Applications of Random Set Theory to Some Problems in Wireless Communications

This dissertation aims at applying the novel formalism of Random Set Theory (RST) to some problems in communication theory: tracking of mobile users that are continuously entering and leaving a wireless network and tracking of abruptly time-varying channel where multipath components are free to appear and disappear. RST allows to solve both problems in an unified framework through Bayes recursive filtering. Indeed, modeling the quantities to estimate as a Finite Random Set (FRS), Bayes recursive filter describes the evolution with time of the filtering density. Successively, estimation rules for RFS are introduced. Numerical simulations as well as analytical results have proved that these novel estimators outperform classical estimators that do not aim at the statistical description of the quantities under investigation.