Scintillation Effects and Tracking of GNSS-Like Signals Transmitted from LEO Satellites and Propagated Through Ionospheric Plasma Irregularities

  • NAVIGATION: Journal of the Institute of Navigation
  • March 2026,
  • 73
  • navi.752;
  • DOI: https://doi.org/10.33012/navi.752

Abstract

In this paper, we present simulation studies of scintillation effects and tracking of global navigation satellite system (GNSS)-like signals propagating from a low Earth orbit (LEO) satellite through ionospheric plasma irregularities to a receiver on the Earth’s surface. Realistic strong scintillation effects are simulated by propagating signals through a phase screen based on real GNSS scintillation signals. Configurations with different phase screen altitudes, LEO satellite orbits, and scintillation severity levels are simulated. We first statistically analyze the number of fades, fading depth and duration, and phase rate disturbance in the signal. A software-defined radio receiver is then applied to process the simulated signals. The impacts of such signals on tracking performance, e.g., C/N0, cycle slip, and loss of lock, are analyzed and compared with that of the same signal traveling through the same irregularity, but from a medium Earth orbit. The results provide a quantitative assessment of the effect of ionospheric plasma irregularities on LEO satellite signal transmissions and receiver processing.

Keywords

1 INTRODUCTION

Low Earth orbit (LEO) satellite-based navigation has been gaining popularity (Kassas, 2021; Reid et al., 2021). Some systems focus on using communication/network signals transmitted from LEO satellites as signals of opportunity for navigation applications (Benzerrouk et al., 2019; Kassas et al., 2021; Khalife et al., 2020; Orabi et al., 2021). Others utilize dedicated LEO-based navigation signals for global navigation satellite system (GNSS) augmentation (Ge et al., 2022; Li et al., 2019; Reid et al., 2018; Yi et al., 2021). All of these signals must travel through the ionosphere before reaching receivers on the ground. The ionosphere introduces phase advances and group delay in range measurements under quiet conditions, which can be corrected via dual-frequency measurements. The more challenging aspect of the ionosphere effect is caused by plasma irregularities, which lead to signal amplitude and carrier-phase fluctuations, collectively referred to as ionospheric scintillation (Morton et al., 2021). For signals transmitted from LEO satellites, our earlier study showed that ionospheric scintillation introduces deeper and more frequent fades and much higher phase dynamics compared with signals transmitted from medium Earth orbit (MEO) satellites (Morton et al., 2022). The resulting amplitude degradation and phase disturbance lead to a lower carrier-to-noise-density ratio (C/N0), more cycle slips, and loss of lock for LEO satellite signal tracking (Xu et al., 2023).

This paper simulates the effect of ionospheric plasma irregularities on GNSS-like L-band signals transmitted from LEO satellites to assess signal degradation and receiver tracking performance. First, a data-consistent ionospheric scintillation simulator, as presented by Jiao et al. (2018), Rino et al. (2018), and Xu et al. (2020), is used to generate an equivalent phase screen based on a phenomenological model, providing a statistical representation of ionospheric irregularities. Weak, moderate, and strong scintillations are defined for signals transmitted from GNSS satellites in a MEO, and phase screens are established accordingly. We then simulate Global Positioning System (GPS) L1 coarse/acquisition (C/A) signals transmitted from different LEOs (as well as the same MEO as GPS satellites for self-consistency checking), traversing phase screens placed at different altitudes, and received by a stationary ground receiver. The wave fields of the scintillation signal at the receiver, i.e., the amplitude and carrier-phase disturbance, are calculated, as well as scintillation indicators to assess the level of severity. Then, the fluctuations and noise are modulated onto nominal GPS L1 C/A signals to produce the scintillation signals. A software-defined receiver (SDR) with a conventional tracking loop architecture is implemented to track the signal, and these results are analyzed to study the impact of such signals on the tracking loop performance.

