Unlocking Sensitivity for Visibility-based Estimators of the 21 cm
  Reionization Power Spectrum
  Radio interferometers designed to measure the cosmological 21 cm power
spectrum require high sensitivity. Several modern low-frequency interferometers
feature drift-scan antennas placed on a regular grid to maximize the number of
instantaneously coherent (redundant) measurements. However, even for such
maximum-redundancy arrays, significant sensitivity comes through partial
coherence between baselines. Current visibility-based power-spectrum pipelines,
though shown to ease control of systematics, lack the ability to make use of
this partial redundancy. We introduce a method to leverage partial redundancy
in such power-spectrum pipelines for drift-scan arrays. Our method
cross-multiplies baseline pairs at a time lag and quantifies the sensitivity
contributions of each pair of baselines. Using the configurations and beams of
the 128-element Donald C. Backer Precision Array for Probing the Epoch of
Reionization (PAPER-128) and staged deployments of the Hydrogen Epoch of
Reionization Array, we illustrate how our method applies to different arrays
and predict the sensitivity improvements associated with pairing partially
coherent baselines. As the number of antennas increases, we find partial
redundancy to be of increasing importance in unlocking the full sensitivity of
upcoming arrays.
