On the statistics of SuperDARN autocorrelation function estimates

Abstract

Time domain signal processing techniques are employed by the Super Dual Auroral Radar Network (SuperDARN) to obtain bulk measurements of the velocity and spectral width of F region ionospheric plasma irregularities. The measurements are obtained by fitting estimates of the mean autocorrelation function (ACF) of the radar target. To accurately and consistently extract target parameters from the mean unnormalized ACF, it is necessary to utilize error-weighted fitting algorithms with a weight given by the variance of the ACF. Currently implemented weights are ad hoc, and a detailed description of the statistical characterization of SuperDARN ACFs is needed. Following the discussions in Farley (1969) and Woodman and Hagfors (1969), which describe the variance for the mean normalized ACF used with incoherent scatter radars, we present analytic expressions for obtaining the variance of the real and imaginary components of the mean unnormalized SuperDARN ACF. These expressions are based on models by André et al. (1999) and Moorcroft (2004) of the voltage signal received by SuperDARN radars but may be used for other soft target radar systems. An algorithm for obtaining the variance of both the magnitude and phase of the mean ACF is also presented. The results of this study may be directly integrated into existing SuperDARN data analysis software and other pulse-Doppler radar systems that utilize estimates of the mean unnormalized ACF.