This paper is organized as follows. The scintillation simulator is summarized in Section 2. Simulation scenarios are presented in Section 3. The scintillation signal generation and receiver tracking algorithms used in this study are detailed in Section 4. The scintillation effects and tracking results are analyzed in Section 5.1 and Section 5.2, respectively. Section 6 summarizes the findings of this work.

2 SCINTILLATION SIMULATOR

The ionosphere scintillation simulator used in this study is based on the published model presented by Xu et al. (2020). The model flow chart presented by Xu et al. (2020) is shown in Figure 1. The simulator is a compact data-consistent simulator that requires only two input parameters: the amplitude scintillation index S4 and the scintillation signal decorrelation time τ0. These two parameters capture the scintillation signal characteristics: S4 indicates the magnitude of the amplitude fluctuation, and τ0 shows the signal temporal variation. These parameters are extracted from ground-based GNSS receiver measurements of real scintillation signals transmitted from GNSS satellites using the irregularity parameter estimation method (Carrano & Rino, 2016). The ground-based measurements of the real scintillation signal S4 and τ0 are referred to as the scintillation initialization data, which are then mapped to a two-component power-law phase screen model (TPPSM) designed to capture strong equatorial scintillation effects (Rino et al., 2018). The TPPSM is defined by a set of five parameters: the turbulence strength U, space-to-time scaling parameter ρF/veff (where ρF is the spatial scale of the irregularity and veff is the effective signal scan velocity across the irregularity), and spectral parameters p1, p2, µ0 (where p1, p2 are the spectrum slopes and µ0 is the corner frequency between the two spectral components). Xu et al. (2020) showed that the two-parameter set U, ρF/veff dominates the temporal characteristics of scintillation signals, while the other three spectral parameters can assume representative empirical values obtained from real data analysis. Therefore, user-defined S4 and τ0 values can be mapped to U and ρF/veff in the TPPSM.

Flow chart of the ionosphere scintillation simulator presented by Xu et al. (2020) PVT: position, velocity, and timing; RX: receiver
FIGURE 1

Flow chart of the ionosphere scintillation simulator presented by Xu et al. (2020) PVT: position, velocity, and timing; RX: receiver

For stationary receivers, a realization of ionospheric structure in the form of a phase screen is produced based on a two-parameter set U, ρF/veff,static generated by the TPPSM. The two-dimensional (2D) phase screen realizations are initiated with a periodic phase screen that is uniformly weighted. Multiple phase screen simulations typically confine the field to a beam to mitigate boundary effects. A plane wave propagating through this structure at the GNSS frequency will yield scintillation indices matching the user-defined S4 and τ0 parameters. Users can also specify a certain propagation geometry corresponding to desired receiver dynamics to calculate a new ρF/veff,dyn. The propagation geometry is calculated based on the receiver position and velocity and the transmitting satellite orbit. The horizontal drift speed of the ionospheric irregularity Vdrift is also a parameter required in the propagation geometry calculation and is obtained numerically by using the ρF/veff,static value (Xu et al., 2020).

With the phase screen model established, a plane wave is propagated through the phase screen realization following the user-defined propagation geometry embedded in ρF/veff,static or ρF/veff,dyn (depending on whether the receiver is stationary or dynamic). The output is the simulated signal wave fields at the receiver, which include the time series of scintillation-induced amplitude and carrier-phase fluctuation δA, δϕ. These fluctuation time series are modulated into the receiver intermediate-frequency (IF) signal and used to generate simulated scintillation signals. A statistical analysis of the fluctuation time series is carried out in Section 5.1.

3 SIMULATION SCENARIOS

This study simulates GPS L1 C/A signals transmitted from a LEO satellite, propagating through a phase screen before reaching receivers on the Earth’s surface. The model represents 2D wave propagation in a plane that cuts across the ionospheric irregularities, capturing their impact on the signal. The “equivalent phase screen” used in this study is a one-dimensional slice, where the structure is defined by the effective signal scan velocity across the irregularity, veff. The initialization data for the scintillation simulation, shown in Figure 1, consist of a GPS pseudorandom noise (PRN) 24 signal received by a ground station in Hong Kong between 12:25 and 12:30 Universal Time on October 15, 2013. This data set includes scintillation disturbances with an average scintillation index of S4 = 0.8 and a decorrelation time of τ0 = 0.76 s. The estimated plasma horizontal drift velocity, Vdrift, is eastward at 96.5 m/s.

