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

TL;DR

This work tackles AoA estimation in a bistatic ISAC system where the sensing receiver lacks instantaneous knowledge of the transmitted waveform and relies on its statistical properties. It shows that the conventional CRB is unreliable in low-SNR, passive sensing scenarios and adopts the Ziv-Zakai Bound (ZZB) to derive meaningful bounds that incorporate prior information. The authors derive analytical ZZB expressions and relate them to the achievable ergodic rate $R_{\text{in}}$, then demonstrate via simulations that ZZB provides a tighter, more realistic performance bound than CRB in threshold and low-SNR regimes, while converging to CRB at high SNR. The results highlight a practical rate–sensing trade-off under Subspace Joint Beamforming and reveal the limitations of CRB-based analyses for passive bistatic ISAC, guiding robust system design and evaluation.

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 Cramér-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.

Figures (5)

• Figure 1: Bistatic Integrated Sensing and Communication (ISAC) system with MIMO setup. The transmitter maintains communication with a Communication RX (CRx), while the Sensing RX (SRx) detects targets through reflected signals.
• Figure 2: Performance comparison of Angle of Arrival (AoA) estimation bounds for different AoA ranges and targets. The plot shows the Root Mean Square Error (RMSE) in degrees versus Sensing SNR for Ziv-Zakai Bound (ZZB), Cramér-Rao Bound (CRB) and A Priori Bound (APB). Results are presented for two AoA ranges: [-30°, 30°] and [-60°, 60°] for single and three target cases.
• Figure 3: Left: Communication rate (bps/Hz) versus beamforming parameter $\alpha$, showing how steering more power toward the user ( $\alpha \rightarrow 1$ ) increases rate. Communication SNR is fixed at 20 dB. Right: Sensing estimation error (ZZB, in degrees) versus $\alpha$, for sensing SNRs of -30 , -20, -10 and 0 dB.
• Figure 4: Comparison of communication rate and sensing performance bounds (CRB and ZZB). Notably, in the low sensing SNR regime (-20 dB and -30 dB), The ZZB curves reveal that beamforming strategies have limited impact on estimation performance.
• Figure 5: Bistatic ISAC performance analysis and trade-offs. Left: Communication rate versus SNR for sensing-optimal and communication-optimal beamforming. Right: Rate-sensing pareto frontiers showing the fundamental trade-off between communication rate and sensing accuracy (ZZB error) at different communication SNR levels for fixed -10 dB Sensing SNR.