On the Existence of Infinite Localizable Nodes in Stochastic Networks

摘要

The ability to localize a majority of nodes is important in many scenarios concerning large-scale stochastic networks. Classical percolation, i.e., the existence of infinite connected components in a stochastic network, has been analyzed in previous studies. However, a single connection is not enough for localization, which requires at least two connections to anchors. In this paper, we generalize classical percolation to localization problems. We find that for distributed localization, phase transition appears around a critical network density, i.e., an infinite localizable subnetwork exists with probability zero in the sub- critical case and with probability one in the super-critical case. Further, simulation methods are developed to estimate upper and lower bounds of critical densities, and precise estimates of densities in angle-of-arrival (AOA) and time-of- arrival (TOA) localization are performed using proposed methods.