The baseline simulation scenarios (Scenarios 1–4) incorporate two parameter sets: a phase screen altitude of hPS = 300/500 km and a LEO satellite altitude of hTX = 550/800 km. Previous studies have suggested that scintillation-producing irregularities primarily occur in the F region (300–400 km) but can extend from the E region (∼100 km) to altitudes as high as ∼800 km, depending on the geophysical conditions (Kelley, 2009; McClure, 1964). Because this study focuses on scintillations affecting signals transmitted from LEO satellites, irregularities are placed below the satellite altitude. By simulating two phase screen altitudes (300 and 500 km), we assess the impact of irregularity height by comparing Scenario 1 with Scenario 3 and Scenario 2 with Scenario 4, keeping the LEO satellite altitude constant in each comparison. In particular, the decorrelation time τ0 serves as a key indicator regarding the impact of the irregularity height, with a smaller τ0 corresponding to higher signal dynamics and stronger scintillation. We compute τ0 along the satellite’s trajectory, with the resulting values listed in Table 1. The results show that τ0 is consistently lower for the higher phase screen altitude in both sets of comparisons. Future studies should simulate a higher LEO satellite altitude and a wider range of phase screen altitudes to more comprehensively capture these effects.

View this table:
TABLE 1

Simulation Scenarios

Scenario 0 replicates the real GPS scintillation signal used for initialization. The simulation scheme, illustrated in Figure 2, has been described in detail by Morton et al. (2022). In Scenario 0, τ0 varies slightly, with an average of approximately 0.8 s—closely matching the value of 0.76 s from the initialization data. This agreement confirms that the placement of the phase screen is appropriate and ensures that the simulation remains self-consistent.

(Left) Scintillation simulation configuration; (right) sky plot of GPS satellite and LEO satellites at 550- and 800-km altitude during the 500-s interval
FIGURE 2

(Left) Scintillation simulation configuration; (right) sky plot of GPS satellite and LEO satellites at 550- and 800-km altitude during the 500-s interval

In each baseline scenario, we selected some representative τ0 values from the calculated τ0 range. For each of the nine sets of selected τ0 values, we generated a 500-s scintillation signal amplitude and carrier-phase fluctuation time series, i.e., δA and δϕ. The highest and lowest τ0 values are marked in red, and the corresponding sub-scenarios (referred to as the LEO max and LEO min scenarios later) are highlighted in Table 1 (the highest/lowest values are for 0–300 s instead of 500 s to align with the LEO max and min scenarios of Morton et al. (2022)). The variations in elevation and decorrelation time τ0 are presented in Figure 3. Because LEO satellites move across a bigger portion of the sky during the simulation period, the changes in both elevation angle and phase dynamics are more significant than those of the GPS satellite. The nine representative τ0 values and their corresponding sub-scenarios are indicated in Figure 3.

(Top) Satellite elevation and (bottom) decorrelation time τ0 of five scenarios during the 500-s interval
FIGURE 3

(Top) Satellite elevation and (bottom) decorrelation time τ0 of five scenarios during the 500-s interval

4 SIGNAL GENERATION AND RECEIVER TRACKING ALGORITHM

Figure 4 presents the scintillation signal generation and tracking process in detail. We first generate correlation values directly based on scintillation-induced amplitude and carrier-phase fluctuation time series δA, δϕ, GPS/LEO satellite orbits, baseline C/N0 (30–70 dB-Hz), and coherent integration time T:

E=δA⋅A⋅R(Δτ−d/2)⋅exp⁡(jΔϕ+jδϕ)+ϵE1

P=δA⋅A⋅R(Δτ)⋅exp⁡(jΔϕ+jδϕ)+ϵP2

L=δA⋅A⋅R(ΔT+d/2)⋅exp⁡(jΔϕ+jδϕ)+ϵL3

Detailed diagram of scintillation signal generation and tracking process AWGN: additive white Gaussian noise
FIGURE 4

