  In this paper, we present a complete analytic probability based description
of mobile-to-mobile uncorrelated scatter channels. The correlation based
description introduced by Bello and Matz is thus complemented by the presented
probabilistic description leading to a common theoretical description of
uncorrelated scatter channels. Furthermore, we introduce novel twodimensional
hybrid characteristic probability density functions, which remain a probability
density in one of the variables and a characteristic function in the other
variable. Such a probability based description allows us to derive a
mathematical model, in which the attenuation of the scattering components is
inherently included in these two-dimensional functions. Therefore, there is no
need to determine the path loss exponent. Additionally, the Doppler probability
density function with the inclusion of the path loss leads to a concave
function of the Doppler spectrum, which is quite different from the Jakes and
Doppler spectra and can be directly parameterized by the velocity vectors and
geometry of the scattering plane. Thus, knowing those parameters permits the
theoretical computation of the Doppler spectra and temporal characteristic
functions. Finally, we present a comparison between the computed probability
based theoretical results and measurement data for a generic mobile-to-mobile
channel. The agreement between the two shows the usefulness of the probability
based description and confirms new shapes of the Doppler power spectra.
