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

TL;DR

This paper explores Bj"orck sequences as a robust alternative to traditional sequences for LEO-based PNT systems, addressing high Doppler effects and proposing new sequence construction and mitigation strategies.

Contribution

It introduces a novel method for constructing Bj"orck sequences for non-prime lengths and evaluates their effectiveness in high Doppler environments compared to Gold sequences.

Findings

Bj"orck sequences outperform Gold sequences in high Doppler conditions.

Proposed strategies mitigate Doppler-dependent sequence misidentification.

Scalable sequence reuse methods enable large LEO constellation deployment.

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.