  SU(1,1) interferometers, based on the usage of nonlinear elements, are
superior to passive interferometers in phase sensitivity. However, the SU(1,1)
interferometer cannot make full use of photons carrying phase information as
the second nonlinear element annihilates some of the photons inside. Here, we
focus on improving phase sensitivity and propose a new protocol based on a
modified SU(1,1) interferometer, where the second nonlinear element is replaced
by a beam splitter. We utilize two coherent states as inputs and implement
balanced homodyne measurement at the output. Our analysis suggests that the
protocol we propose can achieve sub-shot-noise-limited phase sensitivity and is
robust against photon loss and background noise. Our work is important for
practical quantum metrology using SU(1,1) interferometers.
