  We quantify the effect of radio frequency interference (RFI) on measurements
of the 21-cm power spectrum during the Epoch of Reionization (EoR).
Specifically, we investigate how the frequency structure of RFI source emission
generates contamination in higher-order wave modes that is much more
problematic than smooth-spectrum foreground sources. Using a relatively
optimistic EoR model, we find that even a single relatively dim RFI source can
overwhelm the EoR power spectrum signal of $\sim10\text{ mK}^2$ for modes $0.1
\text{ }h\text{ Mpc}^{-1} < k < 2 \text{ }h\text{ Mpc}^{-1}$. If total apparent
RFI flux density in the final power spectrum integration is kept below 1 mJy,
an EoR signal resembling this optimistic model should be detectable for modes
$k < 0.9\text{ }h\text{ Mpc}^{-1}$, given no other systematic contaminants and
an error tolerance as high as 10%. More pessimistic models will be more
restrictive. These results emphasize the need for highly effective RFI
mitigation strategies for telescopes used to search for the EoR.
