astrophysics. There are other observations to measure the EoR. For example, the optical depth to the Thomson scattering of the Cosmic Microwave Background (CMB) photons constrains the duration of the reionization , and the decreasing of the Lyman-$\alpha$ emitter luminosity function yields the neutral fraction at $z>6$ [@2010ApJ...723..869O].

In particular, the 21cm line signal produced from the hyperfine structure of ${\ion{H}{i}}$ is a promising tool to probe the EoR. As the redshifted 21cm line is observed as a function of frequency, one can measure the 21cm line signal along the line of sight. Thus, the redshifted 21cm line provides the 3 dimensional distribution of ${\ion{H}{i}}$ gas, and we can study, for example, the nature of ionizing sources and precise history of reionization via the topology of ionized gases and its statistical property. The power spectrum is a common tool to characterize the parameters of the reionization model (e.g. [@2015MNRAS.449.4246G]).

The redshifted 21cm line signal is observed by radio telescopes. There are many ongoing experiments, such as the the Giant Metrewave Radio Telescope EoR Experiment (GMRT, [@2013MNRAS.433..639P]), the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER, [@2010AJ....139.1468P]), the LOw Frequency ARray (LOFAR, ), and the Murchison Widefield 