The mean and variance of skywave radar sea-echo power spectra for discrete ionospheric multipath

Formulas for the mean and variance of skywave radar sea echo Doppler spectra are transformed from a discrete representation to a general convolution form. While the discrete representation is general enough to represent arbitrary sea echo spectra and arbitrary ionospheric distortion spectra, the derivation of the variance assumes that both spectra are composed of discrete spectra lines that are narrower than the spectral width of the window (or weighting function) applied to the measured time series and that the separation of the spectral lines is large compared with the spectral width of the window. The formulas are shown to be consistent with corresponding formulas derived from a continuous representation under the same physical assumptions. However, the formula for variance based on discrete spectra differs from that derived from a continuous representation under physical conditions that assume more continuous spectra for both the sea echo and the ionospheric distortion.