Randomly Changing Time-Variant Systems

Abstract

Hitherto, we have considered signals and characteristic functions of time-variant system, in particular, the delay spread function $g(t,\tau )$, as deterministic. With the Fourier transform different spectra or transfer functions, such as the Doppler spread function $G(f_{t},f_{\tau })$, have been defined. In many applications, e.g., wireless communications the time-variant channel can take on a fast of different characteristics depending on the environment, the speed of the transmitter or receiver, and other effects. Hence, there is a need for the introduction of a statistical description for the most important system parameters. The use of multivariate probability density functions could help in principle.