Location estimation and detection in wireless sensor networks in the presence of fading

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.