OFDM-Based Positioning with Unknown Data Payloads: Bounds and Applications to LEO PNT

TL;DR

This paper develops bounds, estimators, and signal design strategies for OFDM-based positioning systems that utilize both known pilots and unknown data, with applications to low-Earth-orbit navigation.

Contribution

It introduces the first Ziv-Zakai bound for TOA estimation in OFDM signals with mixed known and unknown resources, improving understanding of low-SNR performance.

Findings

ZZB captures low-SNR threshold effects in TOA estimation

Optimized resource allocation improves positioning accuracy

Maximum-likelihood estimators approach theoretical bounds

Abstract

This paper presents bounds, estimators, and signal design strategies for exploiting both known pilot resources and unknown data payload resources in time-of-arrival (TOA)-based positioning systems with orthogonal frequency-division multiplexing (OFDM) signals. It is the first to derive the Ziv-Zakai bound (ZZB) on TOA estimation for OFDM signals containing both known pilot and unknown data resources. In comparison to the Cramer-Rao bounds (CRBs) derived in prior work, this ZZB captures the low-signal-to-noise ratio (SNR) thresholding effects in TOA estimation and accounts for an unknown carrier phase. The derived ZZB is evaluated against CRBs and empirical TOA error variances. It is then evaluated on signals with resource allocations optimized for pilot-only TOA estimation, quantifying the performance gain over the best-case pilot-only signal designs. Finally, the positioning accuracy of maximum-likelihood and decision-directed estimators is evaluated on simulated low-Earth-orbit non-terrestrial-network channels and compared against their respective ZZBs.