The article describes the IRCTR PARSAX radar system, the S-band high-resolution Doppler polarimetric frequency modulated continuous wave (FM-CW) radar with dual-orthogonal sounding signals, which has the possibility to measure all elements of the radar target polarization scattering matrix simultaneously, in one sweep. The performance of such radar depends of the level of sounding signals orthogonality. In the main operational mode, the radar will be used for atmospheric remote sensing and polarimetric studies of ground-based targets. In such mode it will use a pair of synchronous linearly- frequency modulated (LFM) continuous signals with opposite frequency excursions of 50 MHz and duration of 1 ms. Such a combination of sounding signals has limited orthogonality even for huge BT-products, which produce cross-channel interferences. These interferences in case of radar scene with multiple pointed and distributed targets can completely degrade radar operational performance. In this article, we propose simple and effective technique to suppress interferences and to restore radar performance. The technique has been tested using simulation and has been implemented in multi-channel digital receiver of the PARSAX radar. The real radar measurements presented to illustrate effectiveness of cross-channel interferences suppression. The proposed technique can be useful not only for polarimetric radar design, but also in much wide radar applications, which use waveforms with high orthogonality.