Ziv–Zakai Bound for Joint Parameter Estimation in MIMO Radar Systems

Local bounds, such as the Cramer-Rao bound (CRB), provide inaccurate predictions under low signal-to-noise ratio (SNR) conditions. Global bounds are capable of providing more accurate predictions of the performance of estimators over the full range of SNR. In this paper, we derive the Ziv-Zakai bound (ZZB) for joint location and velocity estimation of a target illuminated by a non-coherent multiple-input multiple-output (MIMO) radar employing orthogonal waveforms and widely spaced antennas. The setup captures the multistatic nature of the target gains, where each pair of transmit-receive elements experience independent gains governed by the Swerling type 1 model. The target returns are observed in the presence of spatially and temporally independent Gaussian clutter-plus-noise. The ZZB for joint delay and Doppler estimation for single-input and single-output (SISO) radar is also developed. We show that the ZZB is a comprehensive metric that captures the effect of the SNR, the ambiguity function (AF) and other parameters of the radar systems. The effects of different system configurations are explored through numerical studies. The results are useful for the analysis of both active and passive radars.