  We investigate the evolution of supermassive binary black holes (BBHs) in
galaxies with realistic property distributions and the gravitational-wave (GW)
radiation from the cosmic population of these BBHs. We incorporate a
comprehensive treatment of the dynamical interactions of the BBHs with their
environments by including the effects of galaxy triaxial shapes and inner
stellar distributions, and generate a large number of BBH evolution tracks. By
combining these BBH evolution tracks, galaxy mass functions, galaxy merger
rates, and supermassive black hole-host galaxy relations into our model, we
obtain the statistical distributions of surviving BBHs, BBH coalescence rates,
the strength of their GW radiation, and the stochastic GW background (GWB)
contributed by the cosmic BBH population. About ~1%-3% (or ~10%) of
supermassive BHs at nearby galactic centers are expected to be binaries with
mass ratio >1/3 (or >1/100). The characteristic strain amplitude of the GWB at
frequency 1/yr is estimated to be ~$2.0^{+1.4}_{-0.8}\times 10^{-16}$, and the
upper bound of its results obtained with the different BH-host galaxy relations
can be up to $5.4\times 10^{-16}$, which await testing by future experiments
(e.g., the Square Kilometer Array, FAST, Next-Generation Very Large Array). The
turnover frequency of the GWB spectrum is at ~0.25nHz. The uncertainties on the
above estimates and prospects for detecting individual sources are also
discussed. The application of the cosmic BBH population to the Laser
Interferometer Space Antenna (LISA) band provides a lower limit to the
detection rate of BBHs by LISA, ~0.9/yr.
