High-Noise Asymptotics of the Ziv-Zakai Bound

Alex Dytso, Martina Cardone, Ian Zieder

Abstract: The Ziv-Zakai bound is a well-known lower bound on the minimum mean squared error. This article analyzes the performance of this bound in the practically relevant high-noise regime for a broad family of observation models. The goal is to understand whether this bound is tight, and in which scenarios it should be used. It is shown that, while the Ziv-Zakai bound is tight for a certain class of symmetric distributions, in general, it is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">not</i> tight in the high-noise regime.