Two versions of the X-mode Doppler reflectometry (DR) synthetic diagnostics are developed within the framework of the ELMFIRE global gyrokinetic modeling of the FT-2 tokamak ohmic discharge. In the ‘fast’ version the DR signal is computed in the linear theory approximation using the reciprocity theorem, utilizing the probing wave field pattern provided by computation and taking into account the 2D plasma inhomogeneity effects; whereas the alternative ‘slow’ version DR synthetic diagnostic is based on the full-wave code IPF-FD3D describing the probing and scattered wave propagation in turbulent plasma. The DR signal frequency spectra and the dependence of their frequency shift, width and shape on the probing antenna position are computed and shown to be similar to those measured in the high-field side probing DR experiment at the FT-2 tokamak. The geodesic acoustic mode characteristics provided by the measurements and by the synthetic DR are close within a 12% accuracy. However, a substantial difference was found in the decay of the DR signal cross-correlation functions with growing frequency shift in the probing wave channels. The quick decrease in the radial correlation DR coherence observed in the experiment and full-wave synthetic diagnostic, compared to the fast synthetic DR, is attributed to the nonlinear effect of the probing wave phase modulation by the turbulence in the former two cases. The variation in the DR signal at a growing incidence angle in the experiment is also shown to be slower than predicted by both of the synthetic diagnostics, presumably due to underestimation of the probing wave phase modulation and consequent nonlinear saturation of the DR signal at lower incidence angles in modeling.