Ionospheric Scintillation Effects on LEO-Transmitted Signals Across Multiple Frequency Bands

Andrew K. Sun; Y. Jade Morton; Charles Rino,; Jiyun Lee

doi:10.33012/navi.772

Ionospheric Scintillation Effects on LEO-Transmitted Signals Across Multiple Frequency Bands

Andrew K. Sun
Andrew K. Sun
¹Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea.
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- For correspondence: [email protected]
Y. Jade Morton
Y. Jade Morton
²Ann and H. J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, USA.
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Charles Rino,
Charles Rino,
²Ann and H. J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, USA.
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and Jiyun Lee
Jiyun Lee
²Ann and H. J. Smead Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, CO, USA.
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- For correspondence: [email protected]

NAVIGATION: Journal of the Institute of Navigation
June 2026,
73
navi.772;
DOI: https://doi.org/10.33012/navi.772

Abstract

Previous studies using a physics-based global navigation satellite system scintillation simulator demonstrated that Global Positioning System-like L1 signals transmitted from low-Earth-orbit (LEO) satellites exhibit higher signal dynamics, resulting in more severe scintillation effects than those from medium-Earth-orbit satellites. This study extends these analyses from L-band to very high frequency, ultra-high frequency, and S-band, evaluating the effects of scintillation on LEO-transmitted signals across a broader range of frequency bands. Key scintillation characteristics, including fading time separation, duration, depth, and phase rate, are examined across frequencies and signal dynamics under different transmission scenarios. The results show that lower-frequency signals experience more frequent and deeper fades with greater phase fluctuations, particularly under higher dynamics of LEO transmissions. Quantitative analysis reveals that the ratios of mean scintillation characteristics (fading time separation, duration, and phase rate) between different signal dynamics cases remain consistent across frequencies. Rare fading overlaps among L-band frequencies suggest the potential for leveraging inter-frequency aiding to improve receiver tracking robustness for LEO transmissions.

Keywords

1 INTRODUCTION

Ionospheric scintillation refers to rapid fluctuations in both the amplitude and phase of radio waves traversing ionospheric plasma irregularities. These fluctuations significantly impact space-based applications, including global navigation satellite systems (GNSSs), which transmit L-band radio signals from medium Earth orbit (MEO) to receivers on or near the Earth's surface. In severe cases, ionospheric scintillation can cause deep signal fades and abrupt phase changes, disrupting the carrier tracking process of GNSS receivers and potentially degrading navigation performance (Breitsch et al., 2020; Humphreys et al., 2010; Jiao & Morton, 2015; Xu & Morton, 2017). To address these challenges, scintillation simulation models have been developed to offer a useful tool for assessing these impacts and developing robust tracking algorithms to mitigate such adverse effects.

The phase screen model has been extensively used to simulate the effects of scintillation on GNSS signals, based on the theory of radio wave propagation through ionospheric plasma irregularities. Phase screens are commonly characterized by power-law spectra, typically implemented as either one-component or two-component power laws. The one-component power-law model has been shown to be suitable for weak to moderate scintillations (Chartier et al., 2016; Deshpande et al., 2016; Ghafoori & Skone, 2015), whereas the two-component power-law phase screen model (TPPSM) more effectively captures strong scintillations (Rino et al., 2014; Carrano & Rino, 2016).

Rino et al. (2018) developed a compact version of the TPPSM that generates statistically equivalent realizations of GNSS complex-field scintillation time series through two-dimensional phase screen calculations. This model provides statistical representations of the phase screen using a compact set of modeling parameters. This model has been demonstrated to facilitate the study of scintillation effects on GNSS signals received on dynamic platforms such as aircraft or low-Earth-orbit (LEO) satellites (Jiao et al., 2018a; Xu et al., 2018). Based on numerical relationships between the modeling parameters and user input parameters, Xu et al. (2020) further streamlined this model by reducing the number of parameters from five to two: the scintillation index S₄ and the intensity decorrelation time τ₀. This simplified phase screen model provides a statistically consistent abstraction of ionospheric irregularities and enables scintillation simulations with varying S₄ and τ₀ values to effectively model different levels of scintillation and signal dynamics.

Recent studies utilizing the scintillation simulator developed by Xu et al. (2020) have shown that scintillation poses greater challenges for signals transmitted from LEO satellites compared with those from MEO satellites under the same ionospheric conditions. Simulation studies have analyzed the impact of scintillation on Global Positioning System (GPS)-like L1 coarse acquisition (C/A) signals propagating from LEO satellites to ground receivers (Morton et al., 2022) and have assessed their signal tracking performance (Xu et al., 2023). Compared with MEO satellites, LEO-transmitted signals have higher scan velocities across the ionosphere, leading to more frequent signal fades and increased phase dynamics under equivalent plasma irregularity conditions (Morton et al., 2022). These differences result in more degraded tracking performance, with a great number of occurrences of loss of lock and cycle slips for signals transmitted from LEO satellites compared with those from MEO satellites (Xu et al., 2023). There is a growing interest in using signals from LEO satellites for future navigation (Kassas, 2020; Prol et al., 2022; Reid et al., 2020) to augment GNSS services and to support remote sensing applications. Understanding the effects of scintillation on signals transmitted from LEO satellites is crucial for ensuring the reliability of these applications. However, previous studies have been limited to L-band frequencies, leaving a critical knowledge gap regarding scintillation behavior across the diverse frequency bands proposed for LEO satellite systems.

