  Massive black hole binaries, with masses in the range 1E3-1E8 Msun, are
expected to be the most powerful sources of gravitational radiation at mHz
frequencies, and hence are among the primary targets for the planned Laser
Interferometer Space Antenna (LISA). We extend and refine our previous analysis
(Sesana et al. 2004), detailing the gravitational wave signal expected from a
cosmological population of massive black hole binaries. As done in our previous
paper, we follow the merger history of dark matter halos, the dynamics of the
massive black holes they host, and their growth via gas accretion and binary
coalescences in a LCDM cosmology. Stellar dynamical processes dominates the
orbital evolution of black hole binaries at large separations, while
gravitational wave emission takes over at small radii, causing the final
coalescence of the pairs. We show that the GW signal from this population, in a
3 year LISA observation, will be resolved into approx 90 discrete events with
S/N>5, among which approx. 35 will be observed above threshold until
coalescence. These "merging events" involve relatively massive binaries, M=10E5
Msun, in the redshift range 2<z<6. The remaining approx. 55 events come from
higher redshift, less massive binaries (M=5E3 Msun at z>6) and, although their
S/N integrated over the duration of the observation can be substantial, the
final coalescence phase is at too high frequency to be directly observable by
space-based interferometers such as LISA. LISA will be able to detect a
fraction approx. 90% of all the coalescences of massive black hole binaries
occurring at z=5. The residual confusion noise from unresolved massive black
hole binaries is expected to be at least an order of magnitude below the
estimated stochastic noise.
