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Telescopes aiming to measure 21cm emission from the Epoch of Reionizationmust toe a careful line, balancing the need for raw sensitivity against thestringent calibration requirements for removing bright foregrounds. It isunclear what the optimal design is for achieving both of these goals. Via apedagogical derivation of an interferometer's response to the power spectrum of21cm reionization fluctuations, we show that even under optimistic scenarios,first-generation arrays will yield low-SNR detections, and that differentcompact array configurations can substantially alter sensitivity. We explorethe sensitivity gains of array configurations that yield high redundancy in theuv-plane -- configurations that have been largely ignored since the advent ofself-calibration for high-dynamic-range imaging. We first introduce amathematical framework to generate optimal minimum-redundancy configurationsfor imaging. We contrast the sensitivity of such configurations withhigh-redundancy configurations, finding that high-redundancy configurations canimprove power-spectrum sensitivity by more than an order of magnitude. Weexplore how high-redundancy array configurations can be tuned to variousangular scales, enabling array sensitivity to be directed away from regions ofthe uv-plane (such as the origin) where foregrounds are brighter and whereinstrumental systematics are more problematic. We demonstrate that a132-antenna deployment of the Precision Array for Probing the Epoch ofReionization (PAPER) observing for 120 days in a high-redundancy configurationwill, under ideal conditions, have the requisite sensitivity to detect thepower spectrum of the 21cm signal from reionization at a 3\sigma level atk<0.25h Mpc^{-1} in a bin of \Delta ln k=1. We discuss the tradeoffs of low-versus high-redundancy configurations.

A Sensitivity and Array-Configuration Study for Measuring the Power Spectrum of 21cm Emission from Reionization