  In this paper, localization using narrowband communication signals are
considered in the presence of fading channels with time of arrival
measurements. When narrowband signals are used for localization, due to
existing hardware constraints, fading channels play a crucial role in
localization accuracy. In a location estimation formulation, the Cramer-Rao
lower bound for localization error is derived under different assumptions on
fading coefficients. For the same level of localization accuracy, the loss in
performance due to Rayleigh fading with known phase is shown to be about 5dB
compared to the case with no fading. Unknown phase causes an additional 1dB
loss. The maximum likelihood estimators are also derived.
  In an alternative distributed detection formulation, each anchor receives a
noisy signal from a node with known location if the node is active. Each anchor
makes a decision as to whether the node is active or not and transmits a bit to
a fusion center once a decision is made. The fusion center combines all the
decisions and uses a design parameter to make the final decision. We derive
optimal thresholds and calculate the probabilities of false alarm and detection
under different assumptions on the knowledge of channel information.
Simulations corroborate our analytical results.