This work extends previous studies to the analysis of scintillation effects on signals at multiple carrier frequency bands, including very high frequency (VHF), ultra-high frequency (UHF), GPS-like L-band, and S-band, transmitted from LEO satellites. We employ the scintillation simulator developed by Xu et al. (2020), extrapolating the modeling parameters to a broader range of frequencies and using various values representing signal dynamics to investigate different signal transmission scenarios. Section 2 summarizes the multi-frequency scintillation simulator initialized with real GNSS scintillation data. Section 3 presents simulation scenarios of signal dynamics for various transmission configurations and carrier frequencies. Section 4 presents an analysis of scintillation characteristics across carrier frequencies and signal dynamics cases to investigate their effects on signals transmitted from LEO satellites, compared with those from MEO satellites. Conclusions and future work are presented in Section 5.

2 SCINTILLATION SIMUATOR ACROSS FREQUENCY BANDS

Figure 1 presents a flow chart of the multi-frequency scintillation simulator developed by Xu et al. (2020). This simulator requires only two input parameters: the scintillation index S₄ and the intensity decorrelation time τ₀. S₄ is the normalized deviation of signal intensity, whereas τ₀ is defined as the time lag at which the autocorrelation function (ACF) of signal intensity drops to 1/e of its peak value. These parameters, derived from ground-based GNSS measurements, serve as the input parameters for the simulations considered in this paper.

Figure 1

Flowchart of the scintillation simulation process

The flowchart shows the scintillation simulation process for the frequency f_s scaled from the reference frequency f_r, based on the simulator presented by D. Xu et al. (2020). PVT: position, velocity, and time; RX: receiver

The simulator is based on the TPPSM, which is specified by a set of parameters ${U, p_{1}, p_{2}, μ_{0}, ρ_{F} / v_{eff}} . U$ represents the universal scattering strength, defined as the normalized phase spectral power at the Fresnel scale ( $ρ_{F} = \sqrt{x / k}$ ), where x is the propagation distance from the effective ionospheric pierce point of the phase screen to the receiver and k is the free-space wavenumber of the carrier frequency (Carrano & Rino, 2016; Rino, 1979a, 1979b). p₁ and p₂ are power-law indices representing the spectral slopes of the phase power spectrum. μ₀ is a normalized break wavenumber corresponding to the point at which the spectrum changes slope. The space-to-time scaling factor $ρ_{F} / v_{eff}$ represents the temporal decorrelation scale of scintillation. This factor absorbs dependencies on propagation geometry and signal scan velocity, with $ρ_{F}$ determining the effective propagation distance and $v_{eff}$ representing the effective scan velocity of the radio wave across the phase screen (Carrano & Rino, 2016; Jiao et al., 2018b; Rino et al., 2018).

Different combinations of S₄ and τ₀ values are mapped to a set of TPPSM parameters ${U, p_{1}, p_{2}, μ_{0}, ρ_{F} / v_{eff}}$ , which determine the phase screen realizations (Xu et al., 2020; Rino et al., 2018). Xu et al. (2020) processed a strong scintillation data set using a maximum-likelihood fitting procedure applied to intensity spectral density functions, referred to as irregularity parameter estimation (Carrano et al., 2012; Carrano & Rino, 2016). Numerical mappings were established based on the estimates of ${U, ρ_{F} / v_{eff}}$ and ${S_{4}, τ_{0}}$ from the real scintillation data set, with the most representative values assumed for the spectral parameters ${p_{1}, p_{2}, μ_{0}}$ based on their empirical distributions.

As previously presented by Morton et al. (2022), the simulator accommodates various scenarios of signal propagation geometry. These scenarios are characterized by distinct $ρ_{F} / v_{eff,dyn}$ values designed to align with the user-defined satellite–receiver platform dynamics. The calculation of $ρ_{F} / v_{eff,dyn}$ involves considering the signal scan velocity at the phase screen ( $v_{scan}$ ) and the drift velocity of the irregularities ( $v_{drift}$ ). The unknown $v_{drift}$ is determined through numerical solutions by comparing the $ρ_{F} / v_{eff,static}$ values derived from satellite orbits and those inferred from τ₀ values. The estimated $v_{drift}$ is then incorporated into the calculation of $ρ_{F} / v_{eff,dyn}$ for the desired signal dynamics, with a consideration of the satellite–receiver geometry, resulting in the corresponding $ρ_{F}$ and $v_{eff}$ values at a given phase screen (Xu et al., 2020). Further details regarding different scenarios of satellite–receiver geometry and signal dynamics are provided in Section 3.

Among the TPPSM parameters, U,μ₀, and $ρ_{F} / v_{eff}$ depend on the carrier frequency, whereas p₁ and p₂ remain consistent across different frequencies. To establish the TPPSM for different frequencies, these three parameters are scaled from a reference frequency (f_r) to a scaling frequency (f_s) using the following Equations (1)–(3) presented by Xu et al. (2020):

$U (f_{S}; f_{r}) = {\begin{cases} U (f_{r}) {(f_{r} / f_{S})}^{\frac{p_{1} + 3}{2}} & μ_{0} (f_{r}) \geq 1, μ_{0} (f_{S}) \geq 1 \\ U (f_{r}) {μ_{0} (f_{r})}^{p_{1} - p_{2}} {(f_{r} / f_{S})}^{\frac{p_{1} + 3}{2}} & μ_{0} (f_{r}) < 1, μ_{0} (f_{S}) \geq 1 \\ U (f_{r}) {μ_{0} (f_{r})}^{p_{2} - p_{1}} {(f_{r} / f_{S})}^{\frac{p_{2} + 3}{2}} & μ_{0} (f_{r}) \geq 1, μ_{0} (f_{S}) < 1 \\ U (f_{r}) {(f_{r} / f_{S})}^{\frac{p_{2} + 3}{2}} & μ_{0} (f_{r}) < 1, μ_{0} (f_{S}) < 1 \end{cases}$ 1

