Exact Cramer Rao Bound for near field source localization

In this paper, we derive the conditional Cramer Rao Bound (CRB) for near field source localization using the exact expression of the time delay parameter. Based on this derivation, several observations and comments are made: (i) The exact CRB allows us to analyze the effect of the near field assumption on the angle of arrival estimation performance, (ii) the second order Taylor expansion of the exact CRB is shown to be different from the CRB given by El Korso et al for an approximate time delay parameter (i.e approximate model), and (iii) we show how the exact CRB can be used to define the `near field localization region' based on a target localization performance. Simulation experiments are provided to better illustrate our different results and observations.