  This paper experimentally and theoretically investigates the fundamental
bounds on radio localization precision of far-field Received Signal Strength
(RSS) measurements. RSS measurements are proportional to power-flow
measurements time-averaged over periods long compared to the coherence time of
the radiation. Our experiments are performed in a novel localization setup
using 2.4GHz quasi-monochromatic radiation, which corresponds to a mean
wavelength of 12.5cm. We experimentally and theoretically show that RSS
measurements are cross-correlated over a minimum distance that approaches the
diffraction limit, which equals half the mean wavelength of the radiation. Our
experiments show that measuring RSS beyond a sampling density of one sample per
half the mean wavelength does not increase localization precision, as the
Root-Mean-Squared-Error (RMSE) converges asymptotically to roughly half the
mean wavelength. This adds to the evidence that the diffraction limit
determines (1) the lower bound on localization precision and (2) the sampling
density that provides optimal localization precision. We experimentally
validate the theoretical relations between Fisher information, Cram\'er-Rao
Lower Bound (CRLB) and uncertainty, where uncertainty is lower bounded by
diffraction as derived from coherence and speckle theory. When we reconcile
Fisher Information with diffraction, the CRLB matches the experimental results
with an accuracy of 97-98%.
