Cramér-Rao bound for time reversal active array direction of arrival estimators in multipath environments

In this paper, we study the Cramér-Rao bound (CRB) for time reversal (TR) based direction of arrival (DOA) estimators operating in a rich multipath environment. Our setup is based on an array of active antennas capable of estimating the range and DOA of a passive target. We derive an analytical expression for the CRB of the TR/DOA estimator and compare it with that of the conventional DOA estimator by expressing the two CRBs in terms of the multipath parameters (multipath´s attenuations and delays). Our analytical results are verified by running Ground Penetrating Radar (GPR) simulations using the electromagnetic Finite Difference Time Domain (FDTD) models. Our simulations illustrate the potential of superior performance with gains of up to 15 dB possible with the TR/DOA estimator over the conventional approach.