Functional integral approach to the transfer function of a stochastic scattering channel

Abstract

We apply the formalism of functional integration to the calculation of the transfer function of a stochastic scattering channel formed by stationary, non-interacting point scatterers. The channel is described through a scattering amplitude density, defined over space, whose random component is characterized by a functional probability distribution. This random component induces in turn a probability distribution for the scattering transfer function, which we compute by means of functional integration in the case of Gaussian distributions. Some geometric configurations relevant to radar operation are worked out, as well as the statistical properties of the transfer function in the large-frequency limit. Extensions of the formulation in order to include scattering phase shifts, i.e. complex scattering amplitudes, and to consider non-Gaussian probability distributions are outlined.