Calibration requirements for Epoch of Reionization 21-cm signal observations - V. Bias and variance in the cylindrical power spectrum from uGMRT Band 3 observations of the ELAIS-N1 field

Detection of the redshifted 21-cm signal from neutral hydrogen requires precise control of systematic effects arising from instrumental calibration. In this work, we investigate the impact of both time- and frequency-dependent residual gain and bandpass errors on the estimation of the multifrequency angular power spectrum (MAPS) using radio interferometric observations. We discuss our previously developed analytical framework for estimating bias and excess variance in 21-cm signal MAPS in the presence of these residual errors and apply it to uGMRT Band-3 observations. The statistical properties of the residual gains are derived from the data themselves, including their temporal and spectral correlations. We introduce a robust technique for additionally flagging poor-quality data. Our results show that the excess variance induced by residual gain and bandpass errors dominates over the bias across the range of angular multipoles considered. The amplitude of this variance is comparable to the expected power spectrum upper limit at redshift $z \sim 2.2$, indicating that residual calibration errors can significantly affect the detectability of the 21-cm signal. We further transform the estimated MAPS into ($k_{\perp}, k_{ll}$) space and find the expected foreground wedge structure. Importantly, we observe a significant power leakage into the nominal EoR window, which we attribute to residual calibration systematics. This highlights that even after standard foreground mitigation, time- and frequency-correlated gain errors can introduce mode-mixing and contaminate the EoR window. Our results emphasise the necessity of improved calibration accuracy and robust characterisation of residual gain statistics for current and upcoming interferometric experiments such as the uGMRT and SKA, to enable reliable detection of the cosmological 21-cm signal.