RSS-Based Localization With a Single Receiver: Method and Stochastic Analysis

A wireless communication environment may not experience direct line-of-sight propagation whereas the number of receivers (Rxs) is often limited. We propose the utilization of only non-line-of-sight (NLoS) received signal strength (RSS) measurements observed at a single Rx to locate a target, via a positioning algorithm accounting for data association ambiguity that may occur in a real-world scenario. Considering the stochastic nature of a network geometry, tractable expressions are derived for the probability of acquiring at least L NLoS RSS measurements during localization. In light of the computational complexity of our solution, we investigate the minimum number of RSS samples required to meet the specified localization accuracy, thereby guiding system design. Furthermore, the probability distribution of the trace of the Cramér-Rao lower bound is obtained analytically, which offers a comprehensive understanding of the fundamental limits of the single-Rx localization scheme without resorting to intensive simulations.