  We present a broadband spectropolarimetric survey of 563 discrete, mostly
unresolved radio sources between 1.3 \& 2.0 GHz using data taken with the
Australia Telescope Compact Array (ATCA). We have used rotation measure
synthesis to identify Faraday complex polarized sources --- i.e. objects whose
frequency-dependent polarization behaviour indicates the presence of material
possessing complicated magnetoionic structure along the line of sight (LOS).
For sources classified as Faraday complex, we have analyzed a number of their
radio and multiwavelength properties to determine whether they differ from
Faraday simple polarized sources (i.e. sources for which LOS magnetoionic
structures are comparatively simple) in these properties. We use this
information to constrain the physical nature of the magnetoionic structures
responsible for generating the observed complexity. We detect Faraday
complexity in 12\% of polarized sources at $\sim1'$ resolution, but demonstrate
that underlying signal-to-noise limitations mean the true percentage is likely
to be significantly higher in the polarized radio source population. We find
that the properties of Faraday complex objects are diverse, but that complexity
is most often associated with depolarization of extended radio sources
possessing a relatively steep total intensity spectrum. We find an association
between Faraday complexity and LOS structure in the Galactic interstellar
medium (ISM), and claim that a significant proportion of the Faraday complexity
we observe may be generated at interfaces of the ISM associated with ionization
fronts near neutral hydrogen structures. Galaxy clusters environments and
internally generated Faraday complexity provide possible alternative
explanations in some cases.
