Calibration schemes with O(N log N) scaling for large-N radio interferometers built on a regular grid

Abstract

ABSTRACT Future generations of radio interferometers targeting the 21 cm signal at cosmological distances with N ≫ 1000 antennas could face a significant computational challenge in building correlators with the traditional architecture, whose computational resource requirement scales as $\mathcal {O}(N^2)$ with array size. The fundamental output of such correlators is the cross-correlation products of all antenna pairs in the array. The FFT-correlator architecture reduces the computational resources scaling to $\mathcal {O}(N\log {N})$ by computing cross-correlation products through a spatial Fourier transform. However, the output of the FFT-correlator is meaningful only when the input antenna voltages are gain- and phase-calibrated. Traditionally, interferometric calibration has used the $\mathcal {O}(N^2)$ cross-correlations produced by a standard correlator. This paper proposes two real-time calibration schemes that could work in parallel with an FFT-correlator as a self-contained $\mathcal {O}(N\log {N})$ correlator system that can be scaled to large-N redundant arrays. We compare the performance and scalability of these two calibration schemes and find that they result in antenna gains whose variance decreases as 1/log N with increase in the size of the array.