Influence of phase on Cramer-Rao lower bounds for joint time delay and Doppler stretch estimation

The Cramer-Rao lower bounds for joint time delay and Doppler stretch estimation have been obtained for wideband signals with known phase already. However, the carrier phase is usually unknown in non-coherent receivers in the applications such as radar and sonar. And accuracy of the joint estimation of time delay and Doppler stretch will be affected by this unknown phase. In this paper, starting with a general wideband signal model with unknown phase, the Cramer-Rao lower bounds for joint time delay and Doppler stretch estimation are derived by using Fisher information matrix. The bounds obtained under unknown and known phases are compared and the relations between them are offered. Further explanations about the relations are also given from the view of information theory. Simulations are provided to support the theoretical results.