We theoretically investigate the recovery of global spectrum (monopole) from
visibilities (cross-correlation only) measured by the interferometer array and
the feasibility of extracting 21 cm signal of cosmic dawn. In our approach, the
global spectrum is obtained by solving the monopole and higher-order components
simultaneously from the visibilities measured with up to thousands of
baselines. Using this algorithm, the monopole of both foreground and the 21 cm
signal can be correctly recovered in a broad range of conditions. We find that
a 3D baseline distribution can have much better performance than a 2D (planar)
baseline distribution, particularly when there is a lack of shorter baselines.
We simulate for ground-based 2D and 3D array configurations, and a cross-shaped
space array located at the Sun-Earth L2 point that can form 3D baselines
through orbital precession. In all simulations we obtain good recovered global
spectrum, and successfully extract the 21 cm signal from it, with reasonable
number of antennas and observation time.Comment: 18 pages, 23 figures, accepted for publication in Ap
