Algorithms for FFT Beamforming Radio Interferometers. (arXiv:1710.08591v2 [astro-ph.IM] UPDATED)

Algorithms for FFT Beamforming Radio Interferometers. (arXiv:1710.08591v2 [astro-ph.IM] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Masui_K/0/1/0/all/0/1">Kiyoshi W. Masui</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Shaw_J/0/1/0/all/0/1">J. Richard Shaw</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Ng_C/0/1/0/all/0/1">Cherry Ng</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Smith_K/0/1/0/all/0/1">Kendrick M. Smith</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Vanderlinde_K/0/1/0/all/0/1">Keith Vanderlinde</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Paradise_A/0/1/0/all/0/1">Adiv Paradise</a>

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
$mathcal{O}(nlog n)$. 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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