On the second order statistics for GPS ionospheric scintillation modeling

Abstract

Equatorial ionospheric scintillation is a phenomenon that occurs frequently, typically during nighttime, affecting radio signals that propagate through the ionosphere. Depending on the temporal and spatial distribution, ionospheric scintillation can represent a problem in the availability and precision for the Global Navigation Satellite System's users. This work is concerned with the statistical evaluation of the amplitude ionospheric scintillation fading events, namely, level crossing rate (LCR) and average fading duration (AFD). Using α-μ model, the LCR and AFD are validated against experimental data obtained in São José dos Campos (23.1°S; 45.8°W; dip latitude 17.3°S), Brazil, a station located near the southern crest of the ionospheric equatorial ionization anomaly. The amplitude scintillation data were collected between December 2001 and January 2002, a period of high solar flux conditions. The obtained results with the proposed model fitted quite well with the experimental data and performed better when compared to the widely used Nakagami-m model. Additionally, this work discusses the estimation of α and μ parameters, and the best fading coefficients found in this analysis are related to scintillation severity. Finally, for theoretical situations in which no set of experimental data are available, this work also presents parameterized equations to describe these fading statistics properly.

Climatology and modeling of ionospheric scintillations and irregularity zonal drifts at the equatorial anomaly crest region

“…According to Moraes et al (2012Moraes et al ( , 2014, the α − µ probability density function of the normalized amplitude envelope r is given by…”

“…Moreover, the AFD and LCR are important in receiver design and model. The former parameter indicates the average amount of time that the amplitude envelope of the received power signal spends below a certain threshold, whereas the latter provides the average number of times within an observation period that the envelope of a fading signal crosses a certain level in the downward or upward direction (e.g., Moraes et al, 2014). According to Yacoub (2007) the AFD (in seconds) for the α − µ distribution is given by…”

“…The values of ω used here are those that provided the minimum absolute error deviation and were based on the previous work (Table 2 and Eq. 13) of Moraes et al (2014). As we are computing the crossing rate for E[r 2 ] = 1, the scale factor ρ for both LCR and AFD can be found as…”

“…(4). The complete outlining of the α − µ distribution for scintillations and for the AFD and LCR calculations can be found in the work of Moraes et al (2012Moraes et al ( , 2014, and therefore their full mathematical description will be limited to the equations presented above. In the present work, the scintillations at the low-latitude station of Cachoeira Paulista are modeled for different values of the S 4 index (from 0.4 to 0.9) and during periods that represent different phases of the solar cycle (solar maximum, solar minimum, and intermediate level).…”

“…Humphreys et al (2009) assumed the GPS amplitude scintillations following the Rice distribution and proposed a model that can be used to test phase-tracking loops for scintillation robustness evaluation. More recently, Moraes et al (2014) demonstrated that the α − µ distribution best describes the variability in the signal amplitude during scintillations and used the same model to evaluate the impact of scintillations on GNSS receiver operations through radio-channel characterization.…”