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Visibility scintillation resulting from wave propagation through theturbulent ionosphere can be an important sources of noise at low radiofrequencies ($\nu\lesssim 200$ MHz). Many low frequency experiments areunderway to detect the power spectrum of brightness temperature fluctuations ofthe neutral-hydrogen $21$-cm signal from the Epoch of Reionization (EOR:$12\gtrsim z\gtrsim 7$, $100\lesssim \nu \lesssim 175$ MHz). In this paper, wederive scintillation noise power-spectra in such experiments while taking intoaccount the effects of typical data processing operations such asself-calibration and Fourier synthesis. We find that for minimally redundantarrays such as LOFAR and MWA, scintillation noise is of the same order ofmagnitude as thermal noise, has a spectral coherence dictated by stretching ofthe snapshot $uv$-coverage with frequency, and thus is confined to the wellknown wedge-like structure in the cylindrical ($2$-dimensional) power spectrumspace. Compact, fully redundant ($d_{\rm core}\lesssim r_{\rm F} \approx 300$ mat $150$ MHz) arrays such as HERA and SKA-LOW (core) will be scintillationnoise dominated at all baselines, but the spatial and frequency coherence ofthis noise will allow it to be removed along with spectrally smoothforegrounds.

Scintillation noise power spectrum and its impact on high redshift 21-cm observations