$μ_{0} (f_{s}; f_{r}) = μ_{0} (f_{r}) \sqrt{f_{r} / f_{s}}$ 2

$ρ_{F} / v_{eff} (f_{s}; f_{r}) = ρ_{F} / v_{eff} (f_{r}) \sqrt{f_{r} / f_{s}}$ 3

These frequency scaling relationships capture how signals at different carrier frequencies are affected by the same ionospheric irregularities. The universal scattering strength U can be expressed as follows (Carrano & Rino, 2016):

$U = {\begin{matrix} C_{p} ρ_{F}^{p_{1} - 1} & μ_{0} \geq 1 \\ C_{p} ρ_{F}^{p_{1} - 1} μ_{0}^{p_{2} - p_{1}} & μ_{0} < 1 \end{matrix}$ 4

The frequency scaling of U depends on whether the normalized spectral break $μ_{0}$ is above or below unity, determining which spectral index governs scattering at the Fresnel scale with $ρ_{F} \propto f^{- 1 / 2}$ . This dependence explains the conditional structure in Equation (1). Equations (2) and (3) indicate that both $μ_{0}$ and $ρ_{F} / v_{eff}$ scale inversely with the square root of frequency, adjusting the spectral break position and the space-to-time scaling factor accordingly.

By using the TPPSM parameters derived from Equations (1)–(3) and applying the same sequence of random noise, the simulator generates realistic scintillations across different frequencies that effectively share the same initial phase screen. This inter-frequency consistency of the simulator enables analyses of scintillation characteristics by assuming that signals at different frequencies propagate through the same ionospheric irregularity structure.

3 SIMULATION SCENARIOS

Scintillation simulations are based on a 5-min segment of initiation data observed in L1 C/A signals from the GPS pseudorandom noise (PRN) 24 satellite collected by a ground receiver located in Hong Kong (22.21°S, 114.26°E) on 5 October 2013, from 12:25 to 12:30 Universal Time (UT) (Morton et al., 2022). The simulations use input parameters of $S_{4} = 0.8$ and $τ_{0} = 0.76 s$ , which represent the average values within the initiation data segment. According to the numerical mappings established by Xu et al. (2020), the corresponding values for U and $ρ_{F} / v_{eff}$ are 1.47 and 1.18 s, respectively, for the GPS L1 frequency. This initial $ρ_{F} / v_{eff}$ value of 1.18 s is adjusted for different signal dynamics scenarios based on distinct satellite transmission and phase screen configurations, as described in Section 3.1. The spectral parameters p₁, p₂, and $μ_{0}$ are set to their representative values of 2.6, 3.7, and 0.6, respectively, based on the empirical profiles established by Xu et al. (2020).

3.1 Signal Dynamics Scenarios

Signal dynamics scenarios are derived from different configurations of MEO and LEO satellite transmissions, as defined by Morton et al. (2022). Each scenario is characterized by distinct $ρ_{F} / v_{eff}$ values, which are determined by a specific combination of LEO satellite transmissions and phase screen configurations. LEO satellite orbits are configured by projecting the satellite orbit from the initiation data (GPS PRN24 satellite during 12:25~12:30 UT, 5 October 2013) at MEO altitude to altitudes (h_TX) of 550 and 800 km. The phase screen is assumed to be located at altitudes (h_PS) of 300 km and 500 km for LEO transmission configurations.

Table 1 presents five scenarios defined by Morton et al. (2022), with scenario 0 representing the GPS satellite at MEO altitude and scenarios 1–4 representing LEO transmissions with different combinations of h_TX and h_PS. Three representative cases are selected for the scintillation simulation, as defined by Morton et al. (2022): MEO, LEO-min, and LEO-max, with corresponding $ρ_{F} / v_{eff}$ values of 1.18, 0.47, and 0.07 s, respectively. The MEO case uses the average value within the range of scenario 0, whereas the LEO-min and LEO-max cases correspond to the maximum (0.47 s in scenario 1) and minimum (0.07 s in scenario 4) $ρ_{F} / v_{eff}$ values among the LEO scenarios, respectively. Each $ρ_{F} / v_{eff}$ value serves as an input for the simulator to effectively generate scintillation for the respective signal dynamics conditions.

View this table:

Table 1

Simulation Scenarios with LEO and MEO Configurations

The table shows the orbit altitude ( $h_{TX}$ ), phase screen altitude ( $h_{PS}$ ), and $ρ_{F} / v_{eff}$ range following the configurations defined by Morton et al. (2022). Asterisks (*) indicate the maximum and minimum $ρ_{F} / v_{eff}$ values in the LEO scenarios, corresponding to the LEO-min and LEO-max cases, respectively.

3.2 Simulation Across Carrier Frequency Bands

Based on Equations (1)–(3), the TPPSM parameters, including the $ρ_{F} / v_{eff}$ values for different signal dynamics scenarios, are scaled from the GPS L1 frequency (1575.42 MHz) to generate scintillation realizations at multiple carrier frequencies: VHF (137.1 MHz), UHF (965 MHz), L5 (1176.45 MHz), L2 (1227.60 MHz), and S-band (2200 MHz). These frequencies were selected for ongoing and planned real scintillation signal validation. The VHF signal at 137.1 MHz corresponds to transmissions from the National Oceanic and Atmospheric Administration (NOAA)-19 satellite, a polar orbiting weather satellite whose signals were captured during a controlled ionosphere disturbance experiment (Morton et al., 2024). The selected frequencies of 965 MHz in the UHF band and 2200 MHz in the S-band are employed for radio-frequency beacon signals transmitted by the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC)-2 satellites (Hsiao et al., 2022) and are being used for assessments of equatorial ionospheric effects.

