Radio Science, Volume 27, Number 3, Pages435-447, May-June 1992 Optimal analysis of incoherent scatterradar data J.M. Holt, D. A. Rhoda, • D. Tetenbaum, and A. P. van Eyken 2 Massachusetts Institute of Technology, Haystack Observatory, Westford (Received July 4, 1990; revised May31, 1991; accepted June 10 1991.) A lag-profile data collection mode has recently become operational at Millstone Hill. A new data analysis technique has been developed in which one ormore matrices of ion-line lagged products are analyzed simultaneously, along with any available a priori information oniono- spheric and system parameters such as ionosonde and plasma-line estimates offoF2. The anal- ysis yields spline function estimates of height-varying ionospheric parameter profiles. The effect of thefull two-dimensional (range-lag) radar ambiguity function is included in this analysis. Millstone Hill single-pulse lag profile data are presented and analyzed and the new technique isshown toproduce ionospheric parameter profile estimates with significantly bet- terheight resolution than would bepossible if the lagprofile matrix were first divided into ACFsby application of a summation rule. 1. INTRODUCTION Incoherent scatter radar [Evans, 1969,1975] is themost pow- erful ground-based technique for studying the Earth's iono- sphere, upper atmosphere, andmagnetosphere. The utilityof the technique arises from theusually excellent agreement be- tween themeasured power spectrum andthetheoretically pre- dicted spectrum. The predicted spectrum is a functionof ionospheric electron density, ion and electron temperature, bulk plasma drift velocity, ion composition, and ion-neutral collision frequency [Dougherty and Farley, 1960, 1961, 1963; Fejer, 1960a, 1960b, 1961; Salpeter, 1960,1961; Hagfors, 1961; Hag- fors and Brockelman, 1971]. These parameters are routinely es- timated by computing least squares fitsof theoretical specm to measured spectra in order to determine ionospheric parameter values which yielda spectrum that best matches themeasured spectrum (in practice, the autocorrelation function (ACF) of the incoherent scatter return,which is the Fourier transform of the power spectrum, is usually used). Thisapproach depends upon theability of theradar to mea- sure the spectrum or ACF in a volume of space within which the variation of the ionospheric parameters may be neglected. At anygiven timethe signal returning to a monostatic radar will include contributions from a volume which extendscT/2 in the INow at MIT Lincoln Laboratory, Lexington, Massachu- setcs. 2Now at EISCAT Scientific Association, Ramfjordmoen, Norway. Copyright 1992 by theAmerican Geophysical Union Paper number 91 RS02922. 0048-6604/92/91 RS-02922508.00 radar line-of-sight direction, where c is thespeed of lightandT is thelength of thetransmitted waveform. This suggests that the waveform should beasshort as possible. However, for theanal- ysis to succeed the waveform must belong enough topermit the ACFtob• measured with sufficient lag extent ore. quivalently thespectrum to be measured with sufficient spectral resolution. If the waveform is tooshort, thespectrum will be smeared or the autocorrelation function will be truncated and too much infor- mation will be lost to allow the ionospheric parameters to be extracted. A further complication arises fromthefiniteimpulse response of thereceiver which causes themeasured signal to be a time average of the signal returning tothe radar. This suggests that the impulse response should boasshort as possible. How- ever, the measured signal includes noise as wellas the incoher- ent scatter return and, as the impulse response decreases, the bandwidth of the measurement increases and the signal-to-noise ratiodecreases. This leads to a decrease in theaccuracy of the extracted parameters. As a consequence of these considerations, simple single- pulse waveforms typically are useful for sw•tral measurements only in the ionospheric F region. In this case the correlation time of themedium (times thespeed of ligh0 is shorter than thedis- tance over which theionospheric parameters change apprecia- bly and adequate spatialand •tral resolution are both achievable with a single pulse. However,as the altitude decreases, thecorrelation timeincreases and thespatial scale of the ionosphere decreases until a pointis reached where ade- quate spatial and spectral resolution can no longer be simulta- neously achieved. The point at which this happens depends both upon theradar wavelength andthe state of the ionosphere but typicallywill occur near 200 km in the transition region between predominantly 0 + ions andpredominantly molecular ions. 435