  Several experimental efforts are underway to measure the power spectrum of
21cm fluctuations from the Epoch of Reionization (EoR) using low-frequency
radio interferometers. Experiments like the Hydrogen Epoch of Reionization
Array (HERA) and Murchison Widefield Array Phase II (MWA) feature
highly-redundant antenna layouts, building sensitivity through redundant
measurements of the same angular Fourier modes, at the expense of diminished UV
coverage. This strategy limits the numbers of independent samples of each power
spectrum mode, thereby increasing the effect of sample variance on the final
power spectrum uncertainty. To better quantify this effect, we measure the
sample variance of a delay-transform based power spectrum estimator, using both
analytic calculations and simulations of flat-spectrum EoR-like signals. We
find that for the shortest baselines in HERA, the sample variance can reach as
high as 20%, and up to 30% for the wider fields-of-view of the MWA. Combining
estimates from all the baselines in a HERA- or MWA-like 37 element redundant
hexagonal array can lower the variance to $1-3$% for some Fourier modes. These
results have important implications for observing and analysis strategies, and
suggest that sample variance can be non-negligible when constraining EoR model
parameters from upcoming 21cm data.
