  We investigate how to recover the spectral properties of underlying
magnetohydrodynamic (MHD) turbulence using fluctuation statistics of
synchrotron polarization radiation, based on the synthetic observations. Taking
spatially coincident, separated, and compounded synchrotron emission and
Faraday rotation regions into account, we extract the power spectrum of
synchrotron polarization intensities integrated along the line of sight. Our
results demonstrate that in the short wavelength range, the power spectra
reflect fluctuation statistics of the perpendicular component of turbulent
magnetic fields, and the spectra at long wavelengths reveal the fluctuation of
the Faraday rotation density, which is a product of the parallel component of
magnetic field and thermal electron density. We find that our numerical results
(in the case of spatially coincident regions) are in agreement with the
analytical prediction in Lazarian \& Pogosyan (2016), and this theoretical
prediction is applicable to more complicated settings, i.e., the spatially
separated and compounded regions. We simulate telescopic observations that
incorporate the effects of telescope angular resolution and noise, and find
that statistics of underlying MHD turbulence can be recovered successfully. We
expect that the technique can be applied to a variety of astrophysical
environments, with existing synchrotron data cubes and a large number of
forthcoming data sets from such as the LOw-Frequency Array for Radio astronomy
(LOFAR), the Square Kilometer Array (SKA) and the Five-hundred-meter Aperture
Spherical radio Telescope (FAST).
