Calibration requirement for Epoch of Reionization 21-cm signal observation – III. Bias and variance in uGMRT ELAIS-N1 field power spectrum

Power spectrum of 21 cm radiation is one of the promising probes to study large scale structure of the universe. Presence of orders of magnitude larger foregrounds in the frequency range for such observations has been one of the major challenge. The foreground contamination also introduce residual calibration errors in the interferometric data. The latter introduce bias in the 21-cm power spectrum estimates and increase systematics. There have been several efforts to understand and improve on the calibration errors. In this work we use an analytical estimate of the bias and variance in redshifted 21-cm power spectrum in presence of time-correlated residual gain errors and foreground. We use the uGMRT Band-3 observations of the ELAIS-N1 field and estimate the bias and variance in the power spectrum from these observation. We first access the statistics of the gain errors and based on the quality of calibration we flag a set of additional antennae. The latter reduce the bias and variance of power spectrum significantly and we found it to be recommended for such analysis. We observe that for the uGMRT baseline configuration and system parameters, the variance is always higher than the bias. The excess variance in the power spectrum reduces with increase of the angular scales and at about ℓ∼6000 the effects from residual gain errors are negligible. Based on our analysis we observe that for an angular multipole of ℓ∼3000, 2000 hours of `on source time' is required with uGMRT to detect redshifted 21-cm signal at 3-σ significance from a redshift of 2.55. In this work we only consider the power spectrum measurement in the plane of the sky, an assessment of residual gain statistics and its effect on multifrequency angular power spectrum estimation will be presented in a companion paper.