An Improved Statistical Point-Source Foreground Model for the Epoch of
  Reionization
  We present a sophisticated statistical point-source foreground model for
low-frequency radio Epoch of Reionization (EoR) experiments using the 21 cm
neutral hydrogen emission line. Motivated by our understanding of the
low-frequency radio sky, we enhance the realism of two model components
compared with existing models: the source count distributions as a function of
flux density and spatial position (source clustering), extending current
formalisms for the foreground covariance of 2D power spectral modes in 21 cm
EoR experiments. The former we generalise to an arbitrarily broken power-law,
and the latter to an arbitrary isotropically-correlated field. This paper
presents expressions for the modified covariance under these extensions, and
shows that for a more realistic source spatial distribution, extra covariance
arises in the EoR window which was previously unaccounted for. Failure to
include this contribution can yield bias in the final power spectrum and
under-estimate uncertainties, potentially leading to a false detection of
signal. The extent of this effect is uncertain, owing to ignorance of physical
model parameters, but we show that it is dependent on the relative abundance of
faint sources, to the effect that our extension will become more important for
future deep surveys. Finally, we show that under some parameter choices,
ignoring source clustering can lead to false detections on large scales, due to
both the induced bias and an artificial reduction in the estimated measurement
uncertainty.
