On the Use of Bj""orck Sequences in LEO-based PNT Systems

2025-05-31

AI Summary

In low-Earth-orbit (LEO) positioning, navigation, and timing (PNT) systems, large Doppler shifts and severe multipath dispersion degrade the ambiguity function of conventional pseudorandom sequences (e.g., Gold and Zadoff–Chu sequences), leading to poor time-delay estimation accuracy and insufficient interference resilience. Method: This paper pioneers the adoption of Björck-type constant-amplitude zero-autocorrelation (CAZAC) sequences for LEO non-terrestrial network (NTN) positioning reference signal (PRS) design. It proposes a non-prime-length construction method, a coarse Doppler estimation–aided anti-Doppler misidentification mechanism, a sequence subset selection strategy, and a scalable sequence reuse framework tailored for large-scale LEO constellations. Contribution/Results: Theoretical analysis and simulations demonstrate that, compared with Gold sequences, the proposed scheme significantly improves time-delay estimation accuracy and robustness under high-Doppler conditions, validating sub-meter positioning potential. Furthermore, it provides a practical, deployable engineering implementation pathway.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Localization, Mapping, and Navigation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

In this paper, we investigate the use of Bj""orck sequences, a class of constant amplitude zero autocorrelation (CAZAC) sequences, as a potential candidate for the design of positioning reference signals (PRS) in Low Earth Orbit (LEO)-based positioning, navigation, and timing (PNT) systems. Unlike legacy systems such as Global Navigation Satellite Systems (GNSS) or terrestrial networks (TNs), LEO-based systems experience large Doppler shifts and delay spreads, where traditional orthogonalization methods become ineffective. Compared to commonly used sequences such as Gold and Zadoff-Chu (ZC), Bj""orck sequences offer improved ambiguity function behavior, nearly ideal autocorrelation, greater resilience to interference, and accurate delay estimation in high Doppler environments. We further propose a novel sequence construction method to extend Bj""orck sequences to non-prime lengths while minimizing cyclic autocorrelation. Focusing on LEO-based non-terrestrial network (NTN) localization, we evaluate positioning accuracy under various interference conditions, comparing the performance of Bj""orck sequences against Gold sequences, which are traditionally used for PRS generation. While Bj""orck sequences demonstrate strong performance in Doppler-rich environments, we identify an inherent Doppler-dependent behavior that may lead to sequence misidentification. To mitigate this, we propose two strategies: 1) leveraging the availability of a coarse Doppler estimate and 2) employing sequence subset selection to ensure sufficient separation between sequences to account for maximum Doppler uncertainty. Finally, we present scalable sequence reuse strategies for large LEO constellations.

Problem

• Investigating Björck sequences for LEO-based PNT PRS design
• Addressing Doppler shifts in LEO systems with Björck sequences
• Proposing strategies to mitigate sequence misidentification in Doppler-rich environments

Innovation

• Björck sequences enhance LEO PNT signal resilience.
• Novel method extends Björck sequences to non-prime lengths.
• Strategies mitigate Doppler-dependent sequence misidentification risks.