The Epoch of Reionization Window: II. Statistical Methods for Foreground
  Wedge Reduction
  For there to be a successful measurement of the 21 cm Epoch of Reionization
(EoR) power spectrum, it is crucial that strong foreground contaminants be
robustly suppressed. These foregrounds come from a variety of sources (such as
Galactic synchrotron emission and extragalactic point sources), but almost all
share the property of being spectrally smooth, and when viewed through the
chromatic response of an interferometer, occupy a signature "wedge" region in
cylindrical $k_\perp k_\parallel$ Fourier space. The complement of the
foreground wedge is termed the "EoR window", and is expected to be mostly
foreground-free, allowing clean measurements of the power spectrum. This paper
is a sequel to a previous paper that established a rigorous mathematical
framework for describing the foreground wedge and the EoR window. Here, we use
our framework to explore statistical methods by which the EoR window can be
enlarged, thereby increasing the sensitivity of a power spectrum measurement.
We adapt the FKP approximation (commonly used in galaxy surveys) for 21 cm
cosmology, and also compare the optimal quadratic estimator to simpler
estimators that ignore covariances between different Fourier modes. The optimal
quadratic estimator is found to suppress foregrounds by an extra factor of
$\sim 10^5$ in power at the peripheries of the EoR window, boosting the
detection of the cosmological signal from $12\sigma$ to $50\sigma$ at the
midpoint of reionization in our fiducial models. If numerical issues can be
finessed, decorrelation techniques allow the EoR window to be further enlarged,
enabling measurements to be made deep within the foreground wedge. These
techniques do not assume that foreground are Gaussian-distributed, and we
additionally prove that a final round of foreground subtraction can be
performed after decorrelation in a way that is guaranteed to have no
cosmological signal loss.
