Inverse problems in radar measurements of stochastic processes in the ionosphere

This paper offers a short introduction to certain radar studies of the ionosphere. Emphasis will be placed on applications of ‘‘incoherent scatter’’ radars relying upon stochastic Thomson scattering to make remarkably detailed measurements of the temperature, density, composition, and other physical parameters in the Earth’s ionosphere. The total backscattered power is proportional to the density, but all the other parameters are derived by detailed inspection of the correlation function of density fluctuations. Measuring the correlation function is quite difficult because of the very small scattering cross section. Furthermore, the ionosphere is ‘‘overspread,’’ which means that density fluctuation decorrelates in significantly less time than it takes a radio pulse to transit the region of interest. Simply stated, this means that one cannot measure the correlation function of the ionosphere with a periodic pulse train. Following a very quick tour of the plasma physics and theoretical correlation function (the forward problem) the intricate interplay of the transmitter waveform design and the inverse problem for parameter estimation—including some unique robustness issues—is shown. It will also be shown that the highest performance transmitter waveforms today are themselves stochastic (or nearly stochastic) processes. The results have a pleasing analogy to the quantum mechanics notion of ‘‘observables,’’ and shed light on the very nature of measurement.