Geometrical channel models for space-time systems

Based on the unified concept of space-time system field theory, a general space-time channel model can be constructed from the statistics of the space-time system field function (S-TSFF) for an arbitrary medium. This statistical characterization of the medium (channel) can be expressed in terms of the space-time correlation function, or, equivalently, the space-time power spectral density of the S-TSFF. The space-time correlation function of the S-TSFF generalizes the concept of the mutual coherence function (MCF) for a random electric field to an arbitrary space-time field. There are three different geometrical channel models depending on the choice of the coordinate systems, e.g. rectangular, cylindrical, and spherical. Using the notions of channel correlation time and correlation distance— i.e. doppler spread and delay spread—various geometrical tap-delay channel models are derived. From a system point of view, the space-time correlation parameters can be interpreted as a measure of the spatial and temporal memory of the channel. It is further demonstrated that the rectangular space-time channel model reduces to the two-dimensional randomly time-varying tap-delay line models introduced by Kailath (1961) and Bello (1963). A dual property for the S-TSFF is observed. This system duality principle shows that the channel response can manifest as a space-time filter put forth by linear system theory (convolution integral in space-time), or as a space-time aperture put forth by optics (convolution integral in space-time spectrum).