  This paper reports on a detailed performance characterization of a recently
developed optical single-sideband (OSSB) laser system based on an IQ modulator
and second-harmonic generation for rubidium atom interferometry experiments.
The measured performance is used to evaluate the noise contributions of this
OSSB laser system when it is applied to drive stimulated Raman transitions in
$^{87}$Rb for precision measurements of gravitational acceleration. The laser
system suppresses unwanted sideband components, but additional phase shift
compensation needs to be applied when performing frequency chirps with such an
OSSB laser system. The total phase noise contribution of the OSSB laser system
in the current experiment is 72 mrad for a single atom-interferometry sequence
with interrogation times of $T=120$ ms, which corresponds to a relative
precision of 32 n$g$ per shot. The dominant noise sources are found in the
relative intensity fluctuations between sideband and carrier components and the
phase noise of the microwave source.
