  The coalescence of massive black hole (BH) binaries due to galaxy mergers
provides a primary source of low-frequency gravitational radiation detectable
by pulsar timing measurements and by the proposed LISA (Laser Interferometry
Space Antenna) observatory. We compute the expected gravitational radiation
signal from sources at all redshifts by combining the predicted merger rate of
galactic halos with recent measurements of the relation between BH mass, M_bh,
and the velocity dispersion of its host galaxy, sigma. Our main findings are as
follows: (i) the nHz frequency background is dominated by BH binaries at
redshifts z<2, and existing limits from pulsar timing data place tight
constraints on the allowed normalization and power-law slope of the M_bh-sigma
relation or on the fraction of BH binaries that proceed to coalescence; (ii)
more than half of all discrete mHz massive BH sources detectable by LISA are
likely to originate at redshifts z>7; (iii) the number of LISA sources per unit
redshift per year should drop substantially after reionization as long as BH
formation is triggered by gas cooling in galaxies. Studies of the highest
redshift sources among the few hundred detectable events per year, will provide
unique information about the physics and history of black hole growth in
galaxies.
