Overcoming real-world obstacles in 21 cm power spectrum estimation: A
  method demonstration and results from early Murchison Widefield Array data
  We present techniques for bridging the gap between idealized inverse
covariance weighted quadratic estimation of 21 cm power spectra and the
real-world challenges presented universally by interferometric observation. By
carefully evaluating various estimators and adapting our techniques for large
but incomplete data sets, we develop a robust power spectrum estimation
framework that preserves the so-called "EoR window" and keeps track of
estimator errors and covariances. We apply our method to observations from the
32-tile prototype of the Murchinson Widefield Array to demonstrate the
importance of a judicious analysis technique. Lastly, we apply our method to
investigate the dependence of the clean EoR window on frequency--especially the
frequency dependence of the so-called "wedge" feature--and establish upper
limits on the power spectrum from z = 6.2 to z = 11.7. Our lowest limit is
Delta(k) < 0.3 Kelvin at 95% confidence at a comoving scale k = 0.046 Mpc^-1
and z = 9.5.
