The Cramer-Rao Lower Bound in the Phase Retrieval Problem

This paper presents an analysis of Cramer-Rao lower bounds (CRLB) in the phase retrieval problem. Previous papers derived Fisher Information Matrices for the phaseless reconstruction setup. Two estimation setups are presented. In the first setup the global phase of the unknown signal is determined by a correlation condition with a fixed reference signal. In the second setup an oracle provides the optimal global phase. The CRLB is derived for each of the two approaches. Surprisingly (or maybe not) they are different.