Theory of the local structure of a field of received signals

A theory for the local, small-scale structure of a field of received signals is presented. The theory relates characteristics of scatterers to parameters of structure functions of different order for signals from overlapping sample volumes. These characteristics include mean three-dimensional velocity, turbulence parameters, and indicators for identification of scatterers. In the context of the theory, the term "received signal" means the incoherent power induced in receiver's channel.

The theory is quite universal in that no limiting assumption involving the sources of radiation is made in its derivation. As a result, the theory applies to sources dominated by self-radiation (such as stars), as well as sources dominated by scattered radiation (such as atmospheric hydrometeors acting as Rayleigh scatterers), or irregularities in atmospheric refractive index which cause Bragg scattering of incident radiation. In the context of the theory, all sources of radiation are referred to as "scatterers". Similarly, no specific characteristics of a remote sensor (such as antenna size or shape, or system operating frequency) are used in the derivation of the theoretical relations, so the theory is independent of specific sensor parameters.

The theoretical relations are applicable to: mixed sources of radiation (e.g., combined Bragg and Rayleigh scatterers); any number, size, material, and spatial distribution of scatterers withing the sample volumes in any media; and any type of radiation (e.g., monochromatic, broadband) at any polarization.

The theoretical relations are asymptotically exact in the sense that they contain no empirical functions or constants. It is shown that the present theory supplements existing theories in new areas without contradiction to existing theories.