Deterministic Ziv-Zakai Bound for Compressive Time Delay Estimation

Abstract

Compressive radar receiver has attracted a lot of research interest due to its capability to keep balance between sub-Nyquist sampling and high resolution. In evaluating the performance of compressive time delay estimator, Cramer-Rao bound (CRB) has been commonly utilized for lower bounding the mean square error (MSE). However, behaving as a local bound, CRB is not tight in the a priori performance region. In this paper, we introduce the Ziv-Zakai bound (ZZB) methodology into compressive sensing framework, and derive a deterministic ZZB for compressive time delay estimators as a function of the compressive sensing kernel. By effectively incorporating the a priori information of the unknown time delay, the derived ZZB performs much tighter than CRB especially in the a priori performance region. Simulation results demonstrate that the derived ZZB outperforms the Bayesian CRB over a wide range of signal-to-noise ratio, where different types of a priori distribution of time delay are considered.