  We study the phase fluctuations in the normal state of generic
two-dimensional superconducting systems with s-wave pairing. The effect of
phase fluctuations of the pairing fields can be dealt with perturbatively using
disorder averaging, after we treat the local superconducting order parameter as
a static disordered background. It is then confirmed that the phase
fluctuations above the two-dimensional Berezinskii-Kosterlitz-Thouless
transition lead to a significant broadening of the single-particle spectrum,
giving birth to the pseudogap phenomenon. Quantitatively, the broadening of
spectral weights near the BCS gap is characterized by the ratio of the
superconducting coherence length and the spatial correlation length of the
superconducting pairing order parameter. Our results are tested on the
fermionic attractive-U Hubbard model on the square lattice, using the unbiased
determinant quantum Monte Carlo method and stochastic analytic continuation.
