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This paper considers the Cramer-Rao lower Bound (CRB) for the source localization problem in the near field.More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this 'exact CRB' can be significantly different from the one given in the literature and based on an approximate time delay expression (usually considered in the Fresnel region). This CRB derivation is then generalized by considering the exact expression of the received power profile (i.e., variable gain case) which, to our best knowledge, has been ignored in the literature. Finally, we exploit the CRB expression to introduce the new concept of Near Field Localization (NFL) region for a target localization performance associated to the application at hand. We illustrate the usefulness of the proposed CRB derivation and its developments as well as the NFL region concept through numerical simulations in different scenarios.

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.

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