ZIV-Zakai Bound for DOA Estimation with Gain-Phase Error

Compared with the commonly used Cramér-Rao bound, the Ziv-Zakai bound (ZZB) is a global tight lower bound for evaluating the performance of parameter estimators. However, the existing ZZB for multi-source direction-of-arrival (DOA) estimation is derived under an ideal array assumption, where the gain-phase error is not taken into account. Hence, when the gain-phase error exists, the existing ZZB cannot provide a global effective bound. To address this problem, we incorporate the gain-phase error term into the ZZB derivation, and formulate the ZZB as an explicit function of the gain-phase error, which reveals that the gain-phase error affects the ZZB by introducing an extra signal-to-noise ratio gain/loss to the received signals. Simulation results demonstrate that the derived ZZB is global effective and tighter than the existing ZZB for multi-source DOA estimation in gain-phase error scenarios.