Ziv — Zakai lower bound on target localization estimation in MIMO radar systems

This paper presents the derivation of the Ziv-Zakai bound (ZZB) for the localization problem in a MIMO radar system. The target is positioned in the near-field of a network of radars of arbitrary geometry. The radars have ideal mutual time and phase synchronization. The target location is estimated by coherent processing exploiting the amplitude and phase information between pairs of radars. An analytical expression is developed for the ZZB relating the estimation mean square error (MSE) to the carrier frequency, signal bandwidth, the number of sensors, and their location. From numerical calculations of the bound, three regions of signal-to-noise ratio (SNR) can be distinguished in the performance of the location estimator: a noise-dominated region, an ambiguity region, and an ambiguity free region. In the noise-dominated region, the signals received by the radars are too weak, and thus the localization error is limited only by the a priori information about the location of the target. In the ambiguity region, the performance of the location estimator is affected by sidelobes. In the ambiguity free region, estimation errors are very small and the ZZB approaches the Cramer-Rao lower bound (CRLB).