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Enhancing 5G NTN VSAT RACH in GNSS-Denied environments

Francesco Menzione, Alejandro Gonzalez-Garrido, Flavien Ronteix-Jacquet, Ottavio M. Picchi

arXiv:2609.29164v1eess.SP

TL;DR

NR-NTN requires a UE GNSS fix for uplink pre-compensation, while AoA-only positioning is generally limited to dozens-of-kilometres accuracy despite PRACH's higher accuracy needs. The paper combines AoA initialization with reconstructed Doppler and range measurements in a multi-epoch filter, achieving 2.83 km for J3 in Nominal conditions and 1.10 km in the Best scenario.

  • Problem

    NR-NTN requires a UE GNSS fix for uplink timing and frequency pre-compensation, while AoA-only positioning is generally limited to dozens-of-kilometres accuracy despite PRACH’s higher accuracy needs.

    Source: §1 · p. 2

  • Method

    A coarse single-beam AoA position initializes reconstructed FoA and ToA observables, which a multi-epoch Levenberg–Marquardt Kalman Filter integrates.

    Source: §1 · p. 3, §6 · p. 28

  • Results

    Integrating Doppler (J2) and Range (J3) achieves 2.83 km for J3 in Nominal conditions and 1.10 km in the Best scenario.

    Source: §5.3 · p. 27

  • Takeaways & Limitations

    The framework with the satellite selection policy enables successful GNSS-free operation across evaluated configurations, though lower-AoA-accuracy configurations require minor requirement relaxation.

    Source: §6 · p. 28

    Some configurations, including those with lower AoA accuracy, require a minor relaxation of differential delay requirements for successful PRACH completion.

    Source: §5.3 · p. 27, §6 · p. 28

Abstract

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The 3GPP 5G non-terrestrial networks (NTN) technology fundamentally relies on a global navigation satellite system (GNSS) fix at the user equipment (UE) to pre-compensate for user-link delay and Doppler shifts prior to any transmission, including the random-access procedure for initial access. In GNSS-denied or interfered environments, this dependency triggers preamble collisions and connection dropouts, undermining satellite-based global connectivity. To address this vulnerability, this paper introduces a novel single-satellite positioning framework designed for higher-frequency (Ku- or Ka-band) 5G NTN very small aperture terminals (VSATs) equipped with a phased-array antenna. The multi-step scheme derives an initial coarse position from angle of arrival (AoA) observables, extracts frequency of arrival (FoA) and time of arrival (ToA) measurements from low Earth orbit (LEO) downlink reference signals, and hybridizes them within a Levenberg-Marquardt navigation filter. Systematic evaluations across static grids and realistic dynamic urban trajectories detail the incremental gains of transitioning from single-epoch AoA error minimization to multi-epoch angular tracking, followed by the integration of Doppler and ranging observables. Grounded in a realistic error budget, the proposed framework reduces initial positioning uncertainty from tens of kilometres down to a few kilometres. This level of positioning accuracy, combined with the GNSS-resilient features introduced in 3GPP Release 20 NR NTN specifications, enables robust initial access in compromised operational environments with minimal relaxation of 3GPP standards.

1 Introduction

GNSS dependence and the single-serving-satellite constraint leave high-frequency NTN VSAT initial access with limited positioning options. The paper combines AoA with reconstructed FoA and ToA in a multi-epoch filter, reporting kilometer-level positioning and assessing PRACH implications.

