On Measuring the 21 cm Global Spectrum of the Cosmic Dawn with an Interferometer Array

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.