Table 2 presents the frequency-scaled parameters calculated from Equations (1)–(3) ( $U, μ_{0}, ρ_{F} / v_{eff}$ ), with the estimated S₄ values for each frequency. The results show that U exhibits higher values at lower frequencies, leading to stronger scintillations with higher S₄ values, where saturation occurs at values near 1. $ρ_{F} / v_{eff}$ shows higher values at lower frequencies, indicating reduced signal dynamics. However, the variations in $ρ_{F} / v_{eff}$ are much smaller than those in U across frequencies, suggesting that $ρ_{F} / v_{eff}$ has a less significant impact on the simulation results.

View this table:

Table 2 Phase Screen Parameters and Estimated S₄ Values for Different Frequencies Across Signal Dynamics Cases

3.3 Scintillation Realizations

For each simulation configuration, 1,000 min of scintillation realizations are generated to obtain statistically significant scintillation characteristics using a sampling interval of 1 ms. Figure 2 presents examples of scintillation signals for different signal dynamics and frequency bands. Figure 2(a) presents the simulated signal intensity (top) and phase (bottom) time series for the L1 signal under the MEO, LEO-min, and LEO-max cases. Figure 2(b) presents the intensity and phase time series for VHF, UHF, L1, and S-band signals under the MEO case. Figure 2(a) shows that higher signal dynamics result in more frequent deep fades and larger phase variations, with LEO-max exhibiting the most rapid variations, consistent with an earlier analysis by Morton et al. (2022). Figure 2(b) shows that lower frequencies experience larger signal fluctuations with more frequent and deeper fades, with VHF signals exhibiting the most intense scintillation effects. This result aligns with the larger scattering strength (U) at lower frequencies, as shown in Table 2. The phase variations in Figure 2(b) show distinct frequency-dependent behavior: VHF signals experience extremely frequent diffraction-induced phase transitions, creating a dense step-like pattern distinct from the background phase variations (Gherm et al., 2012; Breitsch et al., 2020), whereas higher-frequency signals exhibit more gradual phase variations.

Figure 2

Scintillation signal time series across dynamics and frequencies

Panel (a) shows the simulated signal intensity (SI) and phase (ϕ) for the different signal dynamics cases (MEO, LEO-min, and LEO-max) at the L1 frequency. Panel (b) shows time series for VHF, UHF, L1, and S-band signals in the MEO case.

It should be noted that the simulations presented in this study analyze scintillation-induced fading relative to the nominal signal power level, without considering thermal noise or the baseline carrier-to-noise density ratio (C/N₀). In practical scenarios, signals received from LEO and MEO satellites have different strengths, primarily owing to differences in propagation distance. Although these signal power differences affect the practical impact of fading events on receiver tracking performance, our analysis isolates the scintillation-induced fluctuations to establish fundamental comparisons across carrier frequencies and signal dynamics. Evaluations of tracking performance impacts using these relative fading characteristics for specific LEO and MEO systems with their respective received signal levels are reserved for future work.

Figure 3 presents the distributions and statistics of signal intensity under scintillations at the L1 frequency across the different signal dynamics cases: MEO, LEO-min, and LEO-max. Figure 3(a) shows the probability distribution functions (PDFs) of signal intensity, which remain consistent across these cases despite their distinct $ρ_{F} / v_{eff}$ values. Consequently, the S₄ values are consistent across the signal dynamics cases, as shown in Figure 3(c). The intensity ACFs in Figure 3(b) exhibit a decreasing lag as signal dynamics increase from MEO to LEO-min and LEO-max. This trend is further supported by Figure 3(d), where τ₀ is shown to be linearly proportional to $ρ_{F} / v_{eff}$ . This proportional relationship has been previously discussed by Xu et al. (2020).

Figure 3

Signal intensity (SI) statistics for L1 signals across signal dynamics

Panels (a) and (b) show the PDF and ACF for the MEO, LEO-min, and LEO-max cases with $ρ_{F} / v_{eff}$ values of 1.18, 0.47, and 0.07 s, respectively. The black dashed line in (b) indicates $e^{- 1}$ ; the delay at which the ACF intersects this line corresponds to the value of $τ_{0}$ . Panels (c) and (d) show $S_{4}$ and $τ_{0}$ , respectively, plotted against $ρ_{F} / v_{eff}$ values, with black dashed lines representing linear fits.

Figure 4 presents the distributions and statistics of signal intensity under scintillations for the MEO case across different frequencies: VHF, UHF, L1, and S-band. Figure 4(a) shows that lower-frequency signals exhibit a broader spread in distributions compared with higher-frequency signals. Similarly, Figure 4(b) shows a decreasing lag in the ACFs as frequency decreases. This behavior is primarily attributed to the significant increase in U at lower frequencies, as listed in Table 2. In Figure 4(c), the saturation of S₄ values at lower frequencies, resulting from high U values, may contribute to the observed nonlinear behavior. Figure 4(d) further shows that τ₀ values decrease at lower frequencies, driven by stronger scattering associated with the significant increase in U as frequency decreases.

