On the Moments of Probability Distribution Function of Amplitude Scintillation in the Polar Region

The distortions seen in the Global Navigation Satellite Systems radio signal caused by ionospheric irregularities in the polar region are examined through the lens of probability distributions of fluctuations in the recorded scintillation signals. The first four moments of the probability distribution function (PDF) of the amplitude scintillation are computed and analyzed for 106 events collected at Pond Inlet station [Magnetic Coordinates = (80.0 degrees N, 2.6 degrees E)]. As a starting point, the background variation level is investigated using similar computations carried out with about 400 30-s window segments. The resulting distribution for the skewness (third moment) and the kurtosis (fourth moment) strongly indicate that the background fluctuations are nearly Gaussian; given the computed variances, the Rayleigh distribution hypothesis is ruled out. In the case where scintillation is present, we found that the skewness distribution nearly overlaps with the background while the excess kurtosis strongly indicates a departure from normality. More precisely, the PDF appear mostly symmetric and leptokurtic (positive kurtosis K) and exhibit, in some cases, significant flatness (K similar to 1). These results reveal that the analyzed scintillations are statistically consistent with stationarity and therefore vanishing skewness. Moreover, the empirical moments are compared with those derived from probability densities referred in the literature regarding scintillations. We have found that none of the log-normal, Nakagami, Rician and alpha-mu distributions account for the analyzed data. The generalized Gaussian distribution with a shape parameter 1 beta < 2 seems the most probable and the most adequate to account for the results.