  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.