Figure 4

Signal intensity (SI) statistics for the MEO case across frequencies

Panels (a) and (b) show the PDF and ACF, respectively, for VHF (137.1 MHz), UHF (965 MHz), L1 (1575.42 MHz), and S-band (2200 MHz) signals in the MEO case. The black dashed line in (b) indicates $e^{- 1}$ ; the delay at which the ACF intersects this line corresponds to the value of $τ_{0}$ . Panels (c) and (d) show $S_{4}$ and $τ_{0}$ , respectively, plotted against frequency.

4 STATISTICAL ANALYSIS OF SCINTILLATION SIGNAL CHARACTERISTICS

4.1 Scintillation Signal Characteristics

In this study, we analyzed the characteristics of signal fading and phase rate variations. Figure 5 illustrates the fading observed in L1, L2, and L5 signals with a threshold of –10 dB, providing definitions of key fading characteristics: time separation, duration, depth, and overlaps across different frequencies (Jiao et al., 2016). Time separation refers to the interval between two consecutive fades, fading duration represents the length of each fading event, and fading depth indicates the minimum signal level reached during a fading event. Additionally, we calculated the statistics of phase rate specifically within the fading events.

Figure 5

Illustration of signal fading characteristics

The plots show the time separation, duration, depth, and overlaps of fades across different frequency signals, determined using a –10-dB threshold (top) and phase rate variations (bottom). SI: signal intensity

A threshold of –10 dB is commonly used in scintillation studies to identify deep fading events that can potentially cause phase transitions and tracking disruptions. This threshold has been employed in previous analyses (Zernov et al., 2012; Jiao et al., 2016), as it represents a practical signal level for characterizing severe scintillation effects while maintaining sufficient statistical occurrence for analysis. Note that the threshold is relative to the unperturbed signal level, representing the scintillation-induced fading depth independent of baseline signal power.

4.2 Statistical Analysis of Scintillation Characteristics

4.2.1 Time Separation

The time separation between signal fades serves as a measure of the occurrence rate of signal fading. This metric is essential for modeling the stochastic process of deep fades that impact signal reacquisition and tracking (Jiao et al., 2016; Sun et al., 2021). The time separation between fades is defined as the time difference between the points at which the signal intensity falls below the fading threshold, as illustrated in Figure 5.

Figure 6 presents histograms of the time separation between fades below -10 dB for signals at VHF, UHF, L5, L2, L1, and S-band across the signal dynamics cases: MEO, LEO-min, and LEO-max. Higher signal dynamics result in more frequent fades, consistent with the prior analyses by Morton et al. (2022). The average time separation between fades at L1 in the MEO case is 21.69 s, compared with 8.55 s and 1.30 s in the LEO-min and LEO-max cases, respectively. This observation aligns with the proportional relationship between the scintillation time scale $τ_{0}$ and the $ρ_{F} / v_{eff}$ values across various signal dynamics, as shown in Figure 3(d).

Figure 6

Probability distributions of time separation between –10-dB fades

Results are shown for VHF, UHF, L5, L2, L1, and S-band signals in the (a) MEO, (b) LEO-min, and (c) LEO-max cases. The bin widths are 2 s, 1 s, and 0.1 s, respectively. The legends indicate the average time separation and the average number of fades per minute for each case.

The histograms also show shorter time separations between fades at lower frequencies compared with higher frequencies. The VHF signals experience extremely frequent fades, with an average time separation of 0.03 s in the LEO-max case, corresponding to 2327.06 fades per minute. Such frequent fades can severely degrade signal tracking under high signal dynamics, increasing the likelihood of cycle slips and prolonged signal loss during reacquisition. In contrast, the S-band signals experience very few fades, with an average time separation of 112.59 s under the LEO-max case.

Figure 7 complements the histograms in Figure 6 by providing the occurrence rate of –10-dB fades and the average time separation between fades of VHF, UHF, L5, L2, L1, and S-band signals across the signal dynamics cases: MEO, LEO-min, and LEO-max. Figure 7(a) shows that the fading occurrence rate increases significantly with decreasing carrier frequency. The VHF signals experience the highest number of fades, particularly under the LEO-max case, showing the pronounced impact of high signal dynamics on signals at lower frequencies. This trend is consistent across all signal dynamics cases, with the VHF signals experiencing the highest fading occurrence owing to their increased susceptibility to scintillation effects. In contrast, the S-band signals experience only 0.04, 0.09, and 0.53 fades per minute for the MEO, LEO-min, and LEO-max cases, respectively, indicating insignificant scintillation impacts.

Figure 7

Fading occurrence rate and time separation across frequencies

Panel (a) shows the occurrence rate of –10-dB fades. Panel (b) shows the average time separation between fades across frequency for VHF (137.1 MHz), UHF (965 MHz), L5 (1176.45 MHz), L2 (1227.60 MHz), L1 (1575.42 MHz), and S-band (2200 MHz) signals in the MEO, LEO-min, and LEO-max cases.

Figure 7(b) presents the average time separation between –10-dB fades, revealing a clear relationship between frequency and time separation between fades under the different signal dynamics cases. The VHF signals exhibit much shorter time separations than the S-band signals. This trend is consistent across all signal dynamics cases. For the VHF signals, the average time separation is on the order of milliseconds, particularly for the LEO-max case, indicating extremely frequent fades. In contrast, the S-band signals exhibit time separations of hundreds of seconds, even for the LEO-max case. This result demonstrates that signals at higher frequencies are less impacted by scintillation, making them more suitable for traditional tracking methods. Under high signal dynamics, open-loop tracking might be necessary for lower frequencies owing to the rapid and frequent signal fluctuations.

