A method to determine the evolution history of the mean neutral Hydrogen
  fraction
  The light-cone (LC) effect imprints the cosmological evolution of the
redshifted 21-cm signal $T_{\rm b} ({\hat{\bf{n}}}, \nu)$ along the frequency
axis which is the line of sight (LoS) direction of an observer. The effect is
particularly pronounced during the Epoch of Reionization (EoR) when the mean
hydrogen neutral fraction ${\bar{x}_{\rm HI}}(\nu)$ falls rapidly as the
universe evolves. The multi-frequency angular power spectrum (MAPS) ${{\mathcal
C}_{\ell}}(\nu_1,\nu_2)$ quantifies the entire second-order statistics of
$T_{\rm b} ({\hat{\bf{n}}}, \nu)$ considering both the systematic variation
along $\nu$ due to the cosmological evolution and also the statistically
homogeneous and isotropic fluctuations along all the three spatial directions
encoded in ${\hat{\bf{n}}}$ and $\nu$. Here we propose a simple model where the
systematic frequency $(\nu_1,\nu_2)$ dependence of ${{\mathcal
C}_{\ell}}(\nu_1,\nu_2)$ arises entirely due to the evolution of ${\bar{x}_{\rm
HI}}(\nu)$. This provides a new method to observationally determine the
reionization history. Considering a LC simulation of the EoR 21-cm signal, we
use the diagonal elements $\nu_1=\nu_2$ of ${{\mathcal C}_{\ell}}(\nu_1,\nu_2)$
to validate our model. We demonstrate that it is possible to recover the
reionization history across the entire observational bandwidth provided we have
the value ${\bar{x}_{\rm HI}}$ at a single frequency as an external input.