Detailed diagram of scintillation signal generation and tracking process AWGN: additive white Gaussian noise

A=C/2,[Re(ϵE)Re(ϵP)Re(ϵL)],[Im(ϵE)Im(ϵP)Im(ϵL)]∼N(0,N04T[1R(1−d/2)R(1−d)R(1−d/2)1R(1−d/2)R(1−d)R(1−d/2)1])4

where R is the autocorrelation function, Δτ and Δϕ are the code delay and carrier-phase tracking error, and ϵ is the correlation noise. Re(·) and Im(·) are the real and imaginary components, respectively. In this simulation, the E-L correlator spacing d is fixed at 1 chip. This correlation value simulation method (Figure 4, right) follows the same principle as conventional IF signal generation but has a much lower computation and storage burden (enabling large-scale repeating simulations).

A conventional GNSS receiver signal tracking architecture was implemented. The code and carrier tracking loops utilize a 2nd-order delay-locked loop (DLL) and a 2nd/3rd-order phase-locked loop (PLL) for GPS and LEO scenarios, respectively. When tracking is first initiated or loses lock, carrier tracking is initialized using a 1st/2nd-order frequency-locked loop (FLL) for GPS and LEO. A higher-order carrier tracking loop is adopted for LEO scenarios owing to the higher orbit and phase dynamics. In each tracking loop, correlation values are fed into discriminators, which determine the current tracking error and refine local estimates. The discriminators for the DLL, PLL, and FLL are specified in Equations (5)–(8):

lτ=2−d|E|−|L|2|E|+|L|5

lϕ=arctan⁡(Im(P)/Re(P))6

lϕ=arctan⁡(crs/dot)/T7

crsk=Re(Pk−1)Im(Pk)−Re(Pk)Im(Pk−1),dotk=Re(Pk)Re(Pk−1)+Im(Pk)Im(Pk−1)8

The subscript k indicates the k-th coherent integration period. A Kalman filter (KF) is applied to both the code and carrier tracking loops for noise suppression. The KF models are detailed in Appendix A. For an analysis of tracking results, lock detectors for the DLL, PLL, and FLL are first used to determine whether the incoming signal is being correctly tracked in each tracking loop. The lock detectors ηDLL, ηPLL, and ηFLL are computed based on correlation values (Mongrédien et al., 2006; Spilker et al., 1996):

ηDLL=∑M|Pk|∑M|Ek|+|Lk|,ηPLL=(∑MRe(Pk))2−(∑MIm(Pk))2(∑MRe(Pk))2+(∑MIm(Pk))2,ηFLL=|∑Mcrsk2−dotk2crsk2+dotk2|9

These lock detectors reflect the average absolute code, carrier phase, and frequency tracking errors, respectively. A smaller tracking error results in a higher lock detector value, with a maximum of 1. The results are presented in Section 5.2.1. The C/N0 is also estimated based on correlation values, with results provided in Section 5.2.2.

Cycle slips (Section 5.2.3) and loss-of-lock occurrences (Section 5.2.4) are detected using the carrier-phase estimate, lock detectors, and C/N0 estimate. To ensure statistical reliability, each scintillation scenario simulation is repeated 120 times, with different correlation noise values generated for each run.

