Maximum likelihood analysis of systematic errors in interferometric
  observations of the cosmic microwave background
  We investigate the impact of instrumental systematic errors in
interferometric measurements of the cosmic microwave background (CMB)
temperature and polarization power spectra. We simulate interferometric CMB
observations to generate mock visibilities and estimate power spectra using the
statistically optimal maximum likelihood technique. We define a quadratic error
measure to determine allowable levels of systematic error that do not induce
power spectrum errors beyond a given tolerance. As an example, in this study we
focus on differential pointing errors. The effects of other systematics can be
simulated by this pipeline in a straightforward manner. We find that, in order
to accurately recover the underlying B-modes for r=0.01 at 28<l<384,
Gaussian-distributed pointing errors must be controlled to 0.7^\circ rms for an
interferometer with an antenna configuration similar to QUBIC, in agreement
with analytical estimates. Only the statistical uncertainty for 28<l<88 would
be changed at ~10% level. With the same instrumental configuration, we find the
pointing errors would slightly bias the 2-\sigma upper limit of the
tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing
errors on the TB and EB measurements is negligibly small.
