The Topology of Wireless Communication

摘要: This article studies the topological properties of wireless communication maps and their usability in algorithmic design. We consider SINR model, which compares received power a signal at receiver against sum strengths other interfering signals plus background noise. To describe behavior multistation network, we use convenient representation reception map, partitions plane into zones, one per station, complementary region where no station can be heard. diagrams have been studied Avin et al. [2009] for specific case all stations same power. It was shown that zones are convex (hence connected) fat, this used to devise an efficient algorithm fundamental problem point location. Here more general (and common) transmission energies arbitrary (or nonuniform). Under setting, not necessarily or even connected. poses challenge designing location techniques nonuniform as well theoretical understanding geometry (e.g., maximal number connected components they might have). Our key result exhibits striking contrast between d- (d+1)-dimensional network embedded d-dimensional space. Specifically, it is whereas map highly fractured, drawing dimension higher “heals” become (in fact, hyperbolically connected). also provide bounds fatness zones. Subsequently, applications propose new variant approximate