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Several experiments are underway to detect the cosmic-redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signal's power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation and parameter estimation pipeline developed for the Low-Frequency Array (LOFAR) -EoR experiment. We show that LOFAR should be able to detect the EoR in 600 h of integration using the variance statistic. Additionally, the redshift (zr) and duration (Δz) of reionization can be constrained assuming a parametrization. We use an EoR simulation of zr = 7. 68 and Δz = 0. 43 to test the pipeline. We are able to detect the simulated signal with a significance of four standard deviations and extract the EoR parameters as |z ₑ = 7. 72^+0. 37-₀. ₁₈| and | z = 0. 53^+0. 12-₀. ₂₃| in 600 h, assuming that systematic errors can be adequately controlled. We further show that the significance of detection and constraints on EoR parameters can be improved by measuring the cross-variance of the signal by cross-correlating consecutive redshift bins.
Patil et al. (Mon,) studied this question.