  We compute the expected low-frequency gravitational wave signal from
coalescing massive black hole (MBH) binaries at the center of galaxies. We
follow the merging history of halos and associated holes via cosmological Monte
Carlo realizations of the merger hierarchy from early times to the present in a
LCDM cosmology. MBHs get incorporated through a series of mergers into larger
and larger halos, sink to the centre owing to dynamical friction, accrete a
fraction of the gas in the merger remnant to become more massive, and form a
binary system. Stellar dynamical processes dominates the orbital evolution of
the binary at large separations, while gravitational wave emission takes over
at small radii, causing the final coalescence of the system. We discuss the
observability of inspiraling MBH binaries by a low-frequency gravitational wave
experiment such as the planned Laser Interferometer Space Antenna (LISA),
discriminating between resolvable sources and unresolved confusion noise. Over
a 3-year observing period LISA should resolve this GWB into discrete sources,
detecting ~90 individual events above a S/N=5 confidence level, while expected
confusion noise is well below planned LISA capabilities.
