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 $sim10text{ mK}^2$ for modes $0.1 text{ }htext{ Mpc}^{-1} < k < 2 text{ }htext{ Mpc}^{-1}$. 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 $k < 0.9text{ }htext{ Mpc}^{-1}$, 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.
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