1 Introduction

  • Current high-frequency Ku/Ka-band specifications contemplate initial access through one serving satellite, while many uncertainty-reduction approaches rely on simultaneous multi-satellite reception.A VSAT is needed to close the link budget in these bands.Source: §1 · p. 2
  • Phased-array VSATs can derive AoA by steering a single high-gain receive beam, but AoA-only methods generally yield errors of dozens of kilometres rather than the accuracy sought for reliable PRACH access.The cited prior approaches are,,, with higher accuracy needed for reliable PRACH access.Source: §1 · p. 2
  • The proposed framework combines standard AoA positioning with additional receiver capabilities adapted from Signals of Opportunity navigation.The approach addresses single-satellite VSAT localization for improved PRACH.Source: §1 · p. 2
  • An initial coarse AoA fix initializes reconstruction of Doppler (FoA) and ranging (ToA) observables, which a multi-epoch LMKF processes using user-position time correlation and evolving single-satellite-pass geometry.The paper evaluates the framework against a representative 5G NTN scenario using observable characterizations based on signal properties, propagation impairments, and VSAT parameters.Source: §1 · p. 3
  • The evaluation examines incremental gains from single-epoch AoA minimization to multi-epoch angular tracking and then integration of Doppler and ranging, including location uncertainty’s impact on RACH timing advance.The analysis also considers RACH geometry and possible ways to optimize that stage.Source: §1 · p. 3
  • VSAT-accessible observables alone enable kilometer-level positioning, but minimal RRM relaxation remains necessary for successful PRACH preamble reception at the satellite.The framework is compatible with GNSS-resilient features such as Rel-20 two-sequence PRACH.Source: §1 · p. 3

2 5G-NTN system and UE assumptions

The scenario models a 1200-km LEO constellation, satellite coverage and handover, and a 5G NR downlink. The assumed VSAT is a single-beam phased-array terminal with an SDR front end for extracting AoA, FoA, and ToA observables.

2 5G-NTN system and UE assumptions

  • The simulated constellation uses inclined Walker-star and polar shells at 1200 km, with a 20° minimum elevation angle and a Ka-band footprint based on Set-2 parameters in.The polar shell supplements the inclined shell to reduce location uncertainty at higher latitudes; the listed orbital parameters are in Table 1.Source: A. Space Segment · p. 3, Table 1 · p. 4
  • The simulated footprint represents a satellite at (0,0,0) LLA with fourteen beam rings and 547 beams covering down to 20° elevation.Rings 1–12 correspond to elevation masks up to 30°, ring 13 to 25°, and ring 14 to 20°; antenna parameters follow [20] and link-budget parameters match.Source: A. Space Segment · p. 4, Figure 2 · p. 5
  • The simulator emulates handover by selecting the highest-elevation satellite for a ground cell and retaining it until it drops below a scenario-defined threshold.In the illustrated case, handover occurs at 40°; this scheduling threshold is distinct from the masking angle, and both elevation and C/N0 jump at handover.Source: A. Space Segment · pp. 5–6, Figure 3 · p. 6
  • The downlink uses 5G NR CP-OFDM, and the assumed SSB comprises four OFDM symbols and 240 contiguous subcarriers; the analysis uses only the central 127 PSS/SSS subcarriers.The assumed FR2 subcarrier spacing is 120 kHz.Source: B. 5G signal model · pp. 6–7
  • The UE is a Ka-band FR2 VSAT with a phased-array antenna steering one receive beam; approximately 40 dBi gain implies over 4000 elements and an approximately 50 × 50 cm Ka-band aperture.The methodology is also described as applicable to Ku-band; the antenna assumptions are aligned with a commercial receive-band product discussed in.Source: C. VSAT User Equipment assumptions · p. 7
  • A dedicated SDR module is assumed to acquire, track, and extract Doppler and code-phase observables from single-satellite PSS and SSS, while blind AoA acquisition is outside the paper’s scope.Analog beamforming may require serial search across candidate angles; hybrid architectures can accelerate acquisition using reduced MUSIC or Bayesian compressive sensing,.Source: C. VSAT User Equipment assumptions · pp. 7–8

3 AoA, FoA and ToA observable generation in presence of signal propagation and processing impairments

The section builds a realistic simulator for AoA, FoA, and ToA observables, combining receiver-processing limits with propagation and hardware impairments. Receiver error bounds are quantified, and the resulting error budget supplies the baseline for later positioning evaluations.

