Ziv-Zakai Bound for Target Parameter Estimation in Distributed MIMO Radar Systems

• Published in: IEEE transactions on aerospace and electronic systems Vol. 60; no. 5; pp. 7393 - 7410
• Main Authors: Liang, Yuanyuan, Wen, Gongjian, Luo, Dengsanlang, Li, Runzhi, Li, Boyun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Computational modeling; Covariance matrices; Cramer-Rao bounds; Cramér–Rao bound (CRB); Error analysis; Error reduction; Estimation; Lower bounds; MIMO communication; MIMO radar; multiple-input multiple-output (MIMO) radar; Parameter estimation; performance evaluation; Radar equipment; Radar systems; Receivers; Saddle points; Signal to noise ratio; Stochastic models; Stochastic processes; Vectors; Waveforms; Ziv–Zakai bound (ZZB)
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2024.3416426

In the evaluation of the Ziv–Zakai bound (ZZB) for target parameter estimation in distributed multiple-input–multiple-output (MIMO) radar systems, existing models often rely on idealized assumptions, such as completely orthogonal waveforms and temporally white interference, which may not reflect real-world conditions. This article addresses these limitations by developing the ZZB for more realistic scenarios. We derive the ZZBs for joint target position and velocity estimation under both stochastic and deterministic signal models. The derived bounds distinguish the minimum error probabilities with an exact formula for the stochastic model and a saddle point approximation for the deterministic model. Simulation studies confirm that these ZZBs serve as robust lower bounds for the mean-square error (MSE) of maximum a posteriori estimates across diverse signal-to-noise ratios (SNRs). To reduce computational demands, we introduce a Gaussian approximation method based on the moment-matching principle to estimate the minimum error probabilities for both models, significantly reducing complexity while preserving accuracy. Additionally, under ideal conditions, we simplify the ZZBs for both models into a weighted sum of the a priori covariance and the expectation of the conditional Cramér–Rao bound, where the weights depend on the overall SNR. This formulation offers insights into threshold phenomena and yields substantial computational benefits. Our results indicate that this matrix-based approach can achieve time savings of more than one order of magnitude compared to the integral-based ZZB calculation methods.