  Using both the self-consistent Bogoliubov-de Gennes formulation and
non-self-consistent T-matrix approach, we perform a comprehensive investigation
of the in-gap bound states induced by a localized single impurity in iron-based
superconductors. We focus on studying signatures associated with the
unconventional sign-changed s-wave pairing symmetry. For a non-magnetic
impurity, we find that there are two in-gap bounds, symmetric with respect to
zero energy, only in the sign changed s-wave pairing state, not in the
sign-unchanged s-wave state, due to the existence of non-trivial Andreev bound
states caused by the sign change. For a magnetic impurity, we find that due to
the breakdown of the local time-reversal symmetry, there exist only bound state
solutions (with orbital degeneracy) carrying one of the electron-spin
polarizations around the impurity. As increasing the scattering strength, the
system undergoes a quantum phase transition (level crossing) from a
spin-unpolarized ground state to a spin-polarized one. While the results for
the magnetic impurity are qualitatively similar in both the sign-changed and
sign-unchanged s-wave superconducting states, the bound states in the first
case are more robust and there is no $\pi$ phase shift of the SC gap near the
impurity in the strong scattering regime.
