Calibration of an SKA-Low Prototype Station Using Holographic Techniques

Performance of digitally beamformed phased arrays relies on accurate calibration of the array by obtaining gains of each antenna in the array. The stations of the Square Kilometer Array-Low (SKA-Low) are such digital arrays, where the station calibration is currently performed using conventional interferometric techniques. An alternative calibration technique similar to holography of dish based telescopes has been suggested in the past. In this paper, we develop a novel mathematical framework for holography employing tensors, which are multi-way data structures. Self-holography using a reference beam formed with the station under test itself and cross-holography using a different station to obtain the reference beam are unified under the same formalism. Besides, the relation between the two apparently distinct holographic approaches in the literature for phased arrays is shown, and we show that under certain conditions the two methods yield the same results. We test the various holographic techniques on an SKA-Low prototype station Aperture Array Verification System 2 (AAVS2) with the Sun as the calibrator. We perform self-holography of AAVS2 and cross-holography with simultaneous observations carried out with another station Engineering Development Array 2. We find the results from the holographic techniques to be consistent among themselves as well as with a more conventional calibration technique.

Singular spectrum analysis of time series data from low frequency radiometers, with an application to SITARA data

Understanding the temporal characteristics of data from low frequency radio telescopes is of importance in devising suitable calibration strategies. Application of time series analysis techniques to data from radio telescopes can reveal a wealth of information that can aid in calibration. In this paper, we investigate singular spectrum analysis (SSA) as an analysis tool for radio data. We show the intimate connection between SSA and Fourier techniques. We develop the relevant mathematics starting with an idealised periodic dataset and proceeding to include various non-ideal behaviours. We propose a novel technique to obtain long-term gain changes in data, leveraging the periodicity arising from sky drift through the antenna beams. We also simulate several plausible scenarios and apply the techniques to a 30-day time series data collected during June 2021 from SITARA - a short-spacing two element interferometer for global 21-cm detection. Applying the techniques to real data, we find that the first reconstructed component - the trend - has a strong anti-correlation with the local temperature suggesting temperature fluctuations as the most likely origin for the observed variations in the data. We also study the limitations of the calibration in the presence of diurnal gain variations and find that such variations are the likely impediment to calibrating SITARA data with SSA.