5 RESULTS AND ANALYSIS

5.1 Scintillation Signal Statistical Analysis

In this section, we first analyze the scintillation effects, before analyzing the tracking results in the following subsection. We use the carrier phase δϕ and amplitude fluctuation time series δA from the scintillation simulator to obtain the scintillation signal intensity, carrier phase, and carrier-phase rate time series for each scenario. To avoid clutter, only results from three typical sub-scenarios with vastly different dynamics (0.b [GPS], 1.c [LEO min], and 4.b [LEO max]) are shown in Figure 5 and figures later in this subsection. These three sub-scenarios correspond to the GPS satellite transmission and the lowest- and highest-dynamic scenarios associated with the LEO satellite transmission. Figure 5 presents the time series of signal intensity, carrier phase ∆ϕ, and phase rate disturbance ∆ϕ/∆t over the 500-s simulation interval (left), as well as zoomed-in views of a 1.5-s interval (right). The plots clearly show that higher signal dynamics are correlated with deeper fades, larger phase swings, and higher frequency deviations. Fades of over 30 dB, nearly 40 cycles of phase changes, and rapid frequency variations of 40 Hz are observed for sub-scenario 4.b (LEO max). Notably, the deep fades are often accompanied by simultaneous phase and frequency changes (see epoch 352 s and 352.8 s in the zoomed-in view in Figure 5). This finding agrees with earlier observations in real scintillation data (Jiao & Morton, 2015) and in simulations (Breitsch & Morton, 2022).

(Left) Simulated scintillation signal intensity (SI), carrier phase ∆ϕ, and phase rate disturbance time series ∆ϕ/∆t over the 500-s simulation interval; (right) zoomed-in views of a 1.5-s interval
FIGURE 5

(Left) Simulated scintillation signal intensity (SI), carrier phase ∆ϕ, and phase rate disturbance time series ∆ϕ/∆t over the 500-s simulation interval; (right) zoomed-in views of a 1.5-s interval

5.1.1 Statistical Analysis

We scaled the scintillation level of the initiation data to three S4 values (0.3, 0.5, and 0.8) and performed statistical analysis for the three typical sub-scenarios discussed above, resulting in nine simulation configurations. These nine configurations are generated based on a combination of signal dynamics (GPS, LEO min, and LEO max) and S4 values (0.3, 0.5, and 0.8). For each configuration, 1000 min of scintillation realizations were generated. The number of fades with a magnitude greater than 10 dB per minute was counted, as listed in Table 2, as well as the signal decorrelation time τ0 and space-to-time scaling parameter ρF/veff. The decorrelation time is highly correlated with ρF/veff, as expected. As can be seen, no fades with a depth greater than 10 dB occurred when S4 = 0.3 for all three dynamics. For S4 = 0.5, there is an average of 1.5 10-dB fades per minute for LEO max, which corresponds to the highest signal dynamics in this simulated scenario. For S4 = 0.8, the occurrence of 10-dB fades increases from 2.8 times per minute in the GPS (MEO) scenario to almost 40 times per minute. Figure 6 compares the probability distributions of fading depth among the three signal dynamics at S4 = 0.5 (left) and 0.8 (right). For a given S4 value, the distribution of fading depth is similar among the three signal dynamics, and most fades are at the 12.5-dB level. However, for stronger scintillations, the probability of deeper fades does start to rise.

Probability distribution of fading depth among three signal dynamics for S4 = 0.5 (left) and 0.8 (right)
FIGURE 6

Probability distribution of fading depth among three signal dynamics for S4 = 0.5 (left) and 0.8 (right)

View this table:
TABLE 2 Number of Fades Greater than 10 dB per Minute

Figure 7 presents the probability distributions of fading duration for S4 = 0.5 and 0.8 for the three signal dynamics. The most probable fading duration for the GPS, LEO min, and LEO max cases is 250, 125, and 25 ms, respectively. Average fade durations are listed in the plot for each case. Results show that larger S4 values (stronger scintillation) lead to longer fades, whereas higher signal dynamics lead to shorter fades.

Probability distribution of fading duration among three signal dynamics at S4 = 0.5 and 0.8
FIGURE 7

Probability distribution of fading duration among three signal dynamics at S4 = 0.5 and 0.8

Figure 8 displays the probability distributions of phase rate disturbance during fading for the same cases shown in Figure 6 and Figure 7. There is a slight dependence of the phase rate disturbance on scintillation level: stronger scintillation leads to a slightly higher phase rate. The results also show that the phase rate disturbance is much higher for the LEO transmitter than for the GPS transmitter: the average phase rate disturbance ranges from less than 1 Hz for a GPS transmitter to several Hz for a high-dynamic LEO transmitter.

