Pulse-pair Doppler operation from space/air to sea surface is studied through a generalized Kirchhoff theory. Since Doppler fading is crucial for a fast moving platform, a transverse beam-pattern of finite width is taken into account. Correlation signals are derived for both the coherent and incoherent scatterings, which show substantial difference in Doppler velocity. The formalism should be applied to the data analysis of a space/air borne cloud (rain) profiling radar to remove contamination of a platform velocity caused by a mis-pointed beam, obtaining the line-of-sight velocity of weather droplets.
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