Explicit Ziv-Zakai Bound For Multiple Sources Doa Estimation

Abstract

In direction-of-arrival (DOA) estimation, Cramér-Rao bound is widely used to lower bound the mean square error (MSE), which, however, is a local bound. As a global bound, existing Ziv-Zakai bound (ZZB) is restricted by the single source assumption and has not considered the effect of ordering process during MSE calculation. In this paper, we derive an explicit ZZB for multiple sources DOA estimation, where the ZZB derivation framework is first extended to multiple sources case. Further, order statistics are introduced to describe the effect the ordering process on the change of a priori distribution of DOAs, which finally makes the derived ZZB tight over a wide range of signal-to-noise ratio. The derived ZZB reveals the relationship between the number of sources and the convergence performance in the a priori performance region. Simulation results demonstrate the global tightness of the derived ZZB.