
relevant frequencies in our simulations. Similar precision is achieved to clean
the foreground from binary neutron stars (BNSs) that are above the detection
threshold, so that the residual foreground is dominated by sub-threshold BNSs,
which will be the next critical problem to solve for detecting the primordial
SGWB in the 3G era.
