  Multiple antenna arrays play a key role in wireless networks for
communications but also localization and sensing. The use of large antenna
arrays pushes towards a propagation regime in which the wavefront is no longer
plane but spherical. This allows to infer the position and orientation of an
arbitrary source from the received signal without the need of using multiple
anchor nodes. To understand the fundamental limits of large antenna arrays for
localization, this paper fusions wave propagation theory with estimation
theory, and computes the Cram{\'e}r-Rao Bound (CRB) for the estimation of the
three Cartesian coordinates of the source on the basis of the electromagnetic
vector field, observed over a rectangular surface area. To simplify the
analysis, we assume that the source is a dipole, whose center is located on the
line perpendicular to the surface center, with an orientation a priori known.
Numerical and asymptotic results are given to quantify the CRBs, and to gain
insights into the effect of various system parameters on the ultimate
estimation accuracy. It turns out that surfaces of practical size may guarantee
a centimeter-level accuracy in the mmWave bands.
