We investigate the isotropic and anisotropic components of the Stochastic Gravitational
Wave Background (SGWB) originated from unresolved merging compact binaries in
galaxies. We base our analysis on an empirical approach to galactic astrophysics that allows
to follow the evolution of individual systems. We then characterize the energy density of
the SGWB as a tracer of the total matter density, in order to compute the angular power
spectrum of anisotropies with the Cosmic Linear Anisotropy Solving System (CLASS) public
code in full generality. We obtain predictions for the isotropic energy density and for the
angular power spectrum of the SGWB anisotropies, and study the prospect for their observations
with advanced Laser Interferometer Gravitational-Wave and Virgo Observatories
and with the Einstein Telescope. We identify the contributions coming from different type
of sources (binary black holes, binary neutron stars and black hole-neutron star) and from
different redshifts. We examine in detail the spectral shape of the energy density for all types
of sources, comparing the results for the two detectors. We find that the power spectrum of
the SGWB anisotropies behaves like a power law on large angular scales and drops at small
scales: we explain this behavior in terms of the redshift distribution of sources that contribute
most to the signal, and of the sensitivities of the two detectors. Finally, we simulate a high
resolution full sky map of the SGWB starting from the power spectra obtained with CLASS
and including Poisson statistics and clustering properties.
