  We explore the ability of observations of the global brightness temperature
of the 21-cm signal to constrain the reionization history and the properties of
the ionizing sources. In order to describe the reionization signal, we employ
either a commonly-used toy model or a structure formation model that
parameterizes the properties of the ionizing sources. If the structure
formation model captures the actual evolution of the reionization signal, then
detecting the signal is somewhat easier than it would be for the toy model;
using the toy model in this case also leads to systematic errors in
reconstructing the reionization history, though a sufficiently sensitive
experiment should be able to distinguish between the two models. We show that
under optimistic assumptions regarding systematic noise and foreground removal,
one-year observations of the global 21-cm spectrum should be able to detect a
wide range of realistic models and measure the main features of the
reionization history while constraining the key properties of the ionizing
sources.
