An improved formulation for radar backscatter from a volume of oblate spheroidal raindrops is developed, taking account of the beam elevation angle and the raindrop canting angle. The formulation is in terms of scattering coefficients in a matrix, and can be applied to systems using linear, circular, or elliptical polarization. The general formulation reduces to results previously published in the literature for linear polarization differential reflectivity (Z_DR) and for circular polarization depolarization ratio ( CDR). Analysis of the linear polarization case for a dual-polarization radar which can transmit and receive orthogonal linear polarizations in the horizontal-vertical (HV) planes, and the (±45) degree planes are considered. Results are presented showing the effect raindrop parameters have on Z , and linear polarization ratio (LDR) measured in (HV) and (±45°) planes. Analysis of the circular polarization case for a dual polarization radar which can transmit and receive circular polarizations is also considered. Results show that LDR measured in the (±45°) planes is similar to CDR. The dual-polarized radar development program at VPI&SU was discussed and a detailed design of a new radar data collection system is given. With the theory of dual-polarization radar measurement and the practical implementation of such a radar described within this thesis, a more accurate characterization of the propagation effects along a satellite to earth path can be carried out. / M.S.