Probability distribution of phase rate disturbance among three signal dynamics at S4 = 0.5 and 0.8
FIGURE 8

Probability distribution of phase rate disturbance among three signal dynamics at S4 = 0.5 and 0.8

5.2 Scintillation Signal Tracking Analysis

The previous subsection provided a quantitative analysis of the effect of ionospheric irregularities on signals transmitted from a LEO satellite in comparison with the same signal traversing the same irregularity, but transmitted from a MEO satellite. A similar comparison is carried out in this subsection on the tracking of such signals.

5.2.1 Scintillation Signal Tracking Lock Indicator

Three lock detectors were implemented to indicate the tracking condition of the DLL, PLL, and FLL based on correlation values. The use of the PLL or FLL is dependent on the carrier frequency tracking status, as indicated by the FLL lock detector. Measurements from the three lock detectors were averaged over the 500-s interval and the 120 repeating simulations to obtain each loop’s state for each scenario and under different C/N0 conditions. The results are presented in Figure 9. Note that a higher detector value indicates a healthier tracking state. All three subplots show that the tracking loops (especially the PLL and FLL) are in a less healthy state under weaker signal conditions (∼30 dB-Hz). The tracking quality improves as C/N0 increases from 30 to 40 dB-Hz. The best performance is achieved for signals transmitted by a GPS satellite in MEO (0.b). The worst case is associated with LEO signals having maximum signal dynamics (4.b).

Average DLL, PLL, and FLL lock detector values for each simulation scenario as a function of C/N0 value
FIGURE 9

Average DLL, PLL, and FLL lock detector values for each simulation scenario as a function of C/N0 value

5.2.2 C/N0 Distribution

C/N0 is an indicator of receiver tracking performance. For each simulation scenario, the signal transmitted from the LEO satellite was set to reach the receiver with a baseline C/N0 value at 30–70 dB-Hz. The C/N0 was estimated by the receiver at a 1-s interval using the variance summing method (Sharawi et al., 2007). The estimated C/N0 deviates from the baseline C/N0 owing to amplitude scintillation, loss-of-lock, tracking error, and C/N0 estimate error.

The distributions of the estimated C/N0 for each scenario as a function of its corresponding baseline C/N0 are presented in Figure 10. For all scenarios, bimodal distributions are observed at 30 dB-Hz, with unimodal distributions observed for C/N0 at 40–70 dB-Hz, indicating a prevalence of loss of lock at 30 dB-Hz. A statistical analysis of loss of lock for different C/N0 conditions is provided in Section 5.2.4. The shift of distribution peaks toward the left in the LEO scenarios shows that LEO signal tracking is less robust compared with the GPS signal when the signal is weak.

Probability distribution function (PDF) of receiver-estimated C/N0 dependence on set C/N0
FIGURE 10

Probability distribution function (PDF) of receiver-estimated C/N0 dependence on set C/N0

5.2.3 Cycle Slips

Cycle slip detection was performed on the carrier tracking results, and the cycle slip probability for different times and C/N0 values was calculated from repeat simulations. The time series of carrier-phase tracking error in sub-scenario 0.b (GPS), 1.c (LEO min), and 4.b (LEO max) for C/N0 values of 36 and 54 dB-Hz are presented in Figure 11, where cycle slip is highlighted. The results show that higher phase dynamics and lower C/N0 values lead to more frequent cycle slips. While a shorter coherent integration time can theoretically reduce the effect of scintillation on the carrier tracking loops, it causes more frequent and large cycle slips because of tracking loop instability. Statistical cycle slip results for all nine scenarios are presented in Appendix B.

