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

TL;DR

This paper investigates the limitations of traditional estimation bounds in low-SNR bistatic ISAC systems and proposes the Ziv-Zakai Bound as a more reliable metric for sensing performance evaluation.

Contribution

It introduces the use of the Ziv-Zakai Bound for angle estimation in low-SNR ISAC, providing analytical expressions and demonstrating its advantages over the CRB.

Findings

CRB is unreliable in low-SNR sensing scenarios.

ZZB offers a more meaningful lower bound in low-SNR regimes.

Numerical results show the pareto-front between communication and sensing performance.

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.