  Recent studies on stellar evolution have shown that the properties of compact
objects strongly depend on the metallicity of the environment in which they
were formed. Using some very simple assumptions on the metallicity of the
stellar populations, we explore how this property affects the unresolved
gravitational-wave background from extragalactic compact binaries. We obtained
a suit of models using population synthesis code, estimated the
gravitational-wave background they produce, and discuss its detectability with
second- (advanced LIGO, advanced Virgo) and third- (Einstein Telescope)
generation detectors. Our results show that the background is dominated by
binary black holes for all considered models in the frequency range of
terrestrial detectors, and that it could be detected in most cases by advanced
LIGO/Virgo, and with Einstein Telescope with a very high signal-to-noise ratio.
The observed peak in a gravitational wave spectrum depends on the metallicity
of the stellar population.
