  We study properties of gravitational waves (GWs) from rotating core-collapse
of a 15M_odot star by performing three-dimensional general-relativistic
hydrodynamic simulations with an approximate neutrino transport. By
parametrically changing the precollapse angular momentum, we focus on the
effects of rotation on the GW signatures in the early postbounce evolution.
Regarding three-flavor neutrino transport, we solve the energy-averaged set of
radiation energy and momentum based on the Thorne's momentum formalism. In
addition to the gravitational quadrupole radiation from matter motions, we take
into account GWs from anisotropic neutrino emission. With these computations,
our results present several supporting evidences for the previous anticipation
that non-axisymmetric instabilities play an essential role in determining the
postbounce GW signatures. During prompt convection, we find that the waveforms
show narrow-band and highly quasi-periodic signals which persist until the end
of simulations. We point out that such feature reflects the growth of the
one-armed spiral modes. The typical frequency of the quasi-periodic waveforms
can be well explained by the propagating acoustic waves between the stalled
shock and the rotating proto-neutron star surface, which suggests the
appearance of the standing-accretion-shock instability. Although the GW signals
exhibit strong variability between the two polarizations and different observer
directions, they are within the detection limits of next generation detectors
such as by KAGRA and Advanced LIGO, if the source with sufficient angular
momentum is located in our Galaxy.
