This paper is the first in a series of two papers on the use of combined improved hydrodynamic and electromagnetic analytical models for the simulation of the ocean Doppler spectrum at microwave frequencies. Under a linear assumption for the sea surface, we derive statistical expression for the main Doppler characteristics according to asymptotic scattering models. We consider classical models such as the Kirchhoff approximation and the two-scale model, as well as the more recent weighted curvature approximation (WCA). We recover two salient features of Doppler signature in the microwave regime. First, the Doppler characteristics are very sensitive to polarization, with higher mean Doppler shift in horizontal polarization. This is correctly rendered by the WCA but not the classical models. Second, the first two moments of the Doppler spectrum exhibit a nontrivial dependence on incidence angle. Results compare favorably with rigorous numerical computations for 1-D surfaces published in the literature. The simplicity and accuracy of the analytical models provide a valuable tool for the Doppler analysis of 2-D sea surfaces.