A closed-form subspace calibration algorithm for large radio astronomical phased arrays

Calibration of phased array systems is essential to achieve desired system performance. In radio astronomy, this challenge is compounded by the scale of these instruments, which necessitates an approach called self-calibration, in which the observed radio astronomical sources are used for calibration. This requires joint computation of complex-valued receive path gains and source powers of calibration sources in known locations. The problem is compounded by the differences in noise powers between the receive paths. Therefore, existing methods usually resort to iterative algorithms. In this paper, we propose the Calibration of Large Arrays by Sub-Spaces (CLASS) algorithm, providing a closed-form solution based on the data model for this problem. Application to actual data from the Low-Frequency Array (LOFAR) telescope shows that the CLASS method has similar accuracy to the current state-of-the-art technique while, advantageously, operating in a fully automated manner and requiring fewer computational resources.