Impact of station size on calibration of SKA-low

The size of SKA-Low stations affects calibration of the instrument, and the science that can be performed. We analyse the differences in instrumental calibration when varying station size, for a fixed total effective area and array layout. The Cramer-Rao Bound (CRB) is used as a metric to quantify the theoretical optimal performance for estimating direction-dependent station gains (amplitude and phase), in the presence of radiometric (thermal) noise and noise from unmodelled background point sources, and for multiple field calibrators. The multiplicity of the calibrators is approximated by the ratio of the station field-of-view (FOV) to the ionospheric isoplanatic patch size. Smaller stations have larger sky FOV, increasing both the noise from unmodelled background sources and number of calibrators required to determine the full gain characteristics, but are calibrated with a larger number of measurements (more baselines) compared with larger stations. We find that the number of calibrators has little impact on the estimation precision, and the results depend on the noise characteristics of the data. For thermal noise-dominated datasets, larger stations yield improved estimation performance. For datasets where unmodelled background point sources dominate the error budget, performance is comparable for large and small stations.