3.1 Expected receiver processing error

  • At 2 dB array SNR, azimuth error is 0.2° and elevation error is 0.07° for the assumed 64×64 array.The corresponding element SNR is around -34 dB.Source: A. Angle Of Arrival · p. 9
  • Range-rate estimation error remains below 10 cm/s, while ToA accuracy remains below 30 cm across relevant C/N0 regimes.The ToA bound uses an FR2 PSS/SSS waveform with 120 kHz SCS.Source: B. Frequency Of Arrival · p. 11, C. Time Of Arrival · p. 11

3.2 Additional signal propagation impairments models

  • Realistic AoA tracking uncertainty is modeled as 0.3° standard deviation on both azimuth and elevation after combining independent pointing-error sources.The modeled sources include beam misalignment, attitude uncertainty, heating-induced distortion, and tropospheric scintillation.Source: A. Elevation and Azimuth measurement… · p. 11
  • The simulator models clock, ephemeris, satellite-clock, transmission-chain, tropospheric, and multipath errors; per-beam transmission-chain bias remains an uncalibrated random constant.The transmission-chain bias is drawn uniformly from [-30 ns, 30 ns] and held constant for the same Beam ID.Source: B. Pseudo-range and Doppler Impairments · pp. 11–12

3.3 Final Error Budget

  • Table 3 summarizes the complete modeled error budget, and Figure 6 shows a representative realization of the impairments and resulting observables.The generated observables provide the baseline input for the evaluations in Section 5.Source: §3.3 · p. 12, Table 3 · p. 13, Figure 6 · p. 14

4 Multi-step Levenberg-Marquardt (LM) Positioning Algorithm

The paper uses a single-satellite LM-KF framework to move from a coarse AoA position estimate to a joint AoA/FoA/ToA state solution. Its recursive estimation combines an LM measurement update with Kalman prediction and covariance updates.

4 Multi-step Levenberg-Marquardt (LM) Positioning Algorithm

  • The LM-KF integrates a single-satellite, multi-stage pipeline that uses an AoA position estimate to initialize propagation-delay and frequency-offset estimates before joint AoA/FoA/ToA estimation.Levenberg–Marquardt regularization is used to address numerical instability in the sequential estimation framework.Source: §4 · p. 14

4.1 Levenberg–Marquardt Kalman Filter implementation and setting

  • The LM objective follows a Gaussian-error MAP formulation, accepting a suboptimal boosted-Gaussian treatment of non-Gaussian errors to reduce computational overhead.The objective includes a penalty for time correlation in the user-position estimate.Source: §4.1 · p. 15
  • At each epoch, an iterative LM measurement update refines the state, followed by a standard Kalman covariance update using the Joseph formula.The state prediction uses the prior epoch and a time-update constraint in the LM system.Source: §4.1 · p. 15

2. Time Update Step

The estimator configurations progressively add temporal filtering, Doppler, and ranging to AoA-based positioning, while the workflow initializes from the serving satellite’s sub-satellite point. The procedure initializes clock states before handing estimation over to the augmented configurations.

2. Time Update Step

  • The four configurations progress from memoryless AoA positioning (J0), through filtered AoA (J1) and AoA+FoA (J2), to filtered AoA+FoA+ToA with clock bias and drift (J3).The general state is constrained to Earth-surface latitude and longitude because altitude is not directly observable separately from clock bias.Source: §2 · p. 16

