Cramér-Rao Bounds for Holographic Positioning

Multiple antennas arrays combined with high carrier frequencies play a key role in wireless networks for communications but also localization and sensing applications. To understand the fundamental limits of electromagnetically large antenna localization, this paper combines wave propagation theory estimation theory, computes Cramér-Rao Bound (CRB) source position on basis three Cartesian components electric field, observed over rectangular surface area. The problem is referred to as holographic positioning it intrinsically depends radiation angular pattern transmitting source, which typically ignored standard signal processing models. We assume that Hertzian dipole, address both cases, is, without priori knowledge its orientation. simplify analysis gain further insights, we consider case dipole located line perpendicular center. Numerical asymptotic results are given quantify CRBs, effect various system parameters ultimate accuracy. It turns out square surfaces side comparable distance needed guarantee centimeter-level accuracy mmWave bands. Moreover, show CRBs orientation numerically same. provided used benchmark different maximum-likelihood estimators (MLEs) derived discrete representation models field. shows that, if (neglecting pattern), MLE far from CRB. On other hand, approaches CRB when more detailed electromagnetic model considered.