Carrier-phase tracking error for sub-scenario 0.b (GPS), 1.c (LEO min), and 4.b (LEO max) for C/N0 values of 36 and 54 dB-Hz
FIGURE 11

Carrier-phase tracking error for sub-scenario 0.b (GPS), 1.c (LEO min), and 4.b (LEO max) for C/N0 values of 36 and 54 dB-Hz

We counted the total number of cycle slips in all simulation scenarios. The probability of cycle slip occurrence is shown in Figure 12. Figures 12(a) and (c) present the probability of cycle slip for different C/N0 values and phase rate disturbances ∆ϕ/∆t, respectively, while Figure 12(b) provides a heat map that captures the cycle slip dependence on both parameters. Figure 12(a) shows that cycle slip is more frequent as C/N0 decreases, with a peak occurrence at ∼32 dB-Hz. Below 32 dB-Hz, cycle slip becomes less frequent when loss of lock dominates (explained in the next subsection) and the PLL becomes unstable (see Figure 9). Figure 12(b) shows that the number of cycle slips increases as the phase rate disturbance becomes stronger.

Cycle slip probability for different values of phase rate disturbance and C/N0
FIGURE 12

Cycle slip probability for different values of phase rate disturbance and C/N0

5.2.4 Loss of Lock

The average number of loss-of-lock occurrences during the 500-s interval was calculated for all scenarios. The results are displayed in Figure 13. Clearly, signals transmitted from GPS satellites (0.b) are much less likely to lose lock than those from LEO satellites (1.a–4.b). Among the LEO scenarios, the loss-of-lock probability decreases rapidly as C/N0 increases from 30 to 40 dB-Hz and approaches zero once C/N0 is greater than 40 dB-Hz. Between 35 and 40 dB-Hz, the scenarios with higher phase dynamics (such as 4.b) have a higher loss-of-lock probability.

Average number of loss-of-lock occurrences during the 500-s interval as a function of C/N0 for each simulation scenario
FIGURE 13

Average number of loss-of-lock occurrences during the 500-s interval as a function of C/N0 for each simulation scenario

We also counted the total number of loss-of-lock occurrences from all nine LEO scenario, as shown in Figure 14. Figures 14(a) and (c) present the loss-of-lock probability for different values of C/N0 and phase rate disturbance ∆ϕ/∆t, respectively, while Figure 14(b) displays a heat map that combines the loss-of-lock dependence on both C/N0 and phase rate disturbance. Note that the loss-of-lock probability in Figure 14(c) was calculated for C/N0 < 40 dB-Hz, as loss of lock seldom occurred for C/N0 > 40 dB-Hz. While Figure 14(a) shows a clear correlation between loss of lock and C/N0, as shown in Figure 13, Figure 14(c) shows no strong correlation between loss of lock and phase rate disturbance.

Loss-of-lock probability for different values of phase rate disturbance and C/N0
FIGURE 14

Loss-of-lock probability for different values of phase rate disturbance and C/N0

6 CONCLUSIONS

This paper presented simulation studies of the scintillation effects and tracking of GPS-like L-band signals propagating from a LEO satellite through ionospheric plasma irregularities to a receiver on the Earth’s surface. Several different configurations were simulated, including different phase screen altitudes, LEO satellite orbits, and scintillation severity levels defined by the MEO satellite signal. For each configuration, scintillation-induced carrier phase and amplitude disturbance were first generated and analyzed, including the probability distribution of fading number, depth, duration, and phase rate disturbance, before being modulated into a nominal GPS L1 C/A signal. The simulated scintillation signals were tracked by an SDR with conventional DLL/PLL/FLL architecture to study the impact of ionospheric plasma irregularities on the signal tracking process, including C/N0, cycle slip, and loss of lock. Analyses of scintillation effects and tracking were conducted via both case studies and statistical methods, with a comparison to the same signal traveling through the same irregularity, but from a GPS satellite in MEO. Results show that the same ionospheric structure will cause a larger number of fades (Table 2) that are deeper (Figure 6), shorter (Figure 7), and faster, along with shorter decorrelation times (Table 2) for signals transmitted from LEO than from MEO. Tracking results show that the effect of scintillation on the received signal includes amplitude degradation (Figure 10) and phase disturbance (Figure 11), which impact receiver tracking algorithms in slightly different ways. Cycle slips are strongly correlated with both C/N0 and phase rate disturbance (Figure 12), whereas loss of lock is strongly correlated with C/N0 but exhibits little or no dependence on phase rate disturbance (Figure 14).