4.2.2 Fading Duration

The fading duration is defined as the time interval during which the signal intensity remains below the threshold. Longer fading durations increase the probability of cycle slips or loss of signal lock in receiver tracking. Because receivers can reacquire signals once the intensity recovers above the tracking threshold, the fading duration serves as a crucial parameter that determines receiver reacquisition capability (Jiao et al., 2016; Sun et al., 2021).

Figure 8 presents histograms of –10-dB fading durations of VHF, UHF, L5, L2, L1, and S-band signals across the signal dynamics cases. The results show that the LEO-max case with higher signal dynamics exhibits shorter fading durations, with an average value of 0.020 s for the L1 signal, compared with 0.128 s for the LEO-min case and 0.319 s for the MEO case. Similar to the time separation between fades, this observation is consistent with the proportional relationship between the scintillation time scale τ₀ and the $ρ_{F} / v_{eff}$ values across signal dynamics cases, as shown in Figure 3(d).

Figure 8

Probability distributions of –10-dB fading duration

Results are shown for VHF, UHF, L5, L2, L1, and S-band signals in the (a) MEO, (b) LEO-min, and (c) LEO-max cases. The bin widths are 0.15 s, 0.5 s, and 0.01 s, respectively. The legends indicate the average fading duration for each case.

Figure 9 presents the average durations of –10-dB and –20-dB fades for different frequency bands and signal dynamics cases. The analysis reveals that fading durations increase as the frequency decreases from S-band to L5, which corresponds to the gradual increase in scattering strength (U increases from 0.48 to 3.90, as shown in Table 2). This trend indicates that stronger scintillation effects lead to deeper and longer-duration fades at lower frequencies (Jiao et al., 2016; Sun et al., 2023). However, this trend reverses for UHF and VHF, where the scattering strength increases dramatically (U = 7.58 for UHF and 2396.32 for VHF). Although moderate increases in U (S-band through L-band) lead to longer-lasting fades, the higher U values at UHF and especially VHF create a different regime, where fades occur so rapidly that each individual fade becomes extremely brief, resulting in shorter average fading durations. The consistency of this frequency-dependent trend across both –10-dB and –20-dB thresholds demonstrates that the relationship between fading duration and frequency remains stable, even for deeper fading events. These findings have significant implications for signal tracking and reacquisition strategies at lower frequency bands, particularly under high signal dynamics.

Figure 9

Average fading durations across frequencies

Panels (a) and (b) show –10-dB and –20-dB threshold results, respectively, for the average fading duration across frequency for VHF (137.1 MHz), UHF (965 MHz), L5 (1176.45 MHz), L2 (1227.60 MHz), L1 (1575.42 MHz), and S-band (2200 MHz) signals for the MEO, LEO-min, and LEO-max cases.

4.2.3 Fading Depth

The fading depth represents the minimum signal intensity value during a fading event, as illustrated in Figure 5. Figure 10 presents histograms of fading depth below –10 dB for VHF, UHF, L5, L2, L1, and S-band signals across the signal dynamics cases. The results show that signals at lower frequencies exhibit higher probabilities of deeper fading compared with signals at higher frequencies across all signal dynamics cases. This frequency dependence is attributed to the increased scattering strength (U) at lower frequencies, resulting in greater variations in signal intensity and a higher occurrence of deeper fades. The histograms show consistent distribution patterns for each frequency across signal dynamics cases, indicating that fading depth exhibits a relatively weak dependence on signal dynamics.

Figure 10

Probability distributions of fading depth below –10 dB

Results are shown for VHF, UHF, L5, L2, L1, and S-band signals in the (a) MEO, (b) LEO-min, and (c) LEO-max cases. The bin widths are 5 dB. The legends indicate the average fading depth for each case.

Figure 11 presents the average fading depth verses frequency for the different signal dynamics cases. The results confirm the frequency dependence of fading depth shown in Figure 10. As demonstrated in Figure 3, the signal intensity distributions remain nearly identical across different signal dynamics at the same frequency, which explains why the fading depth distributions remain consistent across the MEO, LEO-min, and LEO-max cases, particularly for the L-band frequencies. This consistency arises because the fading depth depends on the intensity distribution defined by the spectral parameters ${U, p_{1}, p_{2}, μ_{0}}$ rather than on the temporal dynamics controlled by $ρ_{F} / v_{eff}$ . However, deviations from this trend occur at the lowest and highest frequencies. The VHF signal shows variations because the extremely brief fades at this frequency approach the 1-ms sampling interval, making it challenging to accurately capture the true minimum intensity values. The S-band signal exhibits deviations due to statistical uncertainties arising from the limited number of fading events in the simulation period.

Figure 11

Average fading depth across frequencies

Results show the average fading depth below –10 dB for VHF (137.1 MHz), UHF (965 MHz), L5 (1176.45 MHz), L2 (1227.60 MHz), L1 (1575.42 MHz), and S-band (2200 MHz) signals for the MEO, LEO-min, and LEO-max cases.

4.2.4 Phase Rate

Figure 12 presents distributions of phase rate during –10-dB fading events for VHF, UHF, L5, L2, L1, and S-band signals across the signal dynamics cases. This analysis shows that the LEO-max case exhibits significantly higher phase rates than the MEO case, consistent with the prior analyses by Morton et al. (2022). In addition, the phase rates show marked increases at lower frequencies.

Figure 12

Probability distributions of phase rate during –10-dB fading

Results are shown for VHF, UHF, L5, L2, L1, and S-band signals in the (a) MEO, (b) LEO-min, and (c) LEO-max cases. The bin widths are 0.4 s, 1 s, and 10 s, respectively. The legends indicate the average phase rate for each case.

