  A critical challenge in measuring the power spectrum of 21cm emission from
cosmic reionization is compensating for the frequency dependence of an
interferometer's sampling pattern, which can cause smooth-spectrum foregrounds
to appear unsmooth and degrade the separation between foregrounds and the
target signal. In this paper, we present an approach to foreground removal that
explicitly accounts for this frequency dependence. We apply the delay
transformation introduced in Parsons & Backer (2009) to each baseline of an
interferometer to concentrate smooth-spectrum foregrounds within the bounds of
the maximum geometric delays physically realizable on that baseline. By
focusing on delay-modes that correspond to image-domain regions beyond the
horizon, we show that it is possible to avoid the bulk of smooth-spectrum
foregrounds. We map the point-spread function of delay-modes to k-space,
showing that delay-modes that are uncorrupted by foregrounds also represent
samples of the three-dimensional power spectrum, and can be used to constrain
cosmic reionization. Because it uses only spectral smoothness to differentiate
foregrounds from the targeted 21cm signature, this per-baseline analysis
approach relies on spectrally- and spatially-smooth instrumental responses for
foreground removal. For sufficient levels of instrumental smoothness relative
to interfering foregrounds, this technique substantially reduces the level of
calibration previously thought necessary to detect 21cm reionization. As a
result, this approach places fewer constraints on antenna configuration within
an array, facilitating the adoption of configurations optimized for
power-spectrum sensitivity. Under these assumptions, we demonstrate the
potential for PAPER to detect 21cm reionization at an amplitude of 10 mK^2 near
k~0.2h Mpc^-1 with 132 dipoles in 7 months of observing.
