Ziv–Zakai Bound for Multisource DOA Estimation
Zongyu Zhang, Zhiguo Shi, Arye Nehorai · 2024
Cram é r–Rao bound (CRB) is the most commonly used bound for evaluating the mean-squared error (MSE) of direction-of-arrival (DOA) estimation. Nevertheless, it only provides tight bound asymptotically. By effectively utilizing the a priori probability density of the parameters, the Ziv–Zakai bound (ZZB) provides a global tight bound over a wide range of signal-to-noise ratio. However, it has been applied only to single-source DOA estimation. In this chapter, we derive an explicit and global tight ZZB for evaluating hybrid coherent/uncorrelated multisource DOA estimation by adopting Woodbury matrix identity, Sylvester's determinant theorem, and order statistics. The derived ZZB is a function of coherence coefficients among coherent sources, reveals the relationship between the MSE convergence in the a priori performance region and the number of sources, and provides a unified expression for both overdetermined and underdetermined DOA estimation. Simulation results demonstrate the advantages of the derived ZZB over CRB in multisource DOA estimation.