Ziv-Zakai Bound for Compressive Time Delay Estimation from Zero-Mean Gaussian Signal

Existing stochastic Ziv-Zakai bound (ZZB) for compressive time delay estimation from compressed measurement relies on a Gaussian approximation, which makes it inaccurate in the asymptotic region when the stochastic component dominates the received signals. In this letter, we apply different random projections on zero-mean Gaussian received signal to obtain multiple compressed measurements, based on which the log-likelihood ratio test is exactly formulated as the difference of two generalized integer Gamma variables. Accordingly, we further derive the exact expression of the stochastic ZZB for compressive time delay estimation from zero-mean Gaussian signal. Simulation results show that the derived ZZB is globally tight to accurately predict the estimation performance regardless of the number of compressed measurements, and it can also accurately predict the threshold signal-to-noise ratio for the estimator when the number of compressed measurements is large.