Ziv-Zakai Bound for Compressive Time Delay Estimation

Compressive radar receiver can keep a good balance between sub-Nyquist sampling and high resolution. To evaluate the performance of compressive time delay estimators, Cramér-Rao bound (CRB) has been derived for lower bounding the mean square error (MSE), which, unfortunately, is a local bound being tight in the asymptotic region only. In this paper, we use the Ziv-Zakai bound (ZZB) methodology to develop a Bayesian MSE bound on compressive time delay estimation by incorporating the a priori information of the unknown time delay. Specifically, we respectively derive deterministic ZZB and stochastic ZZB as functions of compressive sensing (CS) kernel, where there is no restriction on CS kernels and Gaussian noise colors. Simulation results demonstrate that compared with Bayesian CRB, ZZB provides a better performance prediction for minimum MSE estimator of compressive time delay estimation over a wide range of signal-to-noise ratios, where different CS kernels, compression ratios, a priori distributions and Gaussian noise colors are tested.