Some basic functional relationships between the statistics of the signals received in a radar and the statistics of the density fluctuations of a scattering medium are derived. They vary in their degree of generality, but they are all very general in scope. They include monostatic and bistatic radars scattering from either atmospheric, ionospheric, or meteorological media. They are valid for refractive and slightly dispersive media, so they can also be used for HF ionospheric radars. They include the effects of filtering, including receiver filtering, pulse compression coding and decoding schemes, and coherent integration, or any alternative linear digital filtering scheme. Functional relationships to include cross-correlation schemes, such as Faraday rotation experiments and interferometers, are included. Some simplified expressions are derived for frequently encountered situations, where different approximations can be made. These simplified expressions cover a large number of radar techniques currently in use for atmospheric and ionospheric applications.
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