The propagation of the pulse ultrawideband (UWB) signals in plasma media, in particular, in the near-to-Earth's plasma layers was simulated. The dispersive distortions of the UWB signal in that media were estimated. The absorption dispersion and the scattering dispersion were taken into consideration. The radar equation for the distributed target location with UWB signals was modified. The wavelet analysis of the UWB signals was performed. The obtained results with the results of the short-time Fourier transform processing were compared and in new specially constructed format were shown. New set of the analytical wavelets based on the atomic functions and called as the Kravchenko-Rvachev analytical wavelets was proposed. Two new types of UWB signals called as non-linear and fractal UWB signals were suggested. Numerical characteristics for created models of that UWB signal types were calculated. Two time-frequency transforms were proposed to apply for UWB signal analysis.