Figure 13 presents the average phase rates across frequencies for the different signal dynamics cases. The results show pronounced increases in phase rates at lower frequencies, where lower $ρ_{F} / v_{eff}$ values under higher signal dynamics correspond to increased phase rates. The observed trend indicates substantial challenges in signal tracking for signals at lower frequencies due to larger phase rate dynamics. The increased phase rates introduce greater uncertainty in signal tracking by affecting both the pull-in range and the accuracy of the phase-locked loop. These phase rate variations suggest the need for robust tracking strategies at lower frequencies, particularly under high signal dynamics where rapid phase changes can compromise signal tracking stability and accuracy.

Figure 13

Average phase rate across frequencies

Results show the phase rate during –10-dB fading for VHF (137.1 MHz), UHF (965 MHz), L5 (1176.45 MHz), L2 (1227.60 MHz), L1 (1575.42 MHz), and S-band (2200 MHz) signals for the MEO, LEO-min, and LEO-max cases.

4.2.5 Analysis of Temporal Characteristics in Scintillation Across Signal Dynamics

To quantitatively analyze the relationship between scintillation characteristics and signal dynamics, the ratios of these metrics were calculated across the different signal dynamics cases. The analyzed parameters include the time separation and duration of –10-dB fades and the phase rate, which are compared with $ρ_{F} / v_{eff}$ values representing the signal dynamics in scintillation. Figure 14 presents the results for all simulated frequencies.

Figure 14

Ratios of scintillation characteristics between the LEO and MEO cases

The figure shows ratios of the average values for time separation, duration of –10-dB fades, and phase rate across VHF (137.1 MHz), UHF (965 MHz), L5 (1176.45 MHz), L2 (1227.60 MHz), L1 (1575.42 MHz), and S-band (2200 MHz) signals. The dashed lines indicate corresponding $ρ_{F} / v_{eff}$ ratios between the LEO-min (or LEO-max) and MEO cases.

The results shows that the ratios between the LEO and MEO cases for fading separation, duration, and phase rate closely align with those of $ρ_{F} / v_{eff}$ across all simulated frequencies. This result indicates that the temporal characteristics of signal fading (time separation and duration) are directly proportional to $ρ_{F} / v_{eff}$ . This finding aligns with the work of Xu et al. (2020), which demonstrated that the decorrelation time ( $τ_{0}$ ), a representative temporal scale of scintillation, is proportional to $ρ_{F} / v_{eff}$ , as discussed in Section 3.3. Furthermore, this finding suggests that the temporal characteristics of signal fading under two different signal dynamics scenarios can be accurately estimated by scaling them according to their respective $ρ_{F} / v_{eff}$ values.

Deviations in the ratios of mean values can be observed at the highest frequency in S-band and the lowest frequency in VHF. For the S-band signals, the limited number of signal fades during the simulation period may result in insufficient statistical significance in the mean values of each feature. For the VHF signals, excessively rapid variations in signal intensity under LEO-transmitted signal dynamics may lead to shorter signal fades for a fixed sampling interval, potentially causing an overestimation of the temporal scale of signal fading. This deviation may also result from violations of the fundamental assumptions underlying the simulation model, which was originally designed for L-band signals. Consequently, an investigation of the theoretical and sampling limitations of the simulation model is necessary to ensure its reliability across a broader range of frequency bands.

4.2.6 Fading Overlaps

Sufficient time separations in concurrent fades enable the use of frequency diversity during deep fading through inter-frequency aiding (Yang et al., 2019; Yin et al., 2014). As illustrated in Figure 5, fading overlaps refer to instances in which the time durations of fading events overlap across different frequencies. Table 3 summarizes the time fractions of all combinations of fading overlaps in L1, L2, and L5 signals over a simulation period of 1,000 min for the MEO, LEO-min, and LEO-max cases.

View this table:

Table 3 Percentages of –10-dB Fading Overlaps in Simulated L1, L2, and L5 Signals

The results show that concurrent fading across all three frequencies is highly improbable. The highest probability of concurrent fading occurs under higher signal dynamics in the LEO-max case. Even in the LEO-max case, the concurrent fading probabilities remain low: 13.58% for L2 and L5 under L1 fading, 3.53% for L1 and L5 under L2 fading, and 3.10% for L1 and L2 under L5 fading. The probability of concurrent fading is also low between L1 and L2 and between L1 and L5. These results align with actual scintillation observations reported by Jiao et al. (2016), which demonstrate the rarity of concurrent fading across nearby L-band frequencies (L1, L2, and L5). Concurrent fades at widely separated frequencies, such as VHF, UHF, and S-band, are expected to be even more rare.

Table 3 shows that the fading probability remains consistent across the different signal dynamics cases. The probability of L1-only fading ranges from 77.56% to 79.76%, with a variation of approximately 2% from LEO-max to MEO. Similarly, the probability of L5-only fading ranges from 45.52% to 46.29%, with a variation of approximately 0.7% from LEO-max to MEO. The consistent behavior across the different signal dynamics can be attributed to the proportional relationship between the temporal characteristics of signal fading and $ρ_{F} / v_{eff}$ values, as discussed in Section 4.2.5. These findings suggest that a consistent proportion of time separation among fades at different frequencies effectively contributes to frequency diversity in frequency-aided tracking, even under high signal dynamics. Slight increases in fading overlaps observed under higher signal dynamics may be attributed to the discretization of samples, particularly for shorter fades occurring in such conditions.

