Exact conditional and unconditional Cramér–Rao bounds for near field localization

This paper considers the Cramér–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 based on an approximate time delay expression (usually considered in the Fresnel region). In addition, we consider the exact expression of the received power profile (i.e., variable gain case) which, to the best of our knowledge, has been ignored in the literature. Finally, we exploit the CRB expression to introduce the new concept of Near Field Localization Region (NFLR) for a target localization performance associated to the application at hand. We illustrate the usefulness of the proposed CRB derivation as well as the NFLR concept through numerical simulations in different scenarios.