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Observation of redshifted 21-cm signals from neutral hydrogen holds the keyto understanding the structure formation and its evolution during thereionization and post-reionization era. Apart from the presence of orders ofmagnitude larger foregrounds in the observed frequency range, the instrumentaleffects of the interferometers combined with the ionospheric effects present aconsiderable challenge in the extraction of 21-cm signals from strongforegrounds. The systematic effects of time and frequency correlated residualgain errors originating from the measurement process introduce a bias andenhance the variance of the power spectrum measurements. In this work, we studythe effect of time-correlated residual gain errors in the presence of strongforeground. We present a method to produce analytic estimates of the bias andvari ance in the power spectrum. We use simulated observations to confirm theefficacy of this method and then use it to understand various effects of thegain errors. We find that as the standard deviation in the residual gain errorsincreases, the bias in the estimation supersedes the variance. It is observedthat an optimal choice of the time over which the gain solutions are estimatedminimizes the risk. We also find that the interferometers with higher baselinedensities are preferred instruments for these studies.

monthly notices of the royal astronomical society

Calibration requirements for Epoch of Reionization 21-cm signal  observations -- II. Analytical estimation of the bias and variance with  time-correlated residual gains