5 CONCLUSIONS

This paper extended the simulation studies presented by Morton et al. (2022) to investigate the effects of scintillation on signals transmitted from LEO satellites across a wide range of frequency bands. Using the scintillation simulator developed by Xu et al. (2020), we comprehensively represented scintillation effects with distinct signal dynamics by employing the time-to-space scaling parameter $ρ_{F} / v_{eff}$ . This simulator incorporates frequency scaling of modeling parameters, enabling scintillation representations for specific frequencies by effectively applying the same initial phase screen.

The simulator was used to analyze scintillation across multiple frequency bands, including VHF, UHF, L-band (L1, L2, and L5), and S-band, under three signal dynamics scenarios: MEO, LEO-min, and LEO-max. The simulation results show more frequent and shorter fades with higher phase rates under increased signal dynamics, consistent with the findings of Morton et al. (2022). Analysis across frequency bands revealed that signals at lower frequencies exhibit more frequent fades and greater phase fluctuations. These results provide quantitative evidence that signal dynamics determine the temporal scales of scintillation and associated fading characteristics at a given frequency. Specifically, the time separation between fades and fading duration are both proportional to $ρ_{F} / v_{eff}$ , whereas the phase rate is inversely proportional to $ρ_{F} / v_{eff}$ .

The results also show consistently low fading overlap percentages across the L1, L2, and L5 frequencies for various signal dynamics cases. This finding aligns with observations from ground receivers of multi-frequency GNSS signals reported by Jiao et al. (2016). The consistently low fading overlaps suggest the potential for leveraging frequency diversity to improve tracking and navigation operations (Yang et al., 2019), even for highly dynamic platforms like LEO satellite transmissions. These findings contribute to a deeper understanding of ionospheric scintillations and their impact on LEO satellite-based communication and navigation systems.

It is important to note that the scintillation simulation model employed in this study, originally developed for L-band GNSS signals, relies on the parabolic wave equation with a narrow-angle approximation. When this model is extrapolated to lower frequencies and/or extremely high signal dynamics, potential uncertainties arise owing to violations of fundamental modeling assumptions. Specifically, lower frequencies exhibit significantly increased scattering strength (U), leading to stronger wave–medium interactions that challenge the narrow-angle scattering assumption. High signal dynamics may intensify the contributions from wide-angle scattering. Under these conditions, the parabolic approximation incorrectly maintains all spectral components rather than accounting for the physical decay of wide-angle scattered waves, thereby potentially overestimating the contribution of small-scale irregularities. While the model maintains reasonable accuracy for L-band and higher frequencies under moderate signal dynamics, simulation results should be interpreted with caution for lower frequencies and/ or extreme signal dynamics, particularly under extreme scintillation conditions. Future work will address these limitations by implementing full wave propagation solutions for scenarios in which the parabolic approximation becomes less reliable, ensuring accurate scintillation simulations across a broader range of frequencies and dynamics relevant to modern satellite communication and navigation systems.

HOW TO CITE THIS ARTICLE:

Sun, A.K., Morton, Y.J., Rino, C., & Lee, J. (2026). Ionospheric scintillation effects on LEO-transmitted signals across multiple frequency bands. NAVIGATION, 73. https://doi.org/10.33012/navi.772

ACKNOWLEDGMENTS

This paper is a revised version of a proceeding previously published in the Proceedings of the 2024 International Technical Meeting of The Institute of Navigation. This research was funded by Air Force Research Laboratory Space Vehicles Directorate contract # 282109-874X. A. K. Sun was supported by the National Research Foundation of Korea, funded by the Ministry of Science and ICT under Grant 2022M1A3C2069728, Future Space Education Center. GNSS scintillation analysis was performed using the two-parameter simulator developed by CU Sense Lab under Prof. Jade Morton: https://github.com/cu-sense-lab/gnss-scintillation-simulator_2-param. This study uses the scientific colour maps from Crameri (2023), a suite of colour-vision deficiency friendly and perceptually uniform colour maps, available at https://doi.org/10.5281/zenodo.1243862.

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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Ionospheric Scintillation Effects on LEO-Transmitted Signals Across Multiple Frequency Bands

Andrew K. Sun

Andrew K. Sun

Y. Jade Morton

Y. Jade Morton

Charles Rino,

Charles Rino,

and Jiyun Lee

Jiyun Lee

Institute of Navigation

Jun 2026,

73

navi.772;

DOI: 10.33012/navi.772

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Ionospheric Scintillation Effects on LEO-Transmitted Signals Across Multiple Frequency Bands

Andrew K. Sun

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Y. Jade Morton

Y. Jade Morton

Charles Rino,

Charles Rino,

and Jiyun Lee

Jiyun Lee

Institute of Navigation

Jun 2026,

73

navi.772;

DOI: 10.33012/navi.772

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Keywords

Ionospheric scintillation, LEO satellites, Multi-frequency signals, Phase screen model, Signal fading

Ionospheric Scintillation Effects on LEO-Transmitted Signals Across Multiple Frequency Bands

Abstract

1 INTRODUCTION

2 SCINTILLATION SIMUATOR ACROSS FREQUENCY BANDS

3 SIMULATION SCENARIOS

3.1 Signal Dynamics Scenarios

3.2 Simulation Across Carrier Frequency Bands

3.3 Scintillation Realizations

4 STATISTICAL ANALYSIS OF SCINTILLATION SIGNAL CHARACTERISTICS

4.1 Scintillation Signal Characteristics

4.2 Statistical Analysis of Scintillation Characteristics

4.2.1 Time Separation

4.2.2 Fading Duration

4.2.3 Fading Depth

4.2.4 Phase Rate

4.2.5 Analysis of Temporal Characteristics in Scintillation Across Signal Dynamics

4.2.6 Fading Overlaps

5 CONCLUSIONS

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