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Research highlight of Finnish Centre of Excellence in Inverse Problems Research
General purpose incoherent scatter radar measurements
Ionosphere is a partly ionized region of the Earths atmosphere, beginning from approximately 50 kilometers altitude, the highest ion densities located below 500 kilometers, and merging without a clear boundary to the fully ionized magnetosphere. In situ measurements in the ionosphere are especially difficult, as the gas in main parts of the ionosphere is too thick to allow satellites to stay in their orbits, but the altitudes are too high to be reached with balloons either, leaving only rockets available for the in situ studies. Thus, different radar applications allowing the ionosphere to be probed from ground are of crucial importance.
Incoherent scatter is scattering of radio signal from thermal fluctuations in the ionospheric plasma. The scattering is a zero-mean random process, with information of the plasma properties contained in its autocorrelation function. The spectrum of the incoherent scatter is too wide to be measured with conventional radar applications, and special transmission modulations have had to be developed for the incoherent scatter radars. These modulations do not directly provide the scattering autocorrelation function at different heights, but lead to a deconvolution problem instead.
The transmission modulation methods of incoherent scatter radars are usually designed to allow simple solution of the deconvolution problem by means of decoding filters. The Sodankylä Geophysical Observatory has developed a deconvolution method based on statistical inversion, lag profile inversion , which allows the deconvolution problem to be solved with arbitrary transmission modulations. The method also allows incoherent scatter autocorrelation functions to be measured with arbitrary resolutions in time, height, and time-lag.
The decoding-filter-based approach to the deconvolution is not possible to realize unless the radar transmits pulses with uniform inter-pulse periods. As a consequence, it becomes impossible to use the same pulses for all parts of the ionosphere, as the lowest parts of the ionosphere require inter-pulse periods much shorter than the signal roundtrip time to and from the upper ionosphere. With lag profile inversion, the pulses can be transmitted in an aperiodic manner (Fig. 1), allowing the same pulses to be used for measuring all parts of the ionosphere (see Fig. 2). This is the most economical way of using the radar, as all received echoes are fully exploited. These so-called multi-purpose experiments  have been recently developed in the Sodankylä Geophysical Observatory and in the Space Physics Group of the Department of Physics, University of Oulu. The multi-purpose experiments are expected to be especially useful in routine monitoring type measurements, such as the continuous operation of the planned next-generation European incoherent scatter radar, EISCAT_3D.
 I.I. Virtanen, M.S. Lehtinen, T.Nygrén, M. Orispää, and J. Vierinen, Lag profile inversion method for EISCAT data analysis, Annales Geophysicae, 26, 571-581, 2008.
 I.I. Virtanen, J. Vierinen, and M.S. Lehtinen, Phase-coded pulse aperiodic transmitter coding, Annales Geophysicae, 27, 2799-2811, 2009