  Detection of the global redshifted 21-cm signal is an excellent means of
deciphering the physical processes during the Dark Ages and subsequent Epoch of
Reionization (EoR). However, detection of this faint monopole is challenging
due to high precision required in instrumental calibration and modeling of
substantially brighter foregrounds and instrumental systematics. In particular,
modeling of receiver noise with mK accuracy and its separation remains a
formidable task in experiments aiming to detect the global signal using
single-element spectral radiometers. Interferometers do not respond to receiver
noise; therefore, we explore here the theory of the response of interferometers
to global signals. In other words, we discuss the spatial coherence in the
electric field arising from the monopole component of the 21-cm signal and
methods for its detection using sensor arrays. We proceed by first deriving the
response to uniform sky of two-element interferometers made of unit dipole and
resonant loop antennas, then extend the analysis to interferometers made of 1-D
arrays and also consider 2-D aperture antennas. Finally, we describe methods by
which the coherence might be enhanced so that the interferometer measurements
yield improved sensitivity to the monopole component. We conclude that (a) it
is indeed possible to measure the global 21-cm from EoR using interferometers,
(b) a practically useful configuration is with omnidirectional antennas as the
interferometer elements, and (c) that the spatial coherence may be enhanced and
detectability of the global EoR signal may be smoothened using, for example, a
space beam splitter between the interferometer elements.
