Calibration Requirements for Epoch of Reionization 21-cm signal
  observations -- I. Effect of time-correlated gains
  The residual gain errors add to the systematics of the radio interferometric
observations. In case of the high dynamic range observations, these systematic
effects dominates over the thermal noise of the observation. In this work, we
investigate the effect of time-correlated residual gain errors in the
estimation of the power spectrum of the sky brightness distribution in high
dynamic range observations. Particularly, we discuss a methodology to estimate
the bias in the power spectrum estimator of the redshifted 21-cm signal from
neutral hydrogen in the presence of bright extragalactic compact sources. We
find, that for the visibility based power spectrum estimators, particularly
those use nearby baseline correlations to avoid noise bias, the bias in the
power spectrum arises mainly from the time correlation in the residual gain
error. The bias also depends on the baseline distribution for a particular
observation. Analytical calculations show that the bias is dominant for certain
types of baseline pairs used for the visibility correlation. We perform
simulated observation of extragalactic compact sources in the presence of
residual gain errors with the GMRT like array and estimate the bias in the
power spectrum. Our results indicate that in order to estimate the redshifted
21-cm power spectrum, better calibration techniques and estimator development
are required.