HOW TO CITE THIS ARTICLE:

Xu, J., Morton, Y. J., Xu, D., Jiao, Y., & Hinks, J. (2026). Scintillation effects and tracking of GNSS-like signals transmitted from LEO satellites and propagated through ionospheric plasma irregularities. NAVIGATION, 73. https://doi.org/10.33012/navi.752

ACKNOWLEDGMENTS

This project was supported by Air Force Research Laboratory grant #FA9453-20-2-0001. The views expressed are those of the authors and do not necessarily reflect the official policy or position of the Department of the Air Force, the Department of Defense, or the U.S. government.

A | KF MODEL

The fundamental KF models, including the state-space, measurement, observation noise, and process noise models, are detailed in Equations (10)–(12):

xk+1=F⋅xk+wk,yk=Hxk+vk10

Rk=Var(vk),Q=Cov(wk)=GGTσa211

Pk+1|k=FPk|kFT+Q,Kk=Pk+1|kHT(HPk+1|kHT+Rk)−1,Pk+1|k+1=(I−KkH)Pk+1|k12

The specific details of the KFs implemented in the DLL, PLL (2nd/3rd-order), and FLL (1st/2nd-order) are provided in Equations (13)–(15), (16)–(19), and (20)–(23), respectively. These details include the state vector x, measurement y, state-transition matrix F, observation matrix H, observation noise covariance R, and process noise covariance Q:

xDLL=[l^τl^τ˙],yDLL=lτ13

FDLL=[1T01],HDLL=[1−T/2]14

RDLL=d4TC/N0⋅(1+2TC/N0(2−d)),GDLL=[T2/2T]T15

xPLL,2nd=[l^ϕl^ϕ˙],xPLL,3rd=[l^ϕl^ϕ˙l^ϕ¨],yPLL=lϕ16

FPLL,2nd=[1T01],FPLL, 3rd=[1TT2/201T001]17

HPLL,2nd=[1−T/2],HPLL,3rd=[1−T/2−T2/6]18

RPLL=12TC/N0⋅(1+2TC/N0),GPLL,2nd=[T2/2T]T,GPLL,3rd=[T2/2T1]T19

xFLL,1st=[l^ϕ],xFLL,2nd=[l^ϕ˙l^ϕ¨],yFLL=lϕ˙20

FFLL,1st=[1],FFLL,2nd=[1T01]21

HFLL,1st=[1],HFLL,2nd=[1−T/2]22

RFLL=1T3C/N0⋅(1+2TC/N0),GFLL,1st=[T]T,GFLL,2nd=[T1]T23

B | CYCLE SLIP PROBABILITY IN ALL SCENARIOS

The cycle slip probability in all nine scenarios is shown by heat maps in Figure 15, together with the corresponding phase rate disturbance. In the bottom plot, all epochs with over 40% probability of cycle slip are highlighted to reveal their correlation with phase rate disturbance. In each highlighted area, an impulse of phase rate disturbance can be spotted, which indicates that the cycle slip is likely triggered by extreme phase rate disturbance.

(Top) Cycle slip probability for different times and C/N0 values calculated from repeat simulations and (bottom) corresponding phase rate disturbances
FIGURE 15

(Top) Cycle slip probability for different times and C/N0 values calculated from repeat simulations and (bottom) corresponding phase rate disturbances

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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NAVIGATION: Journal of the Institute of Navigation

NAVIGATION: Journal of the Institute of Navigation

Vol. 73

January 2, 2026

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    Scintillation Effects and Tracking of GNSS-Like Signals Transmitted from LEO Satellites and Propagated Through Ionospheric Plasma Irregularities
    • Institute of Navigation
    • Mar 2026,
    • 73
    • navi.752;
    • DOI: 10.33012/navi.752
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Keywords

GNSS receiver tracking loop, ionospheric scintillation, LEO satellite, scintillation simulator