A General Ziv-Zakai Bound for DoA Estimation in MIMO Radar Systems

TL;DR

This work derives a closed-form Ziv-Zakai Bound (ZZB) for multi-target DoA estimation in co-located MIMO radar, explicitly incorporating a general transmit covariance matrix and multiple snapshots. By leveraging a tractable approximation and ZZB machinery, the authors obtain a bound that captures the combined influence of the number of transmit antennas $N$, the number of targets $K$, the snapshot count $L$, and the SNR on estimation performance, and they show the ZZB to be tighter than the CRB in the low-SNR regime. The analysis extends previous SIMO/DOA ZZBs to MIMO settings and ISAC-like waveform ensembles, providing insights into when CRB-based predictions fail and how array size and target count shift the bound's transition between a priori and asymptotic regimes. Numerical results corroborate the bound's tightness in the a priori dominated region and demonstrate design implications for array sizing and sensing performance in ISAC scenarios.

Abstract

This paper derives a Ziv-Zakai Bound (ZZB) on the Mean Squared Error (MSE) for Direction-of-Arrival (DoA) estimation in co-located Multiple-Input Multiple-Output (MIMO) radar systems and provides closed-form expressions that hold for multi-target scenarios. Unlike classical results that address single-input multiple-output systems with complex Gaussian input signals, the developed ZZB in this paper explicitly accounts for a general input covariance matrix, target radar cross-section statistics and multiple snapshot effects, and admits a compact expression that reveals the dependence of the MSE on the number of transmit antennas, number of targets, Signal-to-Noise Ratio (SNR) and the transmit covariance matrix. Numerical simulations validate the tightness of the ZZB in the a priori dominated region and show how the increase of the number of transmit antennas compresses the threshold SNR for the transition to the Cramer-Rao bound (CRB) while the variation of the number of targets shifts the bound's behavior across SNR regimes. The analytical results and numerical simulations demonstrate that the ZZB is tighter than the CRB, particularly in the low SNR regime.

Figures (3)

• Figure 1: Effect of the number of transmit antennas $N$ on ZZB.
• Figure 2: Effect of different number of targets $K$ on ZZB.
• Figure 3: Effect of the a priori distribution of DoAs on ZZB. Subscripts indicate the assumed priors: $[-60,60]$ denotes $\mathcal{U} [-60^{\circ},60^{\circ}]$ and $[-85,85]$ denotes $\mathcal{U} [-85^{\circ},85^{\circ}]$.

Theorems & Definitions (2)

• Remark 1
• Remark 2