Temporal behavior of pulses after propagating through a turbulent ionosphere

A radio signal after propagating through a turbulent ionosphere will suffer distortion owing to dispersion and random scattering. For coarse description of a temporal signal, the temporal moments have been found to be convenient. Past studies have shown that the zeroth moment is related to the total energy in the pulse, the first moment is related to the mean arrival time, and the second moment is related to the mean square pulse width. In the paper, the analysis is extended to the third and fourth moments, which are shown to be related to the skewness and kurtosis of the pulse. In digital communications, an ideal pulse, due to propagation effects, can be distorted and stretched to produce a long tail occupying an interval longer than one communication bit. Using the temporal moments an upper bound of the energy content outside of one chip can be estimated.