4.2 Multi-step procedure

  • The receiver can blind-search SIB19, compute the current sub-satellite point, and use its longitude and latitude to initialize the navigation solver.This initialization uses SSB and does not require processing additional reference signals while idle.Source: §4.2 · p. 17
  • J1 iteratively refines the position from AoA measurements, with covariance bounds initialized around the admissible region near the sub-satellite point.The time update predicts the state from the previous epoch using a static or kinematic transition matrix.Source: §2 · p. 16, §4.2 · p. 17
  • Before J2 and J3 activate, the preliminary AoA solution initializes clock drift from Doppler and clock bias from pseudorange reconstructed using code phase and broadcast timing.The initial covariance for each clock estimate is derived from the error budget and J1 covariance.Source: §4.2 · pp. 17–18
  • After Doppler and ranging observables are initialized, the solver can hand over from J1 to J2 and J3 optimization.Figure 7’s illustrative test shows that memoryless J0 can have instabilities from unfeasible initial points, while the final approach narrows the search around the approximated sub-satellite point.Source: §4.2 · p. 18, Figure 7 · p. 19

5 Simulation results

This section evaluates static and dynamic positioning and relates location uncertainty to differential delay, Doppler, and RACH completion. It also describes how localized position estimates are intended to support seamless mobility and connection continuity across dense LEO constellations.

5.1 Static user simulations

  • The J0 estimator consistently produces errors exceeding 15 km, while enhancing AoA precision serves as a primary driver for achieving 1 km-level positioning performance.Doppler and pseudorange observables remain fundamental to bounding maximum peak errors in this regime.Source: §5.1 · pp. 21, 23
  • Multi-epoch smoothing and the transition to augmented J2/J3 solutions require sequential clock-bias and drift initialization, while convergence delay depends on trajectory geometry and satellite handovers.The results show a transient during the J1-to-J2/J3 transition; detailed transient optimization is outside the paper’s scope.Source: §5.1 · pp. 23–24

5.2 Kinematic user simulation

  • On the dynamic vehicle trajectory, estimated scatter narrows from J0 to J3, and Table 5 reports a statistically significant 95th-percentile error reduction from J0 to J3.The evaluation used a realistic 50-minute trajectory at speeds up to 100 km/h under Worst measurement conditions; performance aligned with static-user baseline expectations.Source: §5.2 · pp. 24–25, Figure 13 · p. 25, Table 5 · p. 25

5.3 Location uncertainty discussion

  • A minor relaxation is necessary to ensure PRACH finalization above 40° for both Nominal and Best configurations; PRACH completion is reported at elevation angles greater than 70°.Source: §5.3 · p. 27
  • J3 achieves 2.83 km positioning uncertainty in Nominal conditions and 1.10 km in Best conditions; J2 and J3 differential delay stays below 20 μs above 40° even under Worst bounds.Differential delay decreases as elevation increases within the valid domain.Source: Figure 14 · p. 26, §5.3 · p. 27
  • A 25 km location uncertainty induces 1.038 ppm differential Doppler, or a 31.14 kHz shift at 30 GHz, but has negligible impact on PRACH detection.At numerology 3, coherent integration over the shift during the 8.92 μs symbol duration does not shift the Zadoff-Chu correlation peak.Source: §5.3 · p. 26
  • Localized position estimates can be exploited to optimize seamless mobility and connection continuity across dense LEO constellations.Source: §5.3 · p. 27

6 Conclusions

The paper’s single-satellite framework combines AoA initialization with reconstructed ToA and FoA observables in an LMKF to improve positioning for high-frequency VSATs. Full multi-observable processing bounds static maximum error below 5 km, and the framework supports GNSS-free PRACH in evaluated configurations.

6 Conclusions

  • The framework initializes position with single-beam AoA, reconstructs ToA and FoA from PSS/SSS, and processes the observables with a custom LMKF.It exploits user time-correlation and sequential changes in satellite geometry.Source: §6 · p. 28
  • Full AoA/FoA/ToA hybridization bounds static maximum position error below 5 km, while the framework enables GNSS-free PRACH in evaluated configurations.For slowly dynamic users, the framework also achieves a similarly tight, reliable steady-state error; some configurations require a minor relaxation of requirements.Source: §6 · p. 28
  • Future work targets non-line-of-sight urban blockage, filter initialization across broader sub-satellite boundaries, beamforming-compatible AoA tracking, satellite selection, and computational efficiency.The current user-state model assumes quasi-stationarity; broader practical implementation remains an area for assessment.Source: §6 · p. 28

Appendix A

Appendix A models the AoA, pseudo-range, and pseudo-range-rate observables used by the positioning algorithm, including their measurement impairments.

