It has been shown that radar depolarization measurements can be successfully used for the purpose of identifying types of ice hydrometeors and estimating their shape parameters such as mean aspect ratios. If propagation effects are limited, circular depolarization ratio (CDR) is more useful for this purpose than linear depolarization ratio (LDR) since CDR does not depend on the hydrometeor orientation in the polarization plane. Most polarimetric radars, however, operate in the linear polarization basis. Moreover, some popular polarimetric measurement schemes such as the simultaneous transmission and simultaneous reception of the horizontally and vertically polarized radar signals (STSR) do not allow direct measurements of depolarization. The STSR measurement scheme is now being considered for the polarization upgrade of the existing network of WSR-88D weather radars, and it has been already implemented with a few research radars including the CSU-CHILL S-band radar and the ETL X-band radar. This study suggests an approach to derive CDR estimates from measurements of the complex scattering amplitudes of vertically and horizontally polarized radar signals measured in the systems that use linear polarizations (including systems that use the STSR scheme). Potential problems for implementing this approach are discussed and some solutions for these problems are suggested. The use of the differential phase shift measurements for correcting CDR estimates for the propagation effects is also considered.