On the Reliability of Estimation Bounds in Low-SNR Bistatic ISAC

2026-01-19

AI Summary

This work addresses the limitations of the conventional Cramér-Rao bound (CRB) in bistatic integrated sensing and communication (ISAC) systems operating under low signal-to-noise ratio (SNR) conditions, where CRB becomes invalid in passive sensing scenarios due to its reliance on instantaneous knowledge of the transmitted signal. To overcome this, the study introduces the Ziv-Zakai bound (ZZB) for the first time in this context, providing a more accurate assessment of angle estimation performance when only the statistical properties of the signal are known at the sensing receiver. By deriving closed-form expressions for both the ZZB and the ergodic communication rate, the paper quantifies the fundamental sensing–communication trade-off and constructs the corresponding Pareto frontier. Numerical results demonstrate that, in the low-SNR regime, the ZZB significantly outperforms the CRB, offering a more reliable performance benchmark for practical ISAC system design.

Technology Category

• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

This paper explores a bistatic Integrated Sensing and Communication (ISAC) framework, where a base station transmits communication signal that serve both direct communication with a user and multi-target parameter estimation through reflections captured by a separate sensing receiver. We assume that the instantaneous knowledge of the transmit signal at the sensing receiver is not available, and the sensing receiver only has knowledge of the statistical properties of the received signal. Unlike prior research that focuses on power allocation or optimal beamforming design for ISAC, we emphasize the inadequacy of the Cram\'er-Rao Bound (and its variant) in low Signal-to-Noise Ratio (SNR) regimes, particularly in passive sensing scenarios. Due to severe path loss and other impairments, the received sensing SNR is often significantly lower than that of direct Line-of-Sight communication, making CRB-based performance evaluation unreliable. To address this, we adopt the Ziv-Zakai Bound (ZZB) for Angle of Arrival estimation, which provides a more meaningful lower bound on estimation error. We derive analytical expressions for the ZZB and the achievable ergodic communication rate as functions of SNR. Through numerical simulations, we analyze the pareto-front between communication and sensing performance, demonstrating why ZZB serves as a better metric in low sensing SNR ISAC where traditional CRB-based approaches fail.

Problem

• Cramér-Rao Bound
• low-SNR
• bistatic ISAC
• Ziv-Zakai Bound
• passive sensing

Innovation

• Ziv-Zakai Bound
• Low-SNR ISAC
• Bistatic Sensing
• Cramér-Rao Bound
• Angle of Arrival Estimation