The case of polarimetric Doppler weather radar employing simultaneous transmission and reception of horizontally (H) and vertically (V) polarized waves is examined. Pulse train switching between orthogonal polarization states is assumed. The H and V components of the transmitted wave are of equal amplitude, and f_HV is their relative phase. The transmitted wave will be, in general, elliptical. In particular, 45° slant linear polarization is obtained when the H and V components of the signal are in phase, f_HV=0°, and circular polarized radiations is transmitted when the H and V components are 90° out of phase, f_HV=90°.

It will be shown that the radar echo signal covariances and cross covariances obtained when a given elliptical polarization is transmitted can be express in terms of the analogous signal covariances and cross covariances for a different elliptical polarization. Assuming the hydrometeors to be axially symmetric with a canting angle distribution symmetric about the mean canting angle, one set of equations for separation of propagation and backscattering effects is developed for all the polarization state of the transmitted wave. The mean apparent canting angle, the degree of common orientation of the hydrometeors, and the differential phase shift are then obtained together with the intrinsic value of the reflectivity, the differential reflectivity, and the copolar correlation coefficient at zero lag time. The analysis of the bias on these radar observables due to the transmission of only one polarization state will be also presented.