Global CD/EoR Signal Detection with a Dense Digital Beamforming Array and Beyond

The global neutral hydrogen 21 cm signal extracted from the all-sky averaged radio spectra is one of the signatures of the Cosmic Dawn and Epoch of Reionization (CD/EoR). The frequency-dependency of antenna beam patterns coupled with the strong foreground emission could introduce artificial spectral structures and cause false detection. A digital beamforming array could be potentially employed to form achromatic station beam patterns to overcome this problem. In this work, we discuss the method of forming achromatic beam patterns with a dense regular beamforming array to detect the global CD/EoR signal, covering topics including the array configuration, antenna weight optimization, and error estimation. We also show that based on the equivalence between a beamforming array and an interferometer, most antennas in the array can be removed by canceling redundant baselines. We present an example array design, optimize the antenna weights, and show the final array configuration by canceling redundant baselines. The performance of the example array is evaluated based on a simulation, which provides a positive indication towards the feasibility of detecting the CD/EoR signal using a dense digital beamforming array.