Appendix A

  • The azimuth and elevation measurements are derived from the line-of-sight unit vector between the user and satellite, expressed in the ENU frame.The model includes systematic azimuth and elevation impairments and Gaussian white receiver-processing noise.Source: §I · p. 29
  • Pseudo-range and pseudo-range rate are reconstructed from receiver code-phase and Doppler measurements and are affected by UE and satellite synchronization and clock stability errors.The model includes UE clock bias and drift, constellation synchronization terms, and systematic and Gaussian noise components.Source: §II · pp. 29–30
  • The measurement models use the target user’s velocity vector in defining the pseudo-range-rate measurement.The appendix presents these observable models as inputs to the positioning algorithm.Source: §II · p. 29, Appendix A · p. 29

Appendix B

Appendix B derives a Cramér–Rao lower bound for time-of-arrival estimation using an OFDM signal with continuous frequency allocation around the DC subcarrier, as used for 5G PSS/SSS.

Appendix B

  • The appendix derives an unsmoothed ToA CRLB for an OFDM signal with continuous subcarrier allocation centered at DC.The stated application is 5G PSS/SSS, with 127 allocated subcarriers when N = 63.Source: Appendix B · pp. 30–31
  • The received subcarrier model treats delay as unknown and includes transmitted modulation symbols, transmit power, subcarrier spacing, and additive zero-mean white Gaussian thermal noise.The appendix identifies the noise variance and notes the distinction between a single noise component and total noise power.Source: Appendix B · p. 30
  • The smoothed ToA estimate variance depends on loop bandwidth and update time, with the 5G PSS update time set to one 10 ms frame.The appendix states that the considered thermal-noise regime supports using the CRLB and that DLL tracking nearly reaches that bound, citing.Source: Appendix B · p. 31

Appendix C

Appendix C specifies coordinate transformations, measurement-model Jacobians, filter state and covariance handling, and assumptions used in the positioning implementation.

Appendix C

  • The appendix uses LLH-to-ECEF and ECEF-to-ENU transformations, with the ENU frame referenced to a specified origin.The line-of-sight vector is obtained through the coordinate mapping for the satellite relative to the user position.Source: A) Latitude, Longitude, Height to… · p. 31, B) Earth Centered Earth Fixed to East,… · pp. 31–32, C) Latitude, Longitude, Height to… · p. 32
  • The target state includes latitude, longitude, and clock bias and drift at zero height, and the appendix gives Jacobian blocks for AoA and FoA/ToA measurements.The measurement model combines azimuth, elevation, pseudo-range rate, and pseudo-range.Source: §II · p. 32
  • The target state omits user velocity under a quasi-stationarity assumption; dynamic users remain applicable when their motion is negligible relative to LEO satellite velocity.Drone and aviation extensions are contemplated when receiver speed is supplied by an external sensor.Source: §II · p. 33
  • Position evolves as a random walk, with process covariance regulating temporal correlation; clock bias and drift use a standard random-ramp model.Measurement covariance accounts for estimated measurement noise and systematic impairments.Source: §III · p. 33
  • Initial covariance is inherited from the main methodology, using an admissible region bounded by ±20° latitude and longitude around the selected sub-satellite point.The bound is based on a conservative minimum user elevation angle of 20° and informs initialization of the full covariance, including clock terms in configurations J2 and J3.Source: §IV · p. 33

Appendix D

Appendix D presents numerical position errors for static scenarios in the best and worst cases. Its figures show estimation accuracy on fixed-location grids.

Appendix D

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