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arXiv · 1710.08591

Algorithms for FFT Beamforming Radio Interferometers

Kiyoshi W. Masui·J. Richard Shaw·Cherry Ng·Kendrick M. Smith·Keith Vanderlinde·Adiv Paradise
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Abstract

Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from $\mathcal{O}(n^2)$ in the number of antennas to $\mathcal{O}(n\log n)$. We develop a formalism for describing this process and apply this formalism to derive a number of algorithms with a range of observational applications. These include algorithms for forming arbitrarily pointed tied-array beams from the regularly spaced Fourier-transform formed beams, sculpting the beams to suppress sidelobes while only losing percent-level sensitivity, and optimally estimating the position of a detected source from its observed brightness in the set of beams. We also discuss the effect that correlations in the visibility-space noise, due to cross-talk and sky contributions, have on the optimality of Fourier transform beamforming, showing that it does not strictly preserve the sky information of the $n^2$ correlation, even for an idealized array. Our results have applications to a number of upcoming interferometers, in particular the Canadian Hydrogen Intensity Mapping Experiment--Fast Radio Burst (CHIME/FRB) project.

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Kiyoshi W. Masui, J. Richard Shaw, Cherry Ng, Kendrick M. Smith, Keith Vanderlinde, Adiv Paradise. 2017-10-24. Algorithms for FFT Beamforming Radio Interferometers. https://arxiv.org/abs/1710.08591

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