A novel polarimetric ultra-wideband radar system operating in the 1-2 GHz frequency for subsurface probing applications is currently under development at the University of Nebraska. The radar system transmits white Gaussian noise. Detection and localization of buried objects is accomplished by correlating the reflected waveform with a time-delayed replica of the transmitted waveform. Broadband dual-polarized log-periodic antennas are used for transmission and reception. A unique signal processing scheme is used to obtain the target's polarimetric amplitude and phase response by frequency translation of the high depth resolution, low bandwidth-duration product, as well as simplified signal processing. This paper describes the unique design features of the radar system, develops the theoretical foundations of noise polarimetry, and provides experimental evidence of the polarimetric and resolution capabilities of the system.