  The gravitational wave radiation emitted by all, resolved and unresolved,
astrophysical sources in the observable universe generates a stochastic
background. This background has a directional dependence inherited from the
inhomogeneities of the matter distribution. This article proposes a new and
independent derivation of the angular dependence of its energy density by
focusing on the total gravitational wave signal produced by an ensemble of
incoherent sources. This approach clarifies the origin of the angular
correlation and the relation between the gravitational wave signal that can be
measured by interferometers and the energy density of the stochastic
background.
