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We have calculated the estimation error of parameters of echo power spectra observed by mesosphere-stratosphere-troposphere (MST) radars by means of computer simulations for least squares fitting and moment methods. The least squares fitting method is shown to be better than the moment method in the region with low signal-to-noise ratio (snr), especially for narrow spectra. However, the estimation error of the fitting method at infinite snr is approximately twice that of the moment method. This has been attributed to the nature of the statistical fluctuation of the power spectral density, which shows a χ2 distribution. For both methods at infinite snr we have derived equations which show the accuracy of the estimates versus observation period and spectral width. When we use the fitting method for the data observed with the MU radar (46.5 MHz), the typical errors of the radial wind velocities are 0.7 and 2.0 m s−1 in the stratosphere and in the mesosphere, respectively. By calculating the logarithm of the spectrum with inifite snr and fitting a parabolic curve to it, the error of the Doppler shift has become approximately 20 times smaller than that of the moment method. It has been shown that this is one technique to achieve the theoretical lower bound of the estimates.