Scattering functions for fading channels with ionospheric scintillation and terrestrial multipath

The MUOS satellite-to-terminal and terminal-to-satellite channel is characterized by ionospheric scintillation and/or terrestrial multipath effects. In earlier literature various channel conditions have been considered and time-frequency correlation functions of the channel fading process have been derived. In practice, in terms of the design of the receivers operating over such channels, functions such as the scattering function, the multipath intensity profile (MIP), and the fading envelope power spectral density (PSD) are of significant interest. The latter two functions - namely, the VHP and the PSD - can be obtained by simple substitutions in the scattering function, i.e., these are the one-dimensional version of the two-dimensional scattering function. The scattering functions for some of the MUOS channel models exist in the literature. However, for some important channel models, such a function is not available, due to significant analytical difficulties. This paper presents the scattering function for such cases in the form of a series involving Bessel functions and the Chebychev and Hermite polynomials