A new concept for solving statistical synthesis problems of radiometric devices and systems (RDS) is developed. The reasonability of using ultra-wideband (UWB) RDSs is substantiated. The basic data of mathematical apparatus of V-transforms employed when processing space-time UWB fields and their statistical characteristics is given. A wide class of UWB RDS statistical synthesis problems (compensation, zero-type, modified modulation type, modulation compensation type, multi-antenna systems including cross-correlation-compensation systems and aperture synthesis systems) of the stationary and scanning types are solved. The appropriateness of using the Kravchenko weighting functions for refinement of primary radiometric images in radiometric scanning devices is substantiated.