Charles S. Carrano, Keith M. Groves, William McNeil, Rezy Pradipta, Patricia H. Doherty, Institute for Scientific Research, Boston College

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Instabilities occur frequently in the post-sunset low latitude ionosphere leading to the generation of irregularities in electron density that can cause rapid fluctuations in the amplitude and phase of radio waves propagating through the disturbed regions. These fluctuations, also known as scintillations, can produce degrade the tracking of signals used by modern Global Navigation Satellite Systems (GNSS). Although dual-frequency receiver systems are able to correct ranging errors introduced by group delay due to the ionosphere, they cannot compensate for scintillations which do not exhibit a simple dependence on frequency. Indeed, dual-frequency systems may have difficulty tracking scintillated signals which can result in erratic range errors and loss-of-lock under severe circumstances. In a seminal paper by Conker et al. (Radio Sci., 2003), the authors proposed a model for GPS tracking loop performance by assuming a Nakagami-m distribution for the fading of the L1 and L2 carrier signals due to scintillation. More recently, the alpha-mu distribution proposed by Yacoub has been shown to describe a wider variety of scintillation conditions than the Nakagami-m distribution (Moraes el al., GPS Solutions., 2012). The alpha-mu fading model is a two parameter distribution that includes Nakagami-m as a special case. It may be parameterized in terms of the scintillation intensity index S4 and an additional measure of severity (alpha) for a given level of S4. In a series of papers, Moraes et al. (Radio Sci., 2014; GPS Solutions, 2018) related the parameters of the alpha-mu distribution (and also the ambient C/No ratio) to the performance of GNSS tracking loops. They corroborated this theoretical model using an extensive set of experimental data at low latitudes. In this paper, we describe our efforts to model GNSS tracking loop performance by simulating the propagation of GNSS signals through ionospheric disturbances, fitting the alpha-mu model to the distribution of simulated signal fades, and inferring the impacts on tracking loop performance using the theory of Moraes et al (2014; 2018). Our Monte-Carlo style simulations capture the salient features of the dependence of phase lock loop (PLL) error, delay lock loop (DLL) error, and mean time between cycle slips on S4 and alpha, as inferred from our own experimental GNSS observations and those of Moraes et al. (2014; 2018). Our phase screen radio propagation model accounts for the motion of the transmitters, the anisotropy and drift of the irregularities, and the oblique angle of propagation, all of which influence how the wave interacts with the disturbed ionospheric medium (Carrano et al., ION GNSS 2012). Output from this radio propagation model consists of amplitude and phase fluctuations that are fully coupled according to the propagation physics. When these fluctuations are used as input to tracking loop models we find that impacts due to scintillation depend on not only irregularity strength but also on the direction of satellite motion relative to Earth’s magnetic field. Hence, the orbital geometries of the different GNSS constellations may influence tracking characteristics to an extent that has not been previously assessed. We show that the parameters of the alpha-mu distribution are related to the spectral index of the irregularities (which is a new result), in addition to the strength of turbulence (which was previously known). A conclusion of our study is that physics-based modeling of the radio propagation effects offers several advantages in system design studies, as compared with the more commonly used approach of simulating realizations of signal fades for given set of alpha-mu parameters. While the latter provides realizations of signal fades with the correct probability density, these fades 1) do not have a realistic power spectral density (PSD) because the Fresnel filtering effect is absent, 2) do not reflect the dependence on the direction of satellite motion and irregularity drift relative to Earth’s magnetic field, and 3) are not self-consistently correlated with the accompanying phase fluctuations. All of these effects influence GNSS tracking loop performance, and they are most accurately described via physics-based modeling. Modeling the propagation effects is also advantageous in that one may evaluate tracking loop response during historical periods of more intense solar activity than is currently observed, and also impacts for GNSS constellations which were not in orbit at the time (Carrano et al., ION GNSS 2012). The modeling framework we employ also serves as a useful standard with which to compare tracking loop performance for different receiver models, which can respond to